Daily Papers

We present E(3)-Pose, a novel fast pose estimation method that jointly and explicitly models rotation equivariance and object symmetry. Our work is motivated by the challenging problem of accounting for fetal head motion during a diagnostic MRI scan. We aim to enable automatic adaptive prescription of 2D diagnostic MRI slices with 6-DoF head pose estimation, supported by 3D MRI volumes rapidly acquired before each 2D slice. Existing methods struggle to generalize to clinical volumes, due to pose ambiguities induced by inherent anatomical symmetries, as well as low resolution, noise, and artifacts. In contrast, E(3)-Pose captures anatomical symmetries and rigid pose equivariance by construction, and yields robust estimates of the fetal head pose. Our experiments on publicly available and representative clinical fetal MRI datasets demonstrate the superior robustness and generalization of our method across domains. Crucially, E(3)-Pose achieves state-of-the-art accuracy on clinical MRI volumes, paving the way for clinical translation. Our implementation is available at github.com/ramyamut/E3-Pose.

We address the problem of fitting a parametric human body model (SMPL) to point cloud data. Optimization-based methods require careful initialization and are prone to becoming trapped in local optima. Learning-based methods address this but do not generalize well when the input pose is far from those seen during training. For rigid point clouds, remarkable generalization has been achieved by leveraging SE(3)-equivariant networks, but these methods do not work on articulated objects. In this work we extend this idea to human bodies and propose ArtEq, a novel part-based SE(3)-equivariant neural architecture for SMPL model estimation from point clouds. Specifically, we learn a part detection network by leveraging local SO(3) invariance, and regress shape and pose using articulated SE(3) shape-invariant and pose-equivariant networks, all trained end-to-end. Our novel pose regression module leverages the permutation-equivariant property of self-attention layers to preserve rotational equivariance. Experimental results show that ArtEq generalizes to poses not seen during training, outperforming state-of-the-art methods by ~44% in terms of body reconstruction accuracy, without requiring an optimization refinement step. Furthermore, ArtEq is three orders of magnitude faster during inference than prior work and has 97.3% fewer parameters. The code and model are available for research purposes at https://arteq.is.tue.mpg.de.

Equivariance to random image transformations is an effective method to learn landmarks of object categories, such as the eyes and the nose in faces, without manual supervision. However, this method does not explicitly guarantee that the learned landmarks are consistent with changes between different instances of the same object, such as different facial identities. In this paper, we develop a new perspective on the equivariance approach by noting that dense landmark detectors can be interpreted as local image descriptors equipped with invariance to intra-category variations. We then propose a direct method to enforce such an invariance in the standard equivariant loss. We do so by exchanging descriptor vectors between images of different object instances prior to matching them geometrically. In this manner, the same vectors must work regardless of the specific object identity considered. We use this approach to learn vectors that can simultaneously be interpreted as local descriptors and dense landmarks, combining the advantages of both. Experiments on standard benchmarks show that this approach can match, and in some cases surpass state-of-the-art performance amongst existing methods that learn landmarks without supervision. Code is available at www.robots.ox.ac.uk/~vgg/research/DVE/.

Equivariance is a fundamental property in computer vision models, yet strict equivariance is rarely satisfied in real-world data, which can limit a model's performance. Controlling the degree of equivariance is therefore desirable. We propose a general framework for constructing soft equivariant models by projecting the model weights into a designed subspace. The method applies to any pre-trained architecture and provides theoretical bounds on the induced equivariance error. Empirically, we demonstrate the effectiveness of our method on multiple pre-trained backbones, including ViT and ResNet, across image classification, semantic segmentation, and human-trajectory prediction tasks. Notably, our approach improves the performance while simultaneously reducing equivariance error on the competitive ImageNet benchmark.

Learning self-supervised representations that are invariant and equivariant to transformations is crucial for advancing beyond traditional visual classification tasks. However, many methods rely on predictor architectures to encode equivariance, despite evidence that architectural choices, such as capsule networks, inherently excel at learning interpretable pose-aware representations. To explore this, we introduce EquiCaps (Equivariant Capsule Network), a capsule-based approach to pose-aware self-supervision that eliminates the need for a specialised predictor for enforcing equivariance. Instead, we leverage the intrinsic pose-awareness capabilities of capsules to improve performance in pose estimation tasks. To further challenge our assumptions, we increase task complexity via multi-geometric transformations to enable a more thorough evaluation of invariance and equivariance by introducing 3DIEBench-T, an extension of a 3D object-rendering benchmark dataset. Empirical results demonstrate that EquiCaps outperforms prior state-of-the-art equivariant methods on rotation prediction, achieving a supervised-level R^2 of 0.78 on the 3DIEBench rotation prediction benchmark and improving upon SIE and CapsIE by 0.05 and 0.04 R^2, respectively. Moreover, in contrast to non-capsule-based equivariant approaches, EquiCaps maintains robust equivariant performance under combined geometric transformations, underscoring its generalisation capabilities and the promise of predictor-free capsule architectures.

Shape assembly aims to reassemble parts (or fragments) into a complete object, which is a common task in our daily life. Different from the semantic part assembly (e.g., assembling a chair's semantic parts like legs into a whole chair), geometric part assembly (e.g., assembling bowl fragments into a complete bowl) is an emerging task in computer vision and robotics. Instead of semantic information, this task focuses on geometric information of parts. As the both geometric and pose space of fractured parts are exceptionally large, shape pose disentanglement of part representations is beneficial to geometric shape assembly. In our paper, we propose to leverage SE(3) equivariance for such shape pose disentanglement. Moreover, while previous works in vision and robotics only consider SE(3) equivariance for the representations of single objects, we move a step forward and propose leveraging SE(3) equivariance for representations considering multi-part correlations, which further boosts the performance of the multi-part assembly. Experiments demonstrate the significance of SE(3) equivariance and our proposed method for geometric shape assembly. Project page: https://crtie.github.io/SE-3-part-assembly/

In this paper, we adopt the Universal Manifold Embedding (UME) framework for the estimation of rigid transformations and extend it, so that it can accommodate scenarios involving partial overlap and differently sampled point clouds. UME is a methodology designed for mapping observations of the same object, related by rigid transformations, into a single low-dimensional linear subspace. This process yields a transformation-invariant representation of the observations, with its matrix form representation being covariant (i.e. equivariant) with the transformation. We extend the UME framework by introducing a UME-compatible feature extraction method augmented with a unique UME contrastive loss and a sampling equalizer. These components are integrated into a comprehensive and robust registration pipeline, named UMERegRobust. We propose the RotKITTI registration benchmark, specifically tailored to evaluate registration methods for scenarios involving large rotations. UMERegRobust achieves better than state-of-the-art performance on the KITTI benchmark, especially when strict precision of (1{\deg}, 10cm) is considered (with an average gain of +9%), and notably outperform SOTA methods on the RotKITTI benchmark (with +45% gain compared the most recent SOTA method).

Learning rotation-invariant distinctive features is a fundamental requirement for point cloud registration. Existing methods often use rotation-sensitive networks to extract features, while employing rotation augmentation to learn an approximate invariant mapping rudely. This makes networks fragile to rotations, overweight, and hinders the distinctiveness of features. To tackle these problems, we propose a novel position-aware rotation-equivariant network, for efficient, light-weighted, and robust registration. The network can provide a strong model inductive bias to learn rotation-equivariant/invariant features, thus addressing the aforementioned limitations. To further improve the distinctiveness of descriptors, we propose a position-aware convolution, which can better learn spatial information of local structures. Moreover, we also propose a feature-based hypothesis proposer. It leverages rotation-equivariant features that encode fine-grained structure orientations to generate reliable model hypotheses. Each correspondence can generate a hypothesis, thus it is more efficient than classic estimators that require multiple reliable correspondences. Accordingly, a contrastive rotation loss is presented to enhance the robustness of rotation-equivariant features against data degradation. Extensive experiments on indoor and outdoor datasets demonstrate that our method significantly outperforms the SOTA methods in terms of registration recall while being lightweight and keeping a fast speed. Moreover, experiments on rotated datasets demonstrate its robustness against rotation variations. Code is available at https://github.com/yaorz97/PARENet.

Integrating a notion of symmetry into point cloud neural networks is a provably effective way to improve their generalization capability. Of particular interest are E(3) equivariant point cloud networks where Euclidean transformations applied to the inputs are preserved in the outputs. Recent efforts aim to extend networks that are E(3) equivariant, to accommodate inputs made of multiple parts, each of which exhibits local E(3) symmetry. In practical settings, however, the partitioning into individually transforming regions is unknown a priori. Errors in the partition prediction would unavoidably map to errors in respecting the true input symmetry. Past works have proposed different ways to predict the partition, which may exhibit uncontrolled errors in their ability to maintain equivariance to the actual partition. To this end, we introduce APEN: a general framework for constructing approximate piecewise-E(3) equivariant point networks. Our primary insight is that functions that are equivariant with respect to a finer partition will also maintain equivariance in relation to the true partition. Leveraging this observation, we propose a design where the equivariance approximation error at each layers can be bounded solely in terms of (i) uncertainty quantification of the partition prediction, and (ii) bounds on the probability of failing to suggest a proper subpartition of the ground truth one. We demonstrate the effectiveness of APEN using two data types exemplifying part-based symmetry: (i) real-world scans of room scenes containing multiple furniture-type objects; and, (ii) human motions, characterized by articulated parts exhibiting rigid movement. Our empirical results demonstrate the advantage of integrating piecewise E(3) symmetry into network design, showing a distinct improvement in generalization compared to prior works for both classification and segmentation tasks.

Learning to predict agent motions with relationship reasoning is important for many applications. In motion prediction tasks, maintaining motion equivariance under Euclidean geometric transformations and invariance of agent interaction is a critical and fundamental principle. However, such equivariance and invariance properties are overlooked by most existing methods. To fill this gap, we propose EqMotion, an efficient equivariant motion prediction model with invariant interaction reasoning. To achieve motion equivariance, we propose an equivariant geometric feature learning module to learn a Euclidean transformable feature through dedicated designs of equivariant operations. To reason agent's interactions, we propose an invariant interaction reasoning module to achieve a more stable interaction modeling. To further promote more comprehensive motion features, we propose an invariant pattern feature learning module to learn an invariant pattern feature, which cooperates with the equivariant geometric feature to enhance network expressiveness. We conduct experiments for the proposed model on four distinct scenarios: particle dynamics, molecule dynamics, human skeleton motion prediction and pedestrian trajectory prediction. Experimental results show that our method is not only generally applicable, but also achieves state-of-the-art prediction performances on all the four tasks, improving by 24.0/30.1/8.6/9.2%. Code is available at https://github.com/MediaBrain-SJTU/EqMotion.

3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equivariant shape completion network, whose modular layers successively canonicalize features, reason over similarity-invariant geometry, and restore the original frame. Under a de-biased evaluation protocol that removes the hidden cues, our model outperforms both equivariant and augmentation baselines on the PCN benchmark. It also sets new cross-domain records on real driving and indoor scans, lowering minimal matching distance on KITTI by 17% and Chamfer distance ell1 on OmniObject3D by 14%. Perhaps surprisingly, ours under the stricter protocol still outperforms competitors under their biased settings. These results establish full SIM(3) equivariance as an effective route to truly generalizable shape completion. Project page: https://sime-completion.github.io.

Popular representation learning methods encourage feature invariance under transformations applied at the input. However, in 3D perception tasks like object localization and segmentation, outputs are naturally equivariant to some transformations, such as rotation. Using pre-training loss functions that encourage equivariance of features under certain transformations provides a strong self-supervision signal while also retaining information of geometric relationships between transformed feature representations. This can enable improved performance in downstream tasks that are equivariant to such transformations. In this paper, we propose a spatio-temporal equivariant learning framework by considering both spatial and temporal augmentations jointly. Our experiments show that the best performance arises with a pre-training approach that encourages equivariance to translation, scaling, and flip, rotation and scene flow. For spatial augmentations, we find that depending on the transformation, either a contrastive objective or an equivariance-by-classification objective yields best results. To leverage real-world object deformations and motion, we consider sequential LiDAR scene pairs and develop a novel 3D scene flow-based equivariance objective that leads to improved performance overall. We show our pre-training method for 3D object detection which outperforms existing equivariant and invariant approaches in many settings.

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in three dimensions to make predictions about novel images. However, imposing SO(3)-equivariance on two-dimensional inputs is difficult because the group of three-dimensional rotations does not have a natural action on the two-dimensional plane. Specifically, it is possible that an element of SO(3) will rotate an image out of plane. We show that an algorithm that learns a three-dimensional representation of the world from two dimensional images must satisfy certain geometric consistency properties which we formulate as SO(2)-equivariance constraints. We use the induced and restricted representations of SO(2) on SO(3) to construct and classify architectures which satisfy these geometric consistency constraints. We prove that any architecture which respects said consistency constraints can be realized as an instance of our construction. We show that three previously proposed neural architectures for 3D pose prediction are special cases of our construction. We propose a new algorithm that is a learnable generalization of previously considered methods. We test our architecture on three pose predictions task and achieve SOTA results on both the PASCAL3D+ and SYMSOL pose estimation tasks.

Recovering camera poses from a set of images is a foundational task in 3D computer vision, which powers key applications such as 3D scene/object reconstructions. Classic methods often depend on feature correspondence, such as keypoints, which require the input images to have large overlap and small viewpoint changes. Such requirements present considerable challenges in scenarios with sparse views. Recent data-driven approaches aim to directly output camera poses, either through regressing the 6DoF camera poses or formulating rotation as a probability distribution. However, each approach has its limitations. On one hand, directly regressing the camera poses can be ill-posed, since it assumes a single mode, which is not true under symmetry and leads to sub-optimal solutions. On the other hand, probabilistic approaches are capable of modeling the symmetry ambiguity, yet they sample the entire space of rotation uniformly by brute-force. This leads to an inevitable trade-off between high sample density, which improves model precision, and sample efficiency that determines the runtime. In this paper, we propose ADen to unify the two frameworks by employing a generator and a discriminator: the generator is trained to output multiple hypotheses of 6DoF camera pose to represent a distribution and handle multi-mode ambiguity, and the discriminator is trained to identify the hypothesis that best explains the data. This allows ADen to combine the best of both worlds, achieving substantially higher precision as well as lower runtime than previous methods in empirical evaluations.

Vision foundation models, particularly the ViT family, have revolutionized image understanding by providing rich semantic features. However, despite their success in 2D comprehension, their abilities on grasping 3D spatial relationships are still unclear. In this work, we evaluate and enhance the 3D awareness of ViT-based models. We begin by systematically assessing their ability to learn 3D equivariant features, specifically examining the consistency of semantic embeddings across different viewpoints. Our findings indicate that improved 3D equivariance leads to better performance on various downstream tasks, including pose estimation, tracking, and semantic transfer. Building on this insight, we propose a simple yet effective finetuning strategy based on 3D correspondences, which significantly enhances the 3D correspondence understanding of existing vision models. Remarkably, even finetuning on a single object for just one iteration results in substantial performance gains. All code and resources will be made publicly available to support further advancements in 3D-aware vision models. Our code is available at https://github.com/qq456cvb/3DCorrEnhance.

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component of prevalent deep neural network architectures to achieve chosen equivariance is a difficult problem and can result in a computationally expensive network during both training and inference. A recently proposed alternative towards equivariance that removes the architectural constraints is to use a simple canonicalization network that transforms the input to a canonical form before feeding it to an unconstrained prediction network. We show here that this approach can effectively be used to make a large pretrained network equivariant. However, we observe that the produced canonical orientations can be misaligned with those of the training distribution, hindering performance. Using dataset-dependent priors to inform the canonicalization function, we are able to make large pretrained models equivariant while maintaining their performance. This significantly improves the robustness of these models to deterministic transformations of the data, such as rotations. We believe this equivariant adaptation of large pretrained models can help their domain-specific applications with known symmetry priors.

Recent interest in point cloud analysis has led rapid progress in designing deep learning methods for 3D models. However, state-of-the-art models are not robust to rotations, which remains an unknown prior to real applications and harms the model performance. In this work, we introduce a novel Patch-wise Rotation-invariant network (PaRot), which achieves rotation invariance via feature disentanglement and produces consistent predictions for samples with arbitrary rotations. Specifically, we design a siamese training module which disentangles rotation invariance and equivariance from patches defined over different scales, e.g., the local geometry and global shape, via a pair of rotations. However, our disentangled invariant feature loses the intrinsic pose information of each patch. To solve this problem, we propose a rotation-invariant geometric relation to restore the relative pose with equivariant information for patches defined over different scales. Utilising the pose information, we propose a hierarchical module which implements intra-scale and inter-scale feature aggregation for 3D shape learning. Moreover, we introduce a pose-aware feature propagation process with the rotation-invariant relative pose information embedded. Experiments show that our disentanglement module extracts high-quality rotation-robust features and the proposed lightweight model achieves competitive results in rotated 3D object classification and part segmentation tasks. Our project page is released at: https://patchrot.github.io/.

Self-supervised learning (SSL) methods have achieved remarkable success in learning image representations allowing invariances in them - but therefore discarding transformation information that some computer vision tasks actually require. While recent approaches attempt to address this limitation by learning equivariant features using linear operators in feature space, they impose restrictive assumptions that constrain flexibility and generalization. We introduce a weaker definition for the transformation relation between image and feature space denoted as equivariance-coherence. We propose a novel SSL auxiliary task that learns equivariance-coherent representations through intermediate transformation reconstruction, which can be integrated with existing joint embedding SSL methods. Our key idea is to reconstruct images at intermediate points along transformation paths, e.g. when training on 30-degree rotations, we reconstruct the 10-degree and 20-degree rotation states. Reconstructing intermediate states requires the transformation information used in augmentations, rather than suppressing it, and therefore fosters features containing the augmented transformation information. Our method decomposes feature vectors into invariant and equivariant parts, training them with standard SSL losses and reconstruction losses, respectively. We demonstrate substantial improvements on synthetic equivariance benchmarks while maintaining competitive performance on downstream tasks requiring invariant representations. The approach seamlessly integrates with existing SSL methods (iBOT, DINOv2) and consistently enhances performance across diverse tasks, including segmentation, detection, depth estimation, and video dense prediction. Our framework provides a practical way for augmenting SSL methods with equivariant capabilities while preserving invariant performance.

We introduce pi^3, a feed-forward neural network that offers a novel approach to visual geometry reconstruction, breaking the reliance on a conventional fixed reference view. Previous methods often anchor their reconstructions to a designated viewpoint, an inductive bias that can lead to instability and failures if the reference is suboptimal. In contrast, pi^3 employs a fully permutation-equivariant architecture to predict affine-invariant camera poses and scale-invariant local point maps without any reference frames. This design makes our model inherently robust to input ordering and highly scalable. These advantages enable our simple and bias-free approach to achieve state-of-the-art performance on a wide range of tasks, including camera pose estimation, monocular/video depth estimation, and dense point map reconstruction. Code and models are publicly available.

Recent progress has been made towards learning invariant or equivariant representations with self-supervised learning. While invariant methods are evaluated on large scale datasets, equivariant ones are evaluated in smaller, more controlled, settings. We aim at bridging the gap between the two in order to learn more diverse representations that are suitable for a wide range of tasks. We start by introducing a dataset called 3DIEBench, consisting of renderings from 3D models over 55 classes and more than 2.5 million images where we have full control on the transformations applied to the objects. We further introduce a predictor architecture based on hypernetworks to learn equivariant representations with no possible collapse to invariance. We introduce SIE (Split Invariant-Equivariant) which combines the hypernetwork-based predictor with representations split in two parts, one invariant, the other equivariant, to learn richer representations. We demonstrate significant performance gains over existing methods on equivariance related tasks from both a qualitative and quantitative point of view. We further analyze our introduced predictor and show how it steers the learned latent space. We hope that both our introduced dataset and approach will enable learning richer representations without supervision in more complex scenarios. Code and data are available at https://github.com/facebookresearch/SIE.

Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate, which frequently happens in practice, these models may be suboptimal due to the architectural restrictions imposed on them. We tackle this issue of approximate symmetries in a setup where symmetries are mixed, i.e., they are symmetries of not single but multiple different types and the degree of approximation varies across these types. Instead of proposing a new architectural restriction as in most of the previous approaches, we present a regularizer-based method for building a model for a dataset with mixed approximate symmetries. The key component of our method is what we call equivariance regularizer for a given type of symmetries, which measures how much a model is equivariant with respect to the symmetries of the type. Our method is trained with these regularizers, one per each symmetry type, and the strength of the regularizers is automatically tuned during training, leading to the discovery of the approximation levels of some candidate symmetry types without explicit supervision. Using synthetic function approximation and motion forecasting tasks, we demonstrate that our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.

In many practical 6D object pose estimation scenarios, we often have access to only a single real-world RGB-D reference view per object, typically without CAD models. Existing methods largely rely on explicit 3D models or multi-view data, which limits their scalability. To address this challenging single-reference model-free setting, we propose OneViewAll, a semantic-prior-guided framework that performs pose estimation via a novel Project-and-Compare paradigm. Instead of relying on computationally expensive CAD-based rendering, our method directly aligns reference and query observations within a projection-equivariant space. OneViewAll progressively integrates hierarchical semantic priors across three levels: (1) category- and scene-level priors for efficient hypothesis initialization; (2) object-level symmetry priors for geometry completion via mirror fusion; and (3) patch-level priors for discriminative refinement. Extensive experiments demonstrate that OneViewAll achieves 92.5\% ADD-0.1 accuracy on the LINEMOD dataset using only one real reference view -- significantly outperforming the CVPR 2025 baseline One2Any (52.6\%). It also yields consistent improvements on YCB-V, Real275, and Toyota-Light while maintaining low inference latency. Our results underscore the efficacy of symmetry-aware projection in handling symmetric, texture-less, and occluded objects.

Current self-supervised algorithms commonly rely on transformations such as data augmentation and masking to learn visual representations. This is achieved by enforcing invariance or equivariance with respect to these transformations after encoding two views of an image. This dominant two-view paradigm often limits the flexibility of learned representations for downstream adaptation by creating performance trade-offs between high-level invariance-demanding tasks such as image classification and more fine-grained equivariance-related tasks. In this work, we proposes seq-JEPA, a world modeling framework that introduces architectural inductive biases into joint-embedding predictive architectures to resolve this trade-off. Without relying on dual equivariance predictors or loss terms, seq-JEPA simultaneously learns two architecturally segregated representations: one equivariant to specified transformations and another invariant to them. To do so, our model processes short sequences of different views (observations) of inputs. Each encoded view is concatenated with an embedding of the relative transformation (action) that produces the next observation in the sequence. These view-action pairs are passed through a transformer encoder that outputs an aggregate representation. A predictor head then conditions this aggregate representation on the upcoming action to predict the representation of the next observation. Empirically, seq-JEPA demonstrates strong performance on both equivariant and invariant benchmarks without sacrificing one for the other. Furthermore, it excels at tasks that inherently require aggregating a sequence of observations, such as path integration across actions and predictive learning across eye movements.

In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks, e.g. improving SimCLR to 72.5% linear probe accuracy on ImageNet. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. Our code, datasets and pre-trained models are available at https://github.com/rdangovs/essl to aid further research in E-SSL.

Point cloud rigid registration is a fundamental problem in 3D computer vision. In the multiview case, we aim to find a set of 6D poses to align a set of objects. Methods based on pairwise registration rely on a subsequent synchronization algorithm, which makes them poorly scalable with the number of views. Generative approaches overcome this limitation, but are based on Gaussian Mixture Models and use an Expectation-Maximization algorithm. Hence, they are not well suited to handle large transformations. Moreover, most existing methods cannot handle high levels of degradations. In this paper, we introduce POLAR (POint cloud LAtent Registration), a multiview registration method able to efficiently deal with a large number of views, while being robust to a high level of degradations and large initial angles. To achieve this, we transpose the registration problem into the latent space of a pretrained autoencoder, design a loss taking degradations into account, and develop an efficient multistart optimization strategy. Our proposed method significantly outperforms state-of-the-art approaches on synthetic and real data. POLAR is available at github.com/pypolar/polar or as a standalone package which can be installed with pip install polaregistration.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

Prior methods that tackle the problem of generalizable object pose estimation highly rely on having dense views of the unseen object. By contrast, we address the scenario where only a single reference view of the object is available. Our goal then is to estimate the relative object pose between this reference view and a query image that depicts the object in a different pose. In this scenario, robust generalization is imperative due to the presence of unseen objects during testing and the large-scale object pose variation between the reference and the query. To this end, we present a new hypothesis-and-verification framework, in which we generate and evaluate multiple pose hypotheses, ultimately selecting the most reliable one as the relative object pose. To measure reliability, we introduce a 3D-aware verification that explicitly applies 3D transformations to the 3D object representations learned from the two input images. Our comprehensive experiments on the Objaverse, LINEMOD, and CO3D datasets evidence the superior accuracy of our approach in relative pose estimation and its robustness in large-scale pose variations, when dealing with unseen objects.

Estimating the 6-DoF pose of a rigid object from a single RGB image is a crucial yet challenging task. Recent studies have shown the great potential of dense correspondence-based solutions, yet improvements are still needed to reach practical deployment. In this paper, we propose a novel pose estimation algorithm named CheckerPose, which improves on three main aspects. Firstly, CheckerPose densely samples 3D keypoints from the surface of the 3D object and finds their 2D correspondences progressively in the 2D image. Compared to previous solutions that conduct dense sampling in the image space, our strategy enables the correspondence searching in a 2D grid (i.e., pixel coordinate). Secondly, for our 3D-to-2D correspondence, we design a compact binary code representation for 2D image locations. This representation not only allows for progressive correspondence refinement but also converts the correspondence regression to a more efficient classification problem. Thirdly, we adopt a graph neural network to explicitly model the interactions among the sampled 3D keypoints, further boosting the reliability and accuracy of the correspondences. Together, these novel components make CheckerPose a strong pose estimation algorithm. When evaluated on the popular Linemod, Linemod-O, and YCB-V object pose estimation benchmarks, CheckerPose clearly boosts the accuracy of correspondence-based methods and achieves state-of-the-art performances. Code is available at https://github.com/RuyiLian/CheckerPose.

Object pose estimation is crucial to robotic perception and typically provides a single-pose estimate. However, a single estimate cannot capture pose uncertainty deriving from visual ambiguity, which can lead to unreliable behavior. Existing pose distribution methods rely heavily on color information, often unavailable in industrial settings. We propose a novel neural network-based method for estimating object pose uncertainty using only 3D colorless data. To the best of our knowledge, this is the first approach that leverages deep learning for pose distribution estimation without relying on RGB input. We validate our method in a real-world bin picking scenario with objects of varying geometric ambiguity. Our current implementation focuses on symmetries in reflection and revolution, but the framework is extendable to full SE(3) pose distribution estimation. Source code available at opde3d.github.io

Shift equivariance is a fundamental principle that governs how we perceive the world - our recognition of an object remains invariant with respect to shifts. Transformers have gained immense popularity due to their effectiveness in both language and vision tasks. While the self-attention operator in vision transformers (ViT) is permutation-equivariant and thus shift-equivariant, patch embedding, positional encoding, and subsampled attention in ViT variants can disrupt this property, resulting in inconsistent predictions even under small shift perturbations. Although there is a growing trend in incorporating the inductive bias of convolutional neural networks (CNNs) into vision transformers, it does not fully address the issue. We propose an adaptive polyphase anchoring algorithm that can be seamlessly integrated into vision transformer models to ensure shift-equivariance in patch embedding and subsampled attention modules, such as window attention and global subsampled attention. Furthermore, we utilize depth-wise convolution to encode positional information. Our algorithms enable ViT, and its variants such as Twins to achieve 100% consistency with respect to input shift, demonstrate robustness to cropping, flipping, and affine transformations, and maintain consistent predictions even when the original models lose 20 percentage points on average when shifted by just a few pixels with Twins' accuracy dropping from 80.57% to 62.40%.

Deep networks for computer vision are not reliable when they encounter adversarial examples. In this paper, we introduce a framework that uses the dense intrinsic constraints in natural images to robustify inference. By introducing constraints at inference time, we can shift the burden of robustness from training to the inference algorithm, thereby allowing the model to adjust dynamically to each individual image's unique and potentially novel characteristics at inference time. Among different constraints, we find that equivariance-based constraints are most effective, because they allow dense constraints in the feature space without overly constraining the representation at a fine-grained level. Our theoretical results validate the importance of having such dense constraints at inference time. Our empirical experiments show that restoring feature equivariance at inference time defends against worst-case adversarial perturbations. The method obtains improved adversarial robustness on four datasets (ImageNet, Cityscapes, PASCAL VOC, and MS-COCO) on image recognition, semantic segmentation, and instance segmentation tasks. Project page is available at equi4robust.cs.columbia.edu.

Current generative models, such as autoregressive and diffusion approaches, decompose high-dimensional data distribution learning into a series of simpler subtasks. However, inherent conflicts arise during the joint optimization of these subtasks, and existing solutions fail to resolve such conflicts without sacrificing efficiency or scalability. We propose a novel equivariant image modeling framework that inherently aligns optimization targets across subtasks by leveraging the translation invariance of natural visual signals. Our method introduces (1) column-wise tokenization which enhances translational symmetry along the horizontal axis, and (2) windowed causal attention which enforces consistent contextual relationships across positions. Evaluated on class-conditioned ImageNet generation at 256x256 resolution, our approach achieves performance comparable to state-of-the-art AR models while using fewer computational resources. Systematic analysis demonstrates that enhanced equivariance reduces inter-task conflicts, significantly improving zero-shot generalization and enabling ultra-long image synthesis. This work establishes the first framework for task-aligned decomposition in generative modeling, offering insights into efficient parameter sharing and conflict-free optimization. The code and models are publicly available at https://github.com/drx-code/EquivariantModeling.

In this paper, we develop rotation-equivariant neural networks for 4D panoptic segmentation. 4D panoptic segmentation is a recently established benchmark task for autonomous driving, which requires recognizing semantic classes and object instances on the road based on LiDAR scans, as well as assigning temporally consistent IDs to instances across time. We observe that the driving scenario is symmetric to rotations on the ground plane. Therefore, rotation-equivariance could provide better generalization and more robust feature learning. Specifically, we review the object instance clustering strategies, and restate the centerness-based approach and the offset-based approach as the prediction of invariant scalar fields and equivariant vector fields. Other sub-tasks are also unified from this perspective, and different invariant and equivariant layers are designed to facilitate their predictions. Through evaluation on the standard 4D panoptic segmentation benchmark of SemanticKITTI, we show that our equivariant models achieve higher accuracy with lower computational costs compared to their non-equivariant counterparts. Moreover, our method sets the new state-of-the-art performance and achieves 1st place on the SemanticKITTI 4D Panoptic Segmentation leaderboard.

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

We propose the MAC-VO, a novel learning-based stereo VO that leverages the learned metrics-aware matching uncertainty for dual purposes: selecting keypoint and weighing the residual in pose graph optimization. Compared to traditional geometric methods prioritizing texture-affluent features like edges, our keypoint selector employs the learned uncertainty to filter out the low-quality features based on global inconsistency. In contrast to the learning-based algorithms that model the scale-agnostic diagonal weight matrix for covariance, we design a metrics-aware covariance model to capture the spatial error during keypoint registration and the correlations between different axes. Integrating this covariance model into pose graph optimization enhances the robustness and reliability of pose estimation, particularly in challenging environments with varying illumination, feature density, and motion patterns. On public benchmark datasets, MAC-VO outperforms existing VO algorithms and even some SLAM algorithms in challenging environments. The covariance map also provides valuable information about the reliability of the estimated poses, which can benefit decision-making for autonomous systems.

Proper evaluations are crucial for better understanding, troubleshooting, interpreting model behaviors and further improving model performance. While using scalar-based error metrics provides a fast way to overview model performance, they are often too abstract to display certain weak spots and lack information regarding important model properties, such as robustness. This not only hinders machine learning models from being more interpretable and gaining trust, but also can be misleading to both model developers and users. Additionally, conventional evaluation procedures often leave researchers unclear about where and how model fails, which complicates model comparisons and further developments. To address these issues, we propose a novel evaluation workflow, named Non-Equivariance Revealed on Orbits (NERO) Evaluation. The goal of NERO evaluation is to turn focus from traditional scalar-based metrics onto evaluating and visualizing models equivariance, closely capturing model robustness, as well as to allow researchers quickly investigating interesting or unexpected model behaviors. NERO evaluation is consist of a task-agnostic interactive interface and a set of visualizations, called NERO plots, which reveals the equivariance property of the model. Case studies on how NERO evaluation can be applied to multiple research areas, including 2D digit recognition, object detection, particle image velocimetry (PIV), and 3D point cloud classification, demonstrate that NERO evaluation can quickly illustrate different model equivariance, and effectively explain model behaviors through interactive visualizations of the model outputs. In addition, we propose consensus, an alternative to ground truths, to be used in NERO evaluation so that model equivariance can still be evaluated with new, unlabeled datasets.

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible updates consistently improve final validation loss, and in several cases training stability, over corresponding AdamW updates.

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y, g cdot y), where g is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group G:= (R_m times Z_n times Z_n), combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group O(n) and the general linear group GL(n). We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

In this paper, we propose a novel local descriptor-based framework, called You Only Hypothesize Once (YOHO), for the registration of two unaligned point clouds. In contrast to most existing local descriptors which rely on a fragile local reference frame to gain rotation invariance, the proposed descriptor achieves the rotation invariance by recent technologies of group equivariant feature learning, which brings more robustness to point density and noise. Meanwhile, the descriptor in YOHO also has a rotation equivariant part, which enables us to estimate the registration from just one correspondence hypothesis. Such property reduces the searching space for feasible transformations, thus greatly improves both the accuracy and the efficiency of YOHO. Extensive experiments show that YOHO achieves superior performances with much fewer needed RANSAC iterations on four widely-used datasets, the 3DMatch/3DLoMatch datasets, the ETH dataset and the WHU-TLS dataset. More details are shown in our project page: https://hpwang-whu.github.io/YOHO/.

This study explores the concept of equivariance in vision-language foundation models (VLMs), focusing specifically on the multimodal similarity function that is not only the major training objective but also the core delivery to support downstream tasks. Unlike the existing image-text similarity objective which only categorizes matched pairs as similar and unmatched pairs as dissimilar, equivariance also requires similarity to vary faithfully according to the semantic changes. This allows VLMs to generalize better to nuanced and unseen multimodal compositions. However, modeling equivariance is challenging as the ground truth of semantic change is difficult to collect. For example, given an image-text pair about a dog, it is unclear to what extent the similarity changes when the pixel is changed from dog to cat? To this end, we propose EqSim, a regularization loss that can be efficiently calculated from any two matched training pairs and easily pluggable into existing image-text retrieval fine-tuning. Meanwhile, to further diagnose the equivariance of VLMs, we present a new challenging benchmark EqBen. Compared to the existing evaluation sets, EqBen is the first to focus on "visual-minimal change". Extensive experiments show the lack of equivariance in current VLMs and validate the effectiveness of EqSim. Code is available at https://github.com/Wangt-CN/EqBen.

Existing methods for instance-level 6D pose estimation typically rely on neural networks that either directly regress the pose in SE(3) or estimate it indirectly via local feature matching. The former struggle with object symmetries, while the latter fail in the absence of distinctive local features. To overcome these limitations, we propose a novel formulation of 6D pose estimation as a conditional flow matching problem in R^3. We introduce Flose, a generative method that infers object poses via a denoising process conditioned on local features. While prior approaches based on conditional flow matching perform denoising solely based on geometric guidance, Flose integrates appearance-based semantic features to mitigate ambiguities caused by object symmetries. We further incorporate RANSAC-based registration to handle outliers. We validate Flose on five datasets from the established BOP benchmark. Flose outperforms prior methods with an average improvement of +4.5 Average Recall. Project Website : https://tev-fbk.github.io/Flose/

Unseen object pose estimation methods often rely on CAD models or multiple reference views, making the onboarding stage costly. To simplify reference acquisition, we aim to estimate the unseen object's pose through a single unposed RGB-D reference image. While previous works leverage reference images as pose anchors to limit the range of relative pose, our scenario presents significant challenges since the relative transformation could vary across the entire SE(3) space. Moreover, factors like occlusion, sensor noise, and extreme geometry could result in low viewpoint overlap. To address these challenges, we present a novel approach and benchmark, termed UNOPose, for unseen one-reference-based object pose estimation. Building upon a coarse-to-fine paradigm, UNOPose constructs an SE(3)-invariant reference frame to standardize object representation despite pose and size variations. To alleviate small overlap across viewpoints, we recalibrate the weight of each correspondence based on its predicted likelihood of being within the overlapping region. Evaluated on our proposed benchmark based on the BOP Challenge, UNOPose demonstrates superior performance, significantly outperforming traditional and learning-based methods in the one-reference setting and remaining competitive with CAD-model-based methods. The code and dataset are available at https://github.com/shanice-l/UNOPose.

Camera pose estimation is a key step in standard 3D reconstruction pipelines that operate on a dense set of images of a single object or scene. However, methods for pose estimation often fail when only a few images are available because they rely on the ability to robustly identify and match visual features between image pairs. While these methods can work robustly with dense camera views, capturing a large set of images can be time-consuming or impractical. We propose SparsePose for recovering accurate camera poses given a sparse set of wide-baseline images (fewer than 10). The method learns to regress initial camera poses and then iteratively refine them after training on a large-scale dataset of objects (Co3D: Common Objects in 3D). SparsePose significantly outperforms conventional and learning-based baselines in recovering accurate camera rotations and translations. We also demonstrate our pipeline for high-fidelity 3D reconstruction using only 5-9 images of an object.

The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations. Recently, a new class of CNNs is proposed in which the conventional layers of CNNs are replaced with equivariant convolution, pooling, and batch-normalization layers. The final classification layer in equivariant neural networks is invariant to different affine geometric transformations such as rotation, reflection and translation, and the scalar value is obtained by either eliminating the spatial dimensions of filter responses using convolution and down-sampling throughout the network or average is taken over the filter responses. In this work, we propose to integrate the orthogonal moments which gives the high-order statistics of the function as an effective means for encoding global invariance with respect to rotation, reflection and translation in fully-connected layers. As a result, the intermediate layers of the network become equivariant while the classification layer becomes invariant. The most widely used Zernike, pseudo-Zernike and orthogonal Fourier-Mellin moments are considered for this purpose. The effectiveness of the proposed work is evaluated by integrating the invariant transition and fully-connected layer in the architecture of group-equivariant CNNs (G-CNNs) on rotated MNIST and CIFAR10 datasets.

This article introduces BEVPlace++, a novel, fast, and robust LiDAR global localization method for unmanned ground vehicles. It uses lightweight convolutional neural networks (CNNs) on Bird's Eye View (BEV) image-like representations of LiDAR data to achieve accurate global localization through place recognition, followed by 3-DoF pose estimation. Our detailed analyses reveal an interesting fact that CNNs are inherently effective at extracting distinctive features from LiDAR BEV images. Remarkably, keypoints of two BEV images with large translations can be effectively matched using CNN-extracted features. Building on this insight, we design a Rotation Equivariant Module (REM) to obtain distinctive features while enhancing robustness to rotational changes. A Rotation Equivariant and Invariant Network (REIN) is then developed by cascading REM and a descriptor generator, NetVLAD, to sequentially generate rotation equivariant local features and rotation invariant global descriptors. The global descriptors are used first to achieve robust place recognition, and then local features are used for accurate pose estimation. Experimental results on seven public datasets and our UGV platform demonstrate that BEVPlace++, even when trained on a small dataset (3000 frames of KITTI) only with place labels, generalizes well to unseen environments, performs consistently across different days and years, and adapts to various types of LiDAR scanners. BEVPlace++ achieves state-of-the-art performance in multiple tasks, including place recognition, loop closure detection, and global localization. Additionally, BEVPlace++ is lightweight, runs in real-time, and does not require accurate pose supervision, making it highly convenient for deployment. \revise{The source codes are publicly available at https://github.com/zjuluolun/BEVPlace2.

Are camera poses necessary for multi-view 3D modeling? Existing approaches predominantly assume access to accurate camera poses. While this assumption might hold for dense views, accurately estimating camera poses for sparse views is often elusive. Our analysis reveals that noisy estimated poses lead to degraded performance for existing sparse-view 3D modeling methods. To address this issue, we present LEAP, a novel pose-free approach, therefore challenging the prevailing notion that camera poses are indispensable. LEAP discards pose-based operations and learns geometric knowledge from data. LEAP is equipped with a neural volume, which is shared across scenes and is parameterized to encode geometry and texture priors. For each incoming scene, we update the neural volume by aggregating 2D image features in a feature-similarity-driven manner. The updated neural volume is decoded into the radiance field, enabling novel view synthesis from any viewpoint. On both object-centric and scene-level datasets, we show that LEAP significantly outperforms prior methods when they employ predicted poses from state-of-the-art pose estimators. Notably, LEAP performs on par with prior approaches that use ground-truth poses while running 400times faster than PixelNeRF. We show LEAP generalizes to novel object categories and scenes, and learns knowledge closely resembles epipolar geometry. Project page: https://hwjiang1510.github.io/LEAP/

Monocular 3D pose estimation is fundamentally ill-posed due to depth ambiguity and occlusions, thereby motivating probabilistic methods that generate multiple plausible 3D pose hypotheses. In particular, diffusion-based models have recently demonstrated strong performance, but their iterative denoising process typically requires many timesteps for each prediction, making inference computationally expensive. In contrast, we leverage Flow Matching (FM) to learn a velocity field defined by an Ordinary Differential Equation (ODE), enabling efficient generation of 3D pose samples with only a few integration steps. We propose a novel generative pose estimation framework, FMPose3D, that formulates 3D pose estimation as a conditional distribution transport problem. It continuously transports samples from a standard Gaussian prior to the distribution of plausible 3D poses conditioned only on 2D inputs. Although ODE trajectories are deterministic, FMPose3D naturally generates various pose hypotheses by sampling different noise seeds. To obtain a single accurate prediction from those hypotheses, we further introduce a Reprojection-based Posterior Expectation Aggregation (RPEA) module, which approximates the Bayesian posterior expectation over 3D hypotheses. FMPose3D surpasses existing methods on the widely used human pose estimation benchmarks Human3.6M and MPI-INF-3DHP, and further achieves state-of-the-art performance on the 3D animal pose datasets Animal3D and CtrlAni3D, demonstrating strong performance across both 3D pose domains. The code is available at https://github.com/AdaptiveMotorControlLab/FMPose3D.

We propose real-time, six degrees of freedom (6DoF), 3D face pose estimation without face detection or landmark localization. We observe that estimating the 6DoF rigid transformation of a face is a simpler problem than facial landmark detection, often used for 3D face alignment. In addition, 6DoF offers more information than face bounding box labels. We leverage these observations to make multiple contributions: (a) We describe an easily trained, efficient, Faster R-CNN--based model which regresses 6DoF pose for all faces in the photo, without preliminary face detection. (b) We explain how pose is converted and kept consistent between the input photo and arbitrary crops created while training and evaluating our model. (c) Finally, we show how face poses can replace detection bounding box training labels. Tests on AFLW2000-3D and BIWI show that our method runs at real-time and outperforms state of the art (SotA) face pose estimators. Remarkably, our method also surpasses SotA models of comparable complexity on the WIDER FACE detection benchmark, despite not been optimized on bounding box labels.

Most modern image-based 6D object pose estimation methods learn to predict 2D-3D correspondences, from which the pose can be obtained using a PnP solver. Because of the non-differentiable nature of common PnP solvers, these methods are supervised via the individual correspondences. To address this, several methods have designed differentiable PnP strategies, thus imposing supervision on the pose obtained after the PnP step. Here, we argue that this conflicts with the averaging nature of the PnP problem, leading to gradients that may encourage the network to degrade the accuracy of individual correspondences. To address this, we derive a loss function that exploits the ground truth pose before solving the PnP problem. Specifically, we linearize the PnP solver around the ground-truth pose and compute the covariance of the resulting pose distribution. We then define our loss based on the diagonal covariance elements, which entails considering the final pose estimate yet not suffering from the PnP averaging issue. Our experiments show that our loss consistently improves the pose estimation accuracy for both dense and sparse correspondence based methods, achieving state-of-the-art results on both Linemod-Occluded and YCB-Video.

Fitting a body to a 3D clothed human point cloud is a common yet challenging task. Traditional optimization-based approaches use multi-stage pipelines that are sensitive to pose initialization, while recent learning-based methods often struggle with generalization across diverse poses and garment types. We propose Equivariant Tightness Fitting for Clothed Humans, or ETCH, a novel pipeline that estimates cloth-to-body surface mapping through locally approximate SE(3) equivariance, encoding tightness as displacement vectors from the cloth surface to the underlying body. Following this mapping, pose-invariant body features regress sparse body markers, simplifying clothed human fitting into an inner-body marker fitting task. Extensive experiments on CAPE and 4D-Dress show that ETCH significantly outperforms state-of-the-art methods -- both tightness-agnostic and tightness-aware -- in body fitting accuracy on loose clothing (16.7% ~ 69.5%) and shape accuracy (average 49.9%). Our equivariant tightness design can even reduce directional errors by (67.2% ~ 89.8%) in one-shot (or out-of-distribution) settings. Qualitative results demonstrate strong generalization of ETCH, regardless of challenging poses, unseen shapes, loose clothing, and non-rigid dynamics. We will release the code and models soon for research purposes at https://boqian-li.github.io/ETCH/.

We address the problem of regressing 3D human pose and shape from a single image, with a focus on 3D accuracy. The current best methods leverage large datasets of 3D pseudo-ground-truth (p-GT) and 2D keypoints, leading to robust performance. With such methods, we observe a paradoxical decline in 3D pose accuracy with increasing 2D accuracy. This is caused by biases in the p-GT and the use of an approximate camera projection model. We quantify the error induced by current camera models and show that fitting 2D keypoints and p-GT accurately causes incorrect 3D poses. Our analysis defines the invalid distances within which minimizing 2D and p-GT losses is detrimental. We use this to formulate a new loss Threshold-Adaptive Loss Scaling (TALS) that penalizes gross 2D and p-GT losses but not smaller ones. With such a loss, there are many 3D poses that could equally explain the 2D evidence. To reduce this ambiguity we need a prior over valid human poses but such priors can introduce unwanted bias. To address this, we exploit a tokenized representation of human pose and reformulate the problem as token prediction. This restricts the estimated poses to the space of valid poses, effectively providing a uniform prior. Extensive experiments on the EMDB and 3DPW datasets show that our reformulated keypoint loss and tokenization allows us to train on in-the-wild data while improving 3D accuracy over the state-of-the-art. Our models and code are available for research at https://tokenhmr.is.tue.mpg.de.

Training accurate 3D human pose estimators requires large amount of 3D ground-truth data which is costly to collect. Various weakly or self supervised pose estimation methods have been proposed due to lack of 3D data. Nevertheless, these methods, in addition to 2D ground-truth poses, require either additional supervision in various forms (e.g. unpaired 3D ground truth data, a small subset of labels) or the camera parameters in multiview settings. To address these problems, we present EpipolarPose, a self-supervised learning method for 3D human pose estimation, which does not need any 3D ground-truth data or camera extrinsics. During training, EpipolarPose estimates 2D poses from multi-view images, and then, utilizes epipolar geometry to obtain a 3D pose and camera geometry which are subsequently used to train a 3D pose estimator. We demonstrate the effectiveness of our approach on standard benchmark datasets i.e. Human3.6M and MPI-INF-3DHP where we set the new state-of-the-art among weakly/self-supervised methods. Furthermore, we propose a new performance measure Pose Structure Score (PSS) which is a scale invariant, structure aware measure to evaluate the structural plausibility of a pose with respect to its ground truth. Code and pretrained models are available at https://github.com/mkocabas/EpipolarPose

Existing novel object 6D pose estimation methods typically rely on CAD models or dense reference views, which are both difficult to acquire. Using only a single reference view is more scalable, but challenging due to large pose discrepancies and limited geometric and spatial information. To address these issues, we propose a Single-Reference-based novel object 6D (SinRef-6D) pose estimation method. Our key idea is to iteratively establish point-wise alignment in the camera coordinate system based on state space models (SSMs). Specifically, iterative camera-space point-wise alignment can effectively handle large pose discrepancies, while our proposed RGB and Points SSMs can capture long-range dependencies and spatial information from a single view, offering linear complexity and superior spatial modeling capability. Once pre-trained on synthetic data, SinRef-6D can estimate the 6D pose of a novel object using only a single reference view, without requiring retraining or a CAD model. Extensive experiments on six popular datasets and real-world robotic scenes demonstrate that we achieve on-par performance with CAD-based and dense reference view-based methods, despite operating in the more challenging single reference setting. Code will be released at https://github.com/CNJianLiu/SinRef-6D.

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the robustness of models towards pre-defined continuous transformation groups. Through the use of specially-derived canonical coordinate systems, ETs incorporate functions that are equivariant by construction with respect to these transformations. We show empirically that ETs can be flexibly composed to improve model robustness towards more complicated transformation groups in several parameters. On a real-world image classification task, ETs improve the sample efficiency of ResNet classifiers, achieving relative improvements in error rate of up to 15% in the limited data regime while increasing model parameter count by less than 1%.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

6D pose estimation of rigid objects is a long-standing and challenging task in computer vision. Recently, the emergence of deep learning reveals the potential of Convolutional Neural Networks (CNNs) to predict reliable 6D poses. Given that direct pose regression networks currently exhibit suboptimal performance, most methods still resort to traditional techniques to varying degrees. For example, top-performing methods often adopt an indirect strategy by first establishing 2D-3D or 3D-3D correspondences followed by applying the RANSAC-based PnP or Kabsch algorithms, and further employing ICP for refinement. Despite the performance enhancement, the integration of traditional techniques makes the networks time-consuming and not end-to-end trainable. Orthogonal to them, this paper introduces a fully learning-based object pose estimator. In this work, we first perform an in-depth investigation of both direct and indirect methods and propose a simple yet effective Geometry-guided Direct Regression Network (GDRN) to learn the 6D pose from monocular images in an end-to-end manner. Afterwards, we introduce a geometry-guided pose refinement module, enhancing pose accuracy when extra depth data is available. Guided by the predicted coordinate map, we build an end-to-end differentiable architecture that establishes robust and accurate 3D-3D correspondences between the observed and rendered RGB-D images to refine the pose. Our enhanced pose estimation pipeline GDRNPP (GDRN Plus Plus) conquered the leaderboard of the BOP Challenge for two consecutive years, becoming the first to surpass all prior methods that relied on traditional techniques in both accuracy and speed. The code and models are available at https://github.com/shanice-l/gdrnpp_bop2022.

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of exactly equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

The intrinsic rotation invariance lies at the core of matching point clouds with handcrafted descriptors. However, it is widely despised by recent deep matchers that obtain the rotation invariance extrinsically via data augmentation. As the finite number of augmented rotations can never span the continuous SO(3) space, these methods usually show instability when facing rotations that are rarely seen. To this end, we introduce RoITr, a Rotation-Invariant Transformer to cope with the pose variations in the point cloud matching task. We contribute both on the local and global levels. Starting from the local level, we introduce an attention mechanism embedded with Point Pair Feature (PPF)-based coordinates to describe the pose-invariant geometry, upon which a novel attention-based encoder-decoder architecture is constructed. We further propose a global transformer with rotation-invariant cross-frame spatial awareness learned by the self-attention mechanism, which significantly improves the feature distinctiveness and makes the model robust with respect to the low overlap. Experiments are conducted on both the rigid and non-rigid public benchmarks, where RoITr outperforms all the state-of-the-art models by a considerable margin in the low-overlapping scenarios. Especially when the rotations are enlarged on the challenging 3DLoMatch benchmark, RoITr surpasses the existing methods by at least 13 and 5 percentage points in terms of Inlier Ratio and Registration Recall, respectively.

Visual recognition models are not invariant to viewpoint changes in the 3D world, as different viewing directions can dramatically affect the predictions given the same object. Although many efforts have been devoted to making neural networks invariant to 2D image translations and rotations, viewpoint invariance is rarely investigated. As most models process images in the perspective view, it is challenging to impose invariance to 3D viewpoint changes based only on 2D inputs. Motivated by the success of adversarial training in promoting model robustness, we propose Viewpoint-Invariant Adversarial Training (VIAT) to improve viewpoint robustness of common image classifiers. By regarding viewpoint transformation as an attack, VIAT is formulated as a minimax optimization problem, where the inner maximization characterizes diverse adversarial viewpoints by learning a Gaussian mixture distribution based on a new attack GMVFool, while the outer minimization trains a viewpoint-invariant classifier by minimizing the expected loss over the worst-case adversarial viewpoint distributions. To further improve the generalization performance, a distribution sharing strategy is introduced leveraging the transferability of adversarial viewpoints across objects. Experiments validate the effectiveness of VIAT in improving the viewpoint robustness of various image classifiers based on the diversity of adversarial viewpoints generated by GMVFool.

We propose a keypoint-based object-level SLAM framework that can provide globally consistent 6DoF pose estimates for symmetric and asymmetric objects alike. To the best of our knowledge, our system is among the first to utilize the camera pose information from SLAM to provide prior knowledge for tracking keypoints on symmetric objects -- ensuring that new measurements are consistent with the current 3D scene. Moreover, our semantic keypoint network is trained to predict the Gaussian covariance for the keypoints that captures the true error of the prediction, and thus is not only useful as a weight for the residuals in the system's optimization problems, but also as a means to detect harmful statistical outliers without choosing a manual threshold. Experiments show that our method provides competitive performance to the state of the art in 6DoF object pose estimation, and at a real-time speed. Our code, pre-trained models, and keypoint labels are available https://github.com/rpng/suo_slam.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Point cloud registration aligns multiple unposed point clouds into a common frame, and is a core step for 3D reconstruction and robot localization. In this work, we cast registration as conditional generation: a learned continuous, point-wise velocity field transports noisy points to a registered scene, from which the pose of each view is recovered. Unlike previous methods that conduct correspondence matching to estimate the transformation between a pair of point clouds and then optimize the pairwise transformations to realize multi-view registration, our model directly generates the registered point cloud. With a lightweight local feature extractor and test-time rigidity enforcement, our approach achieves state-of-the-art results on pairwise and multi-view registration benchmarks, particularly with low overlap, and generalizes across scales and sensor modalities. It further supports downstream tasks including relocalization, multi-robot SLAM, and multi-session map merging. Source code available at: https://github.com/PRBonn/RAP.

The lifting of 3D structure and camera from 2D landmarks is at the cornerstone of the entire discipline of computer vision. Traditional methods have been confined to specific rigid objects, such as those in Perspective-n-Point (PnP) problems, but deep learning has expanded our capability to reconstruct a wide range of object classes (e.g. C3PDO and PAUL) with resilience to noise, occlusions, and perspective distortions. All these techniques, however, have been limited by the fundamental need to establish correspondences across the 3D training data -- significantly limiting their utility to applications where one has an abundance of "in-correspondence" 3D data. Our approach harnesses the inherent permutation equivariance of transformers to manage varying number of points per 3D data instance, withstands occlusions, and generalizes to unseen categories. We demonstrate state of the art performance across 2D-3D lifting task benchmarks. Since our approach can be trained across such a broad class of structures we refer to it simply as a 3D Lifting Foundation Model (3D-LFM) -- the first of its kind.

Camera relocalization methods range from dense image alignment to direct camera pose regression from a query image. Among these, sparse feature matching stands out as an efficient, versatile, and generally lightweight approach with numerous applications. However, feature-based methods often struggle with significant viewpoint and appearance changes, leading to matching failures and inaccurate pose estimates. To overcome this limitation, we propose a novel approach that leverages a globally sparse yet locally dense 3D representation of 2D features. By tracking and triangulating landmarks over a sequence of frames, we construct a sparse voxel map optimized to render image patch descriptors observed during tracking. Given an initial pose estimate, we first synthesize descriptors from the voxels using volumetric rendering and then perform feature matching to estimate the camera pose. This methodology enables the generation of descriptors for unseen views, enhancing robustness to view changes. We extensively evaluate our method on the 7-Scenes and Cambridge Landmarks datasets. Our results show that our method significantly outperforms existing state-of-the-art feature representation techniques in indoor environments, achieving up to a 39% improvement in median translation error. Additionally, our approach yields comparable results to other methods for outdoor scenarios while maintaining lower memory and computational costs.

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we introduce an as-rigid-as-possible regulation term to estimate the deformed normals and propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.

Many theoretical results in deep learning can be traced to symmetry or equivariance of neural networks under parameter transformations. However, existing analyses are typically problem-specific and focus on first-order consequences such as conservation laws, while the implications for second-order structure remain less understood. We develop a general equivariance toolbox that yields coupled first- and second-order constraints on learning dynamics. The framework extends classical Noether-type analyses in three directions: from gradient constraints to Hessian constraints, from symmetry to general equivariance, and from continuous to discrete transformations. At the first order, our framework unifies conservation laws and implicit-bias relations as special cases of a single identity. At the second order, it provides structural predictions about curvature: which directions are flat or sharp, how the gradient aligns with Hessian eigenspaces, and how the loss landscape geometry reflects the underlying transformation structure. We illustrate the framework through several applications, recovering known results while also deriving new characterizations that connect transformation structure to modern empirical observations about optimization geometry.

Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D navigation, which originates from Euclidean transformations between reference frames and enables parameter sharing. To address the challenges of unstructured environments, we formulate the navigation problem as planning on a geometric graph and develop an equivariant message passing network to perform value iteration. Furthermore, to handle multi-camera input, we propose a learnable equivariant layer to lift features to a desired space. We conduct comprehensive evaluations across five diverse tasks encompassing structured and unstructured environments, along with maps of known and unknown, given point goals or semantic goals. Our experiments confirm the substantial benefits on training efficiency, stability, and generalization.

Inferring the 3D structure underlying a set of multi-view images typically requires solving two co-dependent tasks -- accurate 3D reconstruction requires precise camera poses, and predicting camera poses relies on (implicitly or explicitly) modeling the underlying 3D. The classical framework of analysis by synthesis casts this inference as a joint optimization seeking to explain the observed pixels, and recent instantiations learn expressive 3D representations (e.g., Neural Fields) with gradient-descent-based pose refinement of initial pose estimates. However, given a sparse set of observed views, the observations may not provide sufficient direct evidence to obtain complete and accurate 3D. Moreover, large errors in pose estimation may not be easily corrected and can further degrade the inferred 3D. To allow robust 3D reconstruction and pose estimation in this challenging setup, we propose SparseAGS, a method that adapts this analysis-by-synthesis approach by: a) including novel-view-synthesis-based generative priors in conjunction with photometric objectives to improve the quality of the inferred 3D, and b) explicitly reasoning about outliers and using a discrete search with a continuous optimization-based strategy to correct them. We validate our framework across real-world and synthetic datasets in combination with several off-the-shelf pose estimation systems as initialization. We find that it significantly improves the base systems' pose accuracy while yielding high-quality 3D reconstructions that outperform the results from current multi-view reconstruction baselines.

This paper presents a novel preconditioning strategy for the classic 8-point algorithm (8-PA) for estimating an essential matrix from 360-FoV images (i.e., equirectangular images) in spherical projection. To alleviate the effect of uneven key-feature distributions and outlier correspondences, which can potentially decrease the accuracy of an essential matrix, our method optimizes a non-rigid transformation to deform a spherical camera into a new spatial domain, defining a new constraint and a more robust and accurate solution for an essential matrix. Through several experiments using random synthetic points, 360-FoV, and fish-eye images, we demonstrate that our normalization can increase the camera pose accuracy by about 20% without significantly overhead the computation time. In addition, we present further benefits of our method through both a constant weighted least-square optimization that improves further the well known Gold Standard Method (GSM) (i.e., the non-linear optimization by using epipolar errors); and a relaxation of the number of RANSAC iterations, both showing that our normalization outcomes a more reliable, robust, and accurate solution.

Estimating the 6D pose of objects unseen during training is highly desirable yet challenging. Zero-shot object 6D pose estimation methods address this challenge by leveraging additional task-specific supervision provided by large-scale, photo-realistic synthetic datasets. However, their performance heavily depends on the quality and diversity of rendered data and they require extensive training. In this work, we show how to tackle the same task but without training on specific data. We propose FreeZe, a novel solution that harnesses the capabilities of pre-trained geometric and vision foundation models. FreeZe leverages 3D geometric descriptors learned from unrelated 3D point clouds and 2D visual features learned from web-scale 2D images to generate discriminative 3D point-level descriptors. We then estimate the 6D pose of unseen objects by 3D registration based on RANSAC. We also introduce a novel algorithm to solve ambiguous cases due to geometrically symmetric objects that is based on visual features. We comprehensively evaluate FreeZe across the seven core datasets of the BOP Benchmark, which include over a hundred 3D objects and 20,000 images captured in various scenarios. FreeZe consistently outperforms all state-of-the-art approaches, including competitors extensively trained on synthetic 6D pose estimation data. Code will be publicly available at https://andreacaraffa.github.io/freeze.

3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do not generalize well to articulated objects in the wild. We treat an articulated object as an unknown, semi-rigid skeletal structure surrounded by nonrigid material (e.g., skin). Our method simultaneously estimates the visible (explicit) representation (3D shapes, colors, camera parameters) and the implicit skeletal representation, from motion cues in the object video without 3D supervision. Our implicit representation consists of four parts. (1) Skeleton, which specifies how semi-rigid parts are connected. (2) black{Skinning Weights}, which associates each surface vertex with semi-rigid parts with probability. (3) Rigidity Coefficients, specifying the articulation of the local surface. (4) Time-Varying Transformations, which specify the skeletal motion and surface deformation parameters. We introduce an algorithm that uses physical constraints as regularization terms and iteratively estimates both implicit and explicit representations. Our method is category-agnostic, thus eliminating the need for category-specific skeletons, we show that our method outperforms state-of-the-art across standard video datasets.

Although data-driven methods have achieved success in 3D human pose estimation, they often suffer from domain gaps and exhibit limited generalization. In contrast, optimization-based methods excel in fine-tuning for specific cases but are generally inferior to data-driven methods in overall performance. We observe that previous optimization-based methods commonly rely on a projection constraint, which only ensures alignment in 2D space, potentially leading to the overfitting problem. To address this, we propose an Uncertainty-Aware testing-time Optimization (UAO) framework, which keeps the prior information of the pre-trained model and alleviates the overfitting problem using the uncertainty of joints. Specifically, during the training phase, we design an effective 2D-to-3D network for estimating the corresponding 3D pose while quantifying the uncertainty of each 3D joint. For optimization during testing, the proposed optimization framework freezes the pre-trained model and optimizes only a latent state. Projection loss is then employed to ensure the generated poses are well aligned in 2D space for high-quality optimization. Furthermore, we utilize the uncertainty of each joint to determine how much each joint is allowed for optimization. The effectiveness and superiority of the proposed framework are validated through extensive experiments on challenging datasets: Human3.6M, MPI-INF-3DHP, and 3DPW. Notably, our approach outperforms the previous best result by a large margin of 5.5\% on Human3.6M. Code is available at https://github.com/xiu-cs/UAO-Pose3D{https://github.com/xiu-cs/UAO-Pose3D}.

We introduce Rectified Point Flow, a unified parameterization that formulates pairwise point cloud registration and multi-part shape assembly as a single conditional generative problem. Given unposed point clouds, our method learns a continuous point-wise velocity field that transports noisy points toward their target positions, from which part poses are recovered. In contrast to prior work that regresses part-wise poses with ad-hoc symmetry handling, our method intrinsically learns assembly symmetries without symmetry labels. Together with a self-supervised encoder focused on overlapping points, our method achieves a new state-of-the-art performance on six benchmarks spanning pairwise registration and shape assembly. Notably, our unified formulation enables effective joint training on diverse datasets, facilitating the learning of shared geometric priors and consequently boosting accuracy. Project page: https://rectified-pointflow.github.io/.

Mirror reflections are common in everyday environments and can provide stereo information within a single capture, as the real and reflected virtual views are visible simultaneously. We exploit this property by treating the reflection as an auxiliary view and designing a transformation that constructs a physically valid virtual camera, allowing direct pixel-domain generation of the virtual view while adhering to the real-world imaging process. This enables a multi-view stereo setup from a single image, simplifying the imaging process, making it compatible with powerful feed-forward reconstruction models for generalizable and robust 3D reconstruction. To further exploit the geometric symmetry introduced by mirrors, we propose a symmetric-aware loss to refine pose estimation. Our framework also naturally extends to dynamic scenes, where each frame contains a mirror reflection, enabling efficient per-frame geometry recovery. For quantitative evaluation, we provide a fully customizable synthetic dataset of 16 Blender scenes, each with ground-truth point clouds and camera poses. Extensive experiments on real-world data and synthetic data are conducted to illustrate the effectiveness of our method.

Recent advances in RGBD-based category-level object pose estimation have been limited by their reliance on precise depth information, restricting their broader applicability. In response, RGB-based methods have been developed. Among these methods, geometry-guided pose regression that originated from instance-level tasks has demonstrated strong performance. However, we argue that the NOCS map is an inadequate intermediate representation for geometry-guided pose regression method, as its many-to-one correspondence with category-level pose introduces redundant instance-specific information, resulting in suboptimal results. This paper identifies the intra-class variation problem inherent in pose regression based solely on the NOCS map and proposes the Intra-class Variation-Free Consensus (IVFC) map, a novel coordinate representation generated from the category-level consensus model. By leveraging the complementary strengths of the NOCS map and the IVFC map, we introduce GIVEPose, a framework that implements Gradual Intra-class Variation Elimination for category-level object pose estimation. Extensive evaluations on both synthetic and real-world datasets demonstrate that GIVEPose significantly outperforms existing state-of-the-art RGB-based approaches, achieving substantial improvements in category-level object pose estimation. Our code is available at https://github.com/ziqin-h/GIVEPose.

Previous methods solve feature matching and pose estimation using a two-stage process by first finding matches and then estimating the pose. As they ignore the geometric relationships between the two tasks, they focus on either improving the quality of matches or filtering potential outliers, leading to limited efficiency or accuracy. In contrast, we propose an iterative matching and pose estimation framework (IMP) leveraging the geometric connections between the two tasks: a few good matches are enough for a roughly accurate pose estimation; a roughly accurate pose can be used to guide the matching by providing geometric constraints. To this end, we implement a geometry-aware recurrent attention-based module which jointly outputs sparse matches and camera poses. Specifically, for each iteration, we first implicitly embed geometric information into the module via a pose-consistency loss, allowing it to predict geometry-aware matches progressively. Second, we introduce an efficient IMP, called EIMP, to dynamically discard keypoints without potential matches, avoiding redundant updating and significantly reducing the quadratic time complexity of attention computation in transformers. Experiments on YFCC100m, Scannet, and Aachen Day-Night datasets demonstrate that the proposed method outperforms previous approaches in terms of accuracy and efficiency.

Estimating the 6D pose of arbitrary unseen objects from a single reference image is critical for robotics operating in the long-tail of real-world instances. However, this setting is notoriously challenging: 3D models are rarely available, single-view reconstructions lack metric scale, and domain gaps between generated models and real-world images undermine robustness. We propose OnePoseViaGen, a pipeline that tackles these challenges through two key components. First, a coarse-to-fine alignment module jointly refines scale and pose by combining multi-view feature matching with render-and-compare refinement. Second, a text-guided generative domain randomization strategy diversifies textures, enabling effective fine-tuning of pose estimators with synthetic data. Together, these steps allow high-fidelity single-view 3D generation to support reliable one-shot 6D pose estimation. On challenging benchmarks (YCBInEOAT, Toyota-Light, LM-O), OnePoseViaGen achieves state-of-the-art performance far surpassing prior approaches. We further demonstrate robust dexterous grasping with a real robot hand, validating the practicality of our method in real-world manipulation. Project page: https://gzwsama.github.io/OnePoseviaGen.github.io/

Object-centric reconstruction seeks to recover the 3D structure of a scene through composition of independent objects. While this independence can simplify modeling, it discards strong signals that could improve reconstruction, notably repetition where the same object model is seen multiple times in a scene, or across scans. We propose the Joint Reconstruction Model (JRM) to leverage repetition by framing object reconstruction as one of personalized generation: multiple observations share a common subject that should be consistent for all observations, while still adhering to the specific pose and state from each. Prior methods in this direction rely on explicit matching and rigid alignment across observations, making them sensitive to errors and difficult to extend to non-rigid transformations. In contrast, JRM is a 3D flow-matching generative model that implicitly aggregates unaligned observations in its latent space, learning to produce consistent and faithful reconstructions in a data-driven manner without explicit constraints. Evaluations on synthetic and real-world data show that JRM's implicit aggregation removes the need for explicit alignment, improves robustness to incorrect associations, and naturally handles non-rigid changes such as articulation. Overall, JRM outperforms both independent and alignment-based baselines in reconstruction quality.

Automatically discovering composable abstractions from raw perceptual data is a long-standing challenge in machine learning. Recent slot-based neural networks that learn about objects in a self-supervised manner have made exciting progress in this direction. However, they typically fall short at adequately capturing spatial symmetries present in the visual world, which leads to sample inefficiency, such as when entangling object appearance and pose. In this paper, we present a simple yet highly effective method for incorporating spatial symmetries via slot-centric reference frames. We incorporate equivariance to per-object pose transformations into the attention and generation mechanism of Slot Attention by translating, scaling, and rotating position encodings. These changes result in little computational overhead, are easy to implement, and can result in large gains in terms of data efficiency and overall improvements to object discovery. We evaluate our method on a wide range of synthetic object discovery benchmarks namely CLEVR, Tetrominoes, CLEVRTex, Objects Room and MultiShapeNet, and show promising improvements on the challenging real-world Waymo Open dataset.

In this paper, we address the challenge of reconstructing general articulated 3D objects from a single video. Existing works employing dynamic neural radiance fields have advanced the modeling of articulated objects like humans and animals from videos, but face challenges with piece-wise rigid general articulated objects due to limitations in their deformation models. To tackle this, we propose Quasi-Rigid Blend Skinning, a novel deformation model that enhances the rigidity of each part while maintaining flexible deformation of the joints. Our primary insight combines three distinct approaches: 1) an enhanced bone rigging system for improved component modeling, 2) the use of quasi-sparse skinning weights to boost part rigidity and reconstruction fidelity, and 3) the application of geodesic point assignment for precise motion and seamless deformation. Our method outperforms previous works in producing higher-fidelity 3D reconstructions of general articulated objects, as demonstrated on both real and synthetic datasets. Project page: https://chaoyuesong.github.io/REACTO.

Novel View Synthesis (NVS) has traditionally relied on models with explicit 3D inductive biases combined with known camera parameters from Structure-from-Motion (SfM) beforehand. Recent vision foundation models like VGGT take an orthogonal approach -- 3D knowledge is gained implicitly through training data and loss objectives, enabling feed-forward prediction of both camera parameters and 3D representations directly from a set of uncalibrated images. While flexible, VGGT features lack explicit multi-view geometric consistency, and we find that improving such 3D feature consistency benefits both NVS and pose estimation tasks. We introduce Selfi, a self-improving 3D reconstruction pipeline via feature alignment, transforming a VGGT backbone into a high-fidelity 3D reconstruction engine by leveraging its own outputs as pseudo-ground-truth. Specifically, we train a lightweight feature adapter using a reprojection-based consistency loss, which distills VGGT outputs into a new geometrically-aligned feature space that captures spatial proximity in 3D. This enables state-of-the-art performance in both NVS and camera pose estimation, demonstrating that feature alignment is a highly beneficial step for downstream 3D reasoning.

Precise six-degree-of-freedom (6DoF) head pose estimation is crucial for safety-critical applications and human-computer interaction scenarios, yet existing monocular methods still struggle with robust pose estimation. We revisit this problem by introducing TRGv2, a lightweight extension of our previous Translation, Rotation, and Geometry (TRG) network, which explicitly models the bidirectional interaction between facial geometry and head pose. TRGv2 jointly infers facial landmarks and 6DoF pose through an iterative refinement loop with landmark-to-image projection, ensuring metric consistency among face size, rotation, and depth. To further improve generalization to out-of-distribution data, TRGv2 regresses correction parameters instead of directly predicting translation, combining them with a pinhole camera model for analytic depth estimation. In addition, we identify a previously overlooked source of bias in cross-dataset evaluations due to inconsistent head center definitions across different datasets. To address this, we propose a reference system alignment strategy that quantifies and corrects translation bias, enabling fair comparisons across datasets. Extensive experiments on ARKitFace, BIWI, and the challenging DD-Pose benchmarks demonstrate that TRGv2 outperforms state-of-the-art methods in both accuracy and efficiency. Code and newly annotated landmarks for DD-Pose will be publicly available.

Identity-preserving text-to-video generation (IPT2V) empowers users to produce diverse and imaginative videos with consistent human facial identity. Despite recent progress, existing methods often suffer from significant identity distortion under large facial pose variations or facial occlusions. In this paper, we propose FaithfulFaces, a pose-faithful facial identity preservation learning framework to improve IPT2V in complex dynamic scenes. The key of FaithfulFaces is a pose-shared identity aligner that refines and aligns facial poses across distinct views via a pose-shared dictionary and a pose variation-identity invariance constraint. By mapping single-view inputs into a global facial pose representation with explicit Euler angle embeddings, FaithfulFaces provides a pose-faithful facial prior that guides generative foundations toward robust identity-preserving generation. In particular, we develop a specialized pipeline to curate a high-quality video dataset featuring substantial facial pose diversity. Extensive experiments demonstrate that FaithfulFaces achieves state-of-the-art performance, maintaining superior identity consistency and structural clarity even as pose changes and occlusions occur.

In this paper, a novel Diffusion-based 3D Pose estimation (D3DP) method with Joint-wise reProjection-based Multi-hypothesis Aggregation (JPMA) is proposed for probabilistic 3D human pose estimation. On the one hand, D3DP generates multiple possible 3D pose hypotheses for a single 2D observation. It gradually diffuses the ground truth 3D poses to a random distribution, and learns a denoiser conditioned on 2D keypoints to recover the uncontaminated 3D poses. The proposed D3DP is compatible with existing 3D pose estimators and supports users to balance efficiency and accuracy during inference through two customizable parameters. On the other hand, JPMA is proposed to assemble multiple hypotheses generated by D3DP into a single 3D pose for practical use. It reprojects 3D pose hypotheses to the 2D camera plane, selects the best hypothesis joint-by-joint based on the reprojection errors, and combines the selected joints into the final pose. The proposed JPMA conducts aggregation at the joint level and makes use of the 2D prior information, both of which have been overlooked by previous approaches. Extensive experiments on Human3.6M and MPI-INF-3DHP datasets show that our method outperforms the state-of-the-art deterministic and probabilistic approaches by 1.5% and 8.9%, respectively. Code is available at https://github.com/paTRICK-swk/D3DP.

Reconstructing 3D human shape and pose from monocular images is challenging despite the promising results achieved by the most recent learning-based methods. The commonly occurred misalignment comes from the facts that the mapping from images to the model space is highly non-linear and the rotation-based pose representation of body models is prone to result in the drift of joint positions. In this work, we investigate learning 3D human shape and pose from dense correspondences of body parts and propose a Decompose-and-aggregate Network (DaNet) to address these issues. DaNet adopts the dense correspondence maps, which densely build a bridge between 2D pixels and 3D vertices, as intermediate representations to facilitate the learning of 2D-to-3D mapping. The prediction modules of DaNet are decomposed into one global stream and multiple local streams to enable global and fine-grained perceptions for the shape and pose predictions, respectively. Messages from local streams are further aggregated to enhance the robust prediction of the rotation-based poses, where a position-aided rotation feature refinement strategy is proposed to exploit spatial relationships between body joints. Moreover, a Part-based Dropout (PartDrop) strategy is introduced to drop out dense information from intermediate representations during training, encouraging the network to focus on more complementary body parts as well as neighboring position features. The efficacy of the proposed method is validated on both indoor and real-world datasets including Human3.6M, UP3D, COCO, and 3DPW, showing that our method could significantly improve the reconstruction performance in comparison with previous state-of-the-art methods. Our code is publicly available at https://hongwenzhang.github.io/dense2mesh .

Recent joint embedding-based self-supervised methods have surpassed standard supervised approaches on various image recognition tasks such as image classification. These self-supervised methods aim at maximizing agreement between features extracted from two differently transformed views of the same image, which results in learning an invariant representation with respect to appearance and geometric image transformations. However, the effectiveness of these approaches remains unclear in the context of gaze estimation, a structured regression task that requires equivariance under geometric transformations (e.g., rotations, horizontal flip). In this work, we propose SwAT, an equivariant version of the online clustering-based self-supervised approach SwAV, to learn more informative representations for gaze estimation. We demonstrate that SwAT, with ResNet-50 and supported with uncurated unlabeled face images, outperforms state-of-the-art gaze estimation methods and supervised baselines in various experiments. In particular, we achieve up to 57% and 25% improvements in cross-dataset and within-dataset evaluation tasks on existing benchmarks (ETH-XGaze, Gaze360, and MPIIFaceGaze).

Object pose estimation, which plays a vital role in robotics, augmented reality, and autonomous driving, has been of great interest in computer vision. Existing studies either require multi-stage pose regression or rely on 2D-3D feature matching. Though these approaches have shown promising results, they rely heavily on appearance information, requiring complex input (i.e., multi-view reference input, depth, or CAD models) and intricate pipeline (i.e., feature extraction-SfM-2D to 3D matching-PnP). We propose AxisPose, a model-free, matching-free, single-shot solution for robust 6D pose estimation, which fundamentally diverges from the existing paradigm. Unlike existing methods that rely on 2D-3D or 2D-2D matching using 3D techniques, such as SfM and PnP, AxisPose directly infers a robust 6D pose from a single view by leveraging a diffusion model to learn the latent axis distribution of objects without reference views. Specifically, AxisPose constructs an Axis Generation Module (AGM) to capture the latent geometric distribution of object axes through a diffusion model. The diffusion process is guided by injecting the gradient of geometric consistency loss into the noise estimation to maintain the geometric consistency of the generated tri-axis. With the generated tri-axis projection, AxisPose further adopts a Triaxial Back-projection Module (TBM) to recover the 6D pose from the object tri-axis. The proposed AxisPose achieves robust performance at the cross-instance level (i.e., one model for N instances) using only a single view as input without reference images, with great potential for generalization to unseen-object level.

Panoramic imagery offers a full 360° field of view and is increasingly common in consumer devices. However, it introduces non-pinhole distortions that challenge joint pose estimation and 3D reconstruction. Existing feed-forward models, built for perspective cameras, generalize poorly to this setting. We propose PanoVGGT, a permutation-equivariant Transformer framework that jointly predicts camera poses, depth maps, and 3D point clouds from one or multiple panoramas in a single forward pass. The model incorporates spherical-aware positional embeddings and a panorama-specific three-axis SO(3) rotation augmentation, enabling effective geometric reasoning in the spherical domain. To resolve inherent global-frame ambiguity, we further introduce a stochastic anchoring strategy during training. In addition, we contribute PanoCity, a large-scale outdoor panoramic dataset with dense depth and 6-DoF pose annotations. Extensive experiments on PanoCity and standard benchmarks demonstrate that PanoVGGT achieves competitive accuracy, strong robustness, and improved cross-domain generalization. Code and dataset will be released.

Pairwise pose estimation from images with little or no overlap is an open challenge in computer vision. Existing methods, even those trained on large-scale datasets, struggle in these scenarios due to the lack of identifiable correspondences or visual overlap. Inspired by the human ability to infer spatial relationships from diverse scenes, we propose a novel approach, InterPose, that leverages the rich priors encoded within pre-trained generative video models. We propose to use a video model to hallucinate intermediate frames between two input images, effectively creating a dense, visual transition, which significantly simplifies the problem of pose estimation. Since current video models can still produce implausible motion or inconsistent geometry, we introduce a self-consistency score that evaluates the consistency of pose predictions from sampled videos. We demonstrate that our approach generalizes among three state-of-the-art video models and show consistent improvements over the state-of-the-art DUSt3R on four diverse datasets encompassing indoor, outdoor, and object-centric scenes. Our findings suggest a promising avenue for improving pose estimation models by leveraging large generative models trained on vast amounts of video data, which is more readily available than 3D data. See our project page for results: https://inter-pose.github.io/.

3D pose transfer is a challenging generation task that aims to transfer the pose of a source geometry onto a target geometry with the target identity preserved. Many prior methods require keypoint annotations to find correspondence between the source and target. Current pose transfer methods allow end-to-end correspondence learning but require the desired final output as ground truth for supervision. Unsupervised methods have been proposed for graph convolutional models but they require ground truth correspondence between the source and target inputs. We present a novel self-supervised framework for 3D pose transfer which can be trained in unsupervised, semi-supervised, or fully supervised settings without any correspondence labels. We introduce two contrastive learning constraints in the latent space: a mesh-level loss for disentangling global patterns including pose and identity, and a point-level loss for discriminating local semantics. We demonstrate quantitatively and qualitatively that our method achieves state-of-the-art results in supervised 3D pose transfer, with comparable results in unsupervised and semi-supervised settings. Our method is also generalisable to unseen human and animal data with complex topologies.

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging from biology to computer vision. However, a rich yet separate line of learning theoretic research has demonstrated that actually learning shallow, fully-connected (i.e. non-symmetric) networks has exponential complexity in the correlational statistical query (CSQ) model, a framework encompassing gradient descent. In this work, we ask: are known problem symmetries sufficient to alleviate the fundamental hardness of learning neural nets with gradient descent? We answer this question in the negative. In particular, we give lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials, and frame-averaged networks for permutation subgroups, which all scale either superpolynomially or exponentially in the relevant input dimension. Therefore, in spite of the significant inductive bias imparted via symmetry, actually learning the complete classes of functions represented by equivariant neural networks via gradient descent remains hard.

We present a method to combine markerless motion capture and dense pose feature estimation into a single framework. We demonstrate that dense pose information can help for multiview/single-view motion capture, and multiview motion capture can help the collection of a high-quality dataset for training the dense pose detector. Specifically, we first introduce a novel markerless motion capture method that can take advantage of dense parsing capability provided by the dense pose detector. Thanks to the introduced dense human parsing ability, our method is demonstrated much more efficient, and accurate compared with the available state-of-the-art markerless motion capture approach. Second, we improve the performance of available dense pose detector by using multiview markerless motion capture data. Such dataset is beneficial to dense pose training because they are more dense and accurate and consistent, and can compensate for the corner cases such as unusual viewpoints. We quantitatively demonstrate the improved performance of our dense pose detector over the available DensePose. Our dense pose dataset and detector will be made public.

Zero-shot 6D object pose estimation involves the detection of novel objects with their 6D poses in cluttered scenes, presenting significant challenges for model generalizability. Fortunately, the recent Segment Anything Model (SAM) has showcased remarkable zero-shot transfer performance, which provides a promising solution to tackle this task. Motivated by this, we introduce SAM-6D, a novel framework designed to realize the task through two steps, including instance segmentation and pose estimation. Given the target objects, SAM-6D employs two dedicated sub-networks, namely Instance Segmentation Model (ISM) and Pose Estimation Model (PEM), to perform these steps on cluttered RGB-D images. ISM takes SAM as an advanced starting point to generate all possible object proposals and selectively preserves valid ones through meticulously crafted object matching scores in terms of semantics, appearance and geometry. By treating pose estimation as a partial-to-partial point matching problem, PEM performs a two-stage point matching process featuring a novel design of background tokens to construct dense 3D-3D correspondence, ultimately yielding the pose estimates. Without bells and whistles, SAM-6D outperforms the existing methods on the seven core datasets of the BOP Benchmark for both instance segmentation and pose estimation of novel objects.

In this paper, we present a method for unconstrained end-to-end head pose estimation. We address the problem of ambiguous rotation labels by introducing the rotation matrix formalism for our ground truth data and propose a continuous 6D rotation matrix representation for efficient and robust direct regression. This way, our method can learn the full rotation appearance which is contrary to previous approaches that restrict the pose prediction to a narrow-angle for satisfactory results. In addition, we propose a geodesic distance-based loss to penalize our network with respect to the SO(3) manifold geometry. Experiments on the public AFLW2000 and BIWI datasets demonstrate that our proposed method significantly outperforms other state-of-the-art methods by up to 20\%. We open-source our training and testing code along with our pre-trained models: https://github.com/thohemp/6DRepNet.

Real-time dense scene reconstruction during unstable camera motions is crucial for robotics, yet current RGB-D SLAM systems fail when cameras experience large viewpoint changes, fast motions, or sudden shaking. Classical optimization-based methods deliver high accuracy but fail with poor initialization during large motions, while learning-based approaches provide robustness but lack sufficient accuracy for dense reconstruction. We address this challenge through a combination of learning-based initialization with optimization-based refinement. Our method employs a camera pose regression network to predict metric-aware relative poses from consecutive RGB-D frames, which serve as reliable starting points for a randomized optimization algorithm that further aligns depth images with the scene geometry. Extensive experiments demonstrate promising results: our approach outperforms the best competitor on challenging benchmarks, while maintaining comparable accuracy on stable motion sequences. The system operates in real-time, showcasing that combining simple and principled techniques can achieve both robustness for unstable motions and accuracy for dense reconstruction. Project page: https://github.com/siyandong/PROFusion.

Traditionally, monocular 3D human pose estimation employs a machine learning model to predict the most likely 3D pose for a given input image. However, a single image can be highly ambiguous and induces multiple plausible solutions for the 2D-3D lifting step which results in overly confident 3D pose predictors. To this end, we propose DiffPose, a conditional diffusion model, that predicts multiple hypotheses for a given input image. In comparison to similar approaches, our diffusion model is straightforward and avoids intensive hyperparameter tuning, complex network structures, mode collapse, and unstable training. Moreover, we tackle a problem of the common two-step approach that first estimates a distribution of 2D joint locations via joint-wise heatmaps and consecutively approximates them based on first- or second-moment statistics. Since such a simplification of the heatmaps removes valid information about possibly correct, though labeled unlikely, joint locations, we propose to represent the heatmaps as a set of 2D joint candidate samples. To extract information about the original distribution from these samples we introduce our embedding transformer that conditions the diffusion model. Experimentally, we show that DiffPose slightly improves upon the state of the art for multi-hypothesis pose estimation for simple poses and outperforms it by a large margin for highly ambiguous poses.

We introduce Free3D, a simple approach designed for open-set novel view synthesis (NVS) from a single image. Similar to Zero-1-to-3, we start from a pre-trained 2D image generator for generalization, and fine-tune it for NVS. Compared to recent and concurrent works, we obtain significant improvements without resorting to an explicit 3D representation, which is slow and memory-consuming or training an additional 3D network. We do so by encoding better the target camera pose via a new per-pixel ray conditioning normalization (RCN) layer. The latter injects pose information in the underlying 2D image generator by telling each pixel its specific viewing direction. We also improve multi-view consistency via a light-weight multi-view attention layer and multi-view noise sharing. We train Free3D on the Objaverse dataset and demonstrate excellent generalization to various new categories in several new datasets, including OminiObject3D and GSO. We hope our simple and effective approach will serve as a solid baseline and help future research in NVS with more accuracy pose. The project page is available at https://chuanxiaz.com/free3d/.

The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for planar images. Here we give a general description of E(2)-equivariant convolutions in the framework of Steerable CNNs. The theory of Steerable CNNs thereby yields constraints on the convolution kernels which depend on group representations describing the transformation laws of feature spaces. We show that these constraints for arbitrary group representations can be reduced to constraints under irreducible representations. A general solution of the kernel space constraint is given for arbitrary representations of the Euclidean group E(2) and its subgroups. We implement a wide range of previously proposed and entirely new equivariant network architectures and extensively compare their performances. E(2)-steerable convolutions are further shown to yield remarkable gains on CIFAR-10, CIFAR-100 and STL-10 when used as a drop-in replacement for non-equivariant convolutions.

Category-level 3D pose estimation is a fundamentally important problem in computer vision and robotics, e.g. for embodied agents or to train 3D generative models. However, so far methods that estimate the category-level object pose require either large amounts of human annotations, CAD models or input from RGB-D sensors. In contrast, we tackle the problem of learning to estimate the category-level 3D pose only from casually taken object-centric videos without human supervision. We propose a two-step pipeline: First, we introduce a multi-view alignment procedure that determines canonical camera poses across videos with a novel and robust cyclic distance formulation for geometric and appearance matching using reconstructed coarse meshes and DINOv2 features. In a second step, the canonical poses and reconstructed meshes enable us to train a model for 3D pose estimation from a single image. In particular, our model learns to estimate dense correspondences between images and a prototypical 3D template by predicting, for each pixel in a 2D image, a feature vector of the corresponding vertex in the template mesh. We demonstrate that our method outperforms all baselines at the unsupervised alignment of object-centric videos by a large margin and provides faithful and robust predictions in-the-wild. Our code and data is available at https://github.com/GenIntel/uns-obj-pose3d.

Geometric camera calibration is often required for applications that understand the perspective of the image. We propose perspective fields as a representation that models the local perspective properties of an image. Perspective Fields contain per-pixel information about the camera view, parameterized as an up vector and a latitude value. This representation has a number of advantages as it makes minimal assumptions about the camera model and is invariant or equivariant to common image editing operations like cropping, warping, and rotation. It is also more interpretable and aligned with human perception. We train a neural network to predict Perspective Fields and the predicted Perspective Fields can be converted to calibration parameters easily. We demonstrate the robustness of our approach under various scenarios compared with camera calibration-based methods and show example applications in image compositing.

3D Gaussian Splatting (3DGS) has emerged as a key rendering pipeline for digital asset creation due to its balance between efficiency and visual quality. To address the issues of unstable pose estimation and scene representation distortion caused by geometric texture inconsistency in large outdoor scenes with weak or repetitive textures, we approach the problem from two aspects: pose estimation and scene representation. For pose estimation, we leverage LiDAR-IMU Odometry to provide prior poses for cameras in large-scale environments. These prior pose constraints are incorporated into COLMAP's triangulation process, with pose optimization performed via bundle adjustment. Ensuring consistency between pixel data association and prior poses helps maintain both robustness and accuracy. For scene representation, we introduce normal vector constraints and effective rank regularization to enforce consistency in the direction and shape of Gaussian primitives. These constraints are jointly optimized with the existing photometric loss to enhance the map quality. We evaluate our approach using both public and self-collected datasets. In terms of pose optimization, our method requires only one-third of the time while maintaining accuracy and robustness across both datasets. In terms of scene representation, the results show that our method significantly outperforms conventional 3DGS pipelines. Notably, on self-collected datasets characterized by weak or repetitive textures, our approach demonstrates enhanced visualization capabilities and achieves superior overall performance. Codes and data will be publicly available at https://github.com/justinyeah/normal_shape.git.

In this work we integrate ideas from surface-based modeling with neural synthesis: we propose a combination of surface-based pose estimation and deep generative models that allows us to perform accurate pose transfer, i.e. synthesize a new image of a person based on a single image of that person and the image of a pose donor. We use a dense pose estimation system that maps pixels from both images to a common surface-based coordinate system, allowing the two images to be brought in correspondence with each other. We inpaint and refine the source image intensities in the surface coordinate system, prior to warping them onto the target pose. These predictions are fused with those of a convolutional predictive module through a neural synthesis module allowing for training the whole pipeline jointly end-to-end, optimizing a combination of adversarial and perceptual losses. We show that dense pose estimation is a substantially more powerful conditioning input than landmark-, or mask-based alternatives, and report systematic improvements over state of the art generators on DeepFashion and MVC datasets.

Accurate monocular metric depth estimation (MMDE) is crucial to solving downstream tasks in 3D perception and modeling. However, the remarkable accuracy of recent MMDE methods is confined to their training domains. These methods fail to generalize to unseen domains even in the presence of moderate domain gaps, which hinders their practical applicability. We propose a new model, UniDepthV2, capable of reconstructing metric 3D scenes from solely single images across domains. Departing from the existing MMDE paradigm, UniDepthV2 directly predicts metric 3D points from the input image at inference time without any additional information, striving for a universal and flexible MMDE solution. In particular, UniDepthV2 implements a self-promptable camera module predicting a dense camera representation to condition depth features. Our model exploits a pseudo-spherical output representation, which disentangles the camera and depth representations. In addition, we propose a geometric invariance loss that promotes the invariance of camera-prompted depth features. UniDepthV2 improves its predecessor UniDepth model via a new edge-guided loss which enhances the localization and sharpness of edges in the metric depth outputs, a revisited, simplified and more efficient architectural design, and an additional uncertainty-level output which enables downstream tasks requiring confidence. Thorough evaluations on ten depth datasets in a zero-shot regime consistently demonstrate the superior performance and generalization of UniDepthV2. Code and models are available at https://github.com/lpiccinelli-eth/UniDepth

In this paper, we introduce an SE(3) diffusion model-based point cloud registration framework for 6D object pose estimation in real-world scenarios. Our approach formulates the 3D registration task as a denoising diffusion process, which progressively refines the pose of the source point cloud to obtain a precise alignment with the model point cloud. Training our framework involves two operations: An SE(3) diffusion process and an SE(3) reverse process. The SE(3) diffusion process gradually perturbs the optimal rigid transformation of a pair of point clouds by continuously injecting noise (perturbation transformation). By contrast, the SE(3) reverse process focuses on learning a denoising network that refines the noisy transformation step-by-step, bringing it closer to the optimal transformation for accurate pose estimation. Unlike standard diffusion models used in linear Euclidean spaces, our diffusion model operates on the SE(3) manifold. This requires exploiting the linear Lie algebra se(3) associated with SE(3) to constrain the transformation transitions during the diffusion and reverse processes. Additionally, to effectively train our denoising network, we derive a registration-specific variational lower bound as the optimization objective for model learning. Furthermore, we show that our denoising network can be constructed with a surrogate registration model, making our approach applicable to different deep registration networks. Extensive experiments demonstrate that our diffusion registration framework presents outstanding pose estimation performance on the real-world TUD-L, LINEMOD, and Occluded-LINEMOD datasets.

Feed-forward multi-frame 3D reconstruction models often degrade on videos with object motion. Global-reference becomes ambiguous under multiple motions, while the local pointmap relies heavily on estimated relative poses and can drift, causing cross-frame misalignment and duplicated structures. We propose TrajVG, a reconstruction framework that makes cross-frame 3D correspondence an explicit prediction by estimating camera-coordinate 3D trajectories. We couple sparse trajectories, per-frame local point maps, and relative camera poses with geometric consistency objectives: (i) bidirectional trajectory-pointmap consistency with controlled gradient flow, and (ii) a pose consistency objective driven by static track anchors that suppresses gradients from dynamic regions. To scale training to in-the-wild videos where 3D trajectory labels are scarce, we reformulate the same coupling constraints into self-supervised objectives using only pseudo 2D tracks, enabling unified training with mixed supervision. Extensive experiments across 3D tracking, pose estimation, pointmap reconstruction, and video depth show that TrajVG surpasses the current feedforward performance baseline.

Learning visual representations with self-supervised learning has become popular in computer vision. The idea is to design auxiliary tasks where labels are free to obtain. Most of these tasks end up providing data to learn specific kinds of invariance useful for recognition. In this paper, we propose to exploit different self-supervised approaches to learn representations invariant to (i) inter-instance variations (two objects in the same class should have similar features) and (ii) intra-instance variations (viewpoint, pose, deformations, illumination, etc). Instead of combining two approaches with multi-task learning, we argue to organize and reason the data with multiple variations. Specifically, we propose to generate a graph with millions of objects mined from hundreds of thousands of videos. The objects are connected by two types of edges which correspond to two types of invariance: "different instances but a similar viewpoint and category" and "different viewpoints of the same instance". By applying simple transitivity on the graph with these edges, we can obtain pairs of images exhibiting richer visual invariance. We use this data to train a Triplet-Siamese network with VGG16 as the base architecture and apply the learned representations to different recognition tasks. For object detection, we achieve 63.2% mAP on PASCAL VOC 2007 using Fast R-CNN (compare to 67.3% with ImageNet pre-training). For the challenging COCO dataset, our method is surprisingly close (23.5%) to the ImageNet-supervised counterpart (24.4%) using the Faster R-CNN framework. We also show that our network can perform significantly better than the ImageNet network in the surface normal estimation task.

We propose FoundPose, a model-based method for 6D pose estimation of unseen objects from a single RGB image. The method can quickly onboard new objects using their 3D models without requiring any object- or task-specific training. In contrast, existing methods typically pre-train on large-scale, task-specific datasets in order to generalize to new objects and to bridge the image-to-model domain gap. We demonstrate that such generalization capabilities can be observed in a recent vision foundation model trained in a self-supervised manner. Specifically, our method estimates the object pose from image-to-model 2D-3D correspondences, which are established by matching patch descriptors from the recent DINOv2 model between the image and pre-rendered object templates. We find that reliable correspondences can be established by kNN matching of patch descriptors from an intermediate DINOv2 layer. Such descriptors carry stronger positional information than descriptors from the last layer, and we show their importance when semantic information is ambiguous due to object symmetries or a lack of texture. To avoid establishing correspondences against all object templates, we develop an efficient template retrieval approach that integrates the patch descriptors into the bag-of-words representation and can promptly propose a handful of similarly looking templates. Additionally, we apply featuremetric alignment to compensate for discrepancies in the 2D-3D correspondences caused by coarse patch sampling. The resulting method noticeably outperforms existing RGB methods for refinement-free pose estimation on the standard BOP benchmark with seven diverse datasets and can be seamlessly combined with an existing render-and-compare refinement method to achieve RGB-only state-of-the-art results. Project page: evinpinar.github.io/foundpose.

Recent advancements in Gaussian-based human body reconstruction have achieved notable success in creating animatable avatars. However, there are ongoing challenges to fully exploit the SMPL model's prior knowledge and enhance the visual fidelity of these models to achieve more refined avatar reconstructions. In this paper, we introduce AniGaussian which addresses the above issues with two insights. First, we propose an innovative pose guided deformation strategy that effectively constrains the dynamic Gaussian avatar with SMPL pose guidance, ensuring that the reconstructed model not only captures the detailed surface nuances but also maintains anatomical correctness across a wide range of motions. Second, we tackle the expressiveness limitations of Gaussian models in representing dynamic human bodies. We incorporate rigid-based priors from previous works to enhance the dynamic transform capabilities of the Gaussian model. Furthermore, we introduce a split-with-scale strategy that significantly improves geometry quality. The ablative study experiment demonstrates the effectiveness of our innovative model design. Through extensive comparisons with existing methods, AniGaussian demonstrates superior performance in both qualitative result and quantitative metrics.

6D object pose estimation remains challenging for many applications due to dependencies on complete 3D models, multi-view images, or training limited to specific object categories. These requirements make generalization to novel objects difficult for which neither 3D models nor multi-view images may be available. To address this, we propose a novel method One2Any that estimates the relative 6-degrees of freedom (DOF) object pose using only a single reference-single query RGB-D image, without prior knowledge of its 3D model, multi-view data, or category constraints. We treat object pose estimation as an encoding-decoding process, first, we obtain a comprehensive Reference Object Pose Embedding (ROPE) that encodes an object shape, orientation, and texture from a single reference view. Using this embedding, a U-Net-based pose decoding module produces Reference Object Coordinate (ROC) for new views, enabling fast and accurate pose estimation. This simple encoding-decoding framework allows our model to be trained on any pair-wise pose data, enabling large-scale training and demonstrating great scalability. Experiments on multiple benchmark datasets demonstrate that our model generalizes well to novel objects, achieving state-of-the-art accuracy and robustness even rivaling methods that require multi-view or CAD inputs, at a fraction of compute.

Recent works on pose-based gait recognition have demonstrated the potential of using such simple information to achieve results comparable to silhouette-based methods. However, the generalization ability of pose-based methods on different datasets is undesirably inferior to that of silhouette-based ones, which has received little attention but hinders the application of these methods in real-world scenarios. To improve the generalization ability of pose-based methods across datasets, we propose a Generalized Pose-based Gait recognition (GPGait) framework. First, a Human-Oriented Transformation (HOT) and a series of Human-Oriented Descriptors (HOD) are proposed to obtain a unified pose representation with discriminative multi-features. Then, given the slight variations in the unified representation after HOT and HOD, it becomes crucial for the network to extract local-global relationships between the keypoints. To this end, a Part-Aware Graph Convolutional Network (PAGCN) is proposed to enable efficient graph partition and local-global spatial feature extraction. Experiments on four public gait recognition datasets, CASIA-B, OUMVLP-Pose, Gait3D and GREW, show that our model demonstrates better and more stable cross-domain capabilities compared to existing skeleton-based methods, achieving comparable recognition results to silhouette-based ones. Code is available at https://github.com/BNU-IVC/FastPoseGait.

Camera pose estimation is a long-standing computer vision problem that to date often relies on classical methods, such as handcrafted keypoint matching, RANSAC and bundle adjustment. In this paper, we propose to formulate the Structure from Motion (SfM) problem inside a probabilistic diffusion framework, modelling the conditional distribution of camera poses given input images. This novel view of an old problem has several advantages. (i) The nature of the diffusion framework mirrors the iterative procedure of bundle adjustment. (ii) The formulation allows a seamless integration of geometric constraints from epipolar geometry. (iii) It excels in typically difficult scenarios such as sparse views with wide baselines. (iv) The method can predict intrinsics and extrinsics for an arbitrary amount of images. We demonstrate that our method PoseDiffusion significantly improves over the classic SfM pipelines and the learned approaches on two real-world datasets. Finally, it is observed that our method can generalize across datasets without further training. Project page: https://posediffusion.github.io/

We present a real-time approach for multi-person 3D motion capture at over 30 fps using a single RGB camera. It operates successfully in generic scenes which may contain occlusions by objects and by other people. Our method operates in subsequent stages. The first stage is a convolutional neural network (CNN) that estimates 2D and 3D pose features along with identity assignments for all visible joints of all individuals.We contribute a new architecture for this CNN, called SelecSLS Net, that uses novel selective long and short range skip connections to improve the information flow allowing for a drastically faster network without compromising accuracy. In the second stage, a fully connected neural network turns the possibly partial (on account of occlusion) 2Dpose and 3Dpose features for each subject into a complete 3Dpose estimate per individual. The third stage applies space-time skeletal model fitting to the predicted 2D and 3D pose per subject to further reconcile the 2D and 3D pose, and enforce temporal coherence. Our method returns the full skeletal pose in joint angles for each subject. This is a further key distinction from previous work that do not produce joint angle results of a coherent skeleton in real time for multi-person scenes. The proposed system runs on consumer hardware at a previously unseen speed of more than 30 fps given 512x320 images as input while achieving state-of-the-art accuracy, which we will demonstrate on a range of challenging real-world scenes.

Foundation video generation models such as WAN 2.2 exhibit strong text- and image-conditioned synthesis abilities but remain constrained to the same-view generation setting. In this work, we introduce Exo2EgoSyn, an adaptation of WAN 2.2 that unlocks Exocentric-to-Egocentric(Exo2Ego) cross-view video synthesis. Our framework consists of three key modules. Ego-Exo View Alignment(EgoExo-Align) enforces latent-space alignment between exocentric and egocentric first-frame representations, reorienting the generative space from the given exo view toward the ego view. Multi-view Exocentric Video Conditioning (MultiExoCon) aggregates multi-view exocentric videos into a unified conditioning signal, extending WAN2.2 beyond its vanilla single-image or text conditioning. Furthermore, Pose-Aware Latent Injection (PoseInj) injects relative exo-to-ego camera pose information into the latent state, guiding geometry-aware synthesis across viewpoints. Together, these modules enable high-fidelity ego view video generation from third-person observations without retraining from scratch. Experiments on ExoEgo4D validate that Exo2EgoSyn significantly improves Ego2Exo synthesis, paving the way for scalable cross-view video generation with foundation models. Source code and models will be released publicly.

6D object pose estimation, which predicts the transformation of an object relative to the camera, remains challenging for unseen objects. Existing approaches typically rely on explicitly constructing feature correspondences between the query image and either the object model or template images. In this work, we propose PoseGAM, a geometry-aware multi-view framework that directly predicts object pose from a query image and multiple template images, eliminating the need for explicit matching. Built upon recent multi-view-based foundation model architectures, the method integrates object geometry information through two complementary mechanisms: explicit point-based geometry and learned features from geometry representation networks. In addition, we construct a large-scale synthetic dataset containing more than 190k objects under diverse environmental conditions to enhance robustness and generalization. Extensive evaluations across multiple benchmarks demonstrate our state-of-the-art performance, yielding an average AR improvement of 5.1% over prior methods and achieving up to 17.6% gains on individual datasets, indicating strong generalization to unseen objects. Project page: https://windvchen.github.io/PoseGAM/ .

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Scale variation is a fundamental challenge in computer vision. Objects of the same class can have different sizes, and their perceived size is further affected by the distance from the camera. These variations are local to the objects, i.e., different object sizes may change differently within the same image. To effectively handle scale variations, we present a deep equilibrium canonicalizer (DEC) to improve the local scale equivariance of a model. DEC can be easily incorporated into existing network architectures and can be adapted to a pre-trained model. Notably, we show that on the competitive ImageNet benchmark, DEC improves both model performance and local scale consistency across four popular pre-trained deep-nets, e.g., ViT, DeiT, Swin, and BEiT. Our code is available at https://github.com/ashiq24/local-scale-equivariance.

Monocular object pose estimation, as a pivotal task in computer vision and robotics, heavily depends on accurate 2D-3D correspondences, which often demand costly CAD models that may not be readily available. Object 3D reconstruction methods offer an alternative, among which recent advancements in 3D Gaussian Splatting (3DGS) afford a compelling potential. Yet its performance still suffers and tends to overfit with fewer input views. Embracing this challenge, we introduce SGPose, a novel framework for sparse view object pose estimation using Gaussian-based methods. Given as few as ten views, SGPose generates a geometric-aware representation by starting with a random cuboid initialization, eschewing reliance on Structure-from-Motion (SfM) pipeline-derived geometry as required by traditional 3DGS methods. SGPose removes the dependence on CAD models by regressing dense 2D-3D correspondences between images and the reconstructed model from sparse input and random initialization, while the geometric-consistent depth supervision and online synthetic view warping are key to the success. Experiments on typical benchmarks, especially on the Occlusion LM-O dataset, demonstrate that SGPose outperforms existing methods even under sparse view constraints, under-scoring its potential in real-world applications.

We introduce UPose3D, a novel approach for multi-view 3D human pose estimation, addressing challenges in accuracy and scalability. Our method advances existing pose estimation frameworks by improving robustness and flexibility without requiring direct 3D annotations. At the core of our method, a pose compiler module refines predictions from a 2D keypoints estimator that operates on a single image by leveraging temporal and cross-view information. Our novel cross-view fusion strategy is scalable to any number of cameras, while our synthetic data generation strategy ensures generalization across diverse actors, scenes, and viewpoints. Finally, UPose3D leverages the prediction uncertainty of both the 2D keypoint estimator and the pose compiler module. This provides robustness to outliers and noisy data, resulting in state-of-the-art performance in out-of-distribution settings. In addition, for in-distribution settings, UPose3D yields performance rivalling methods that rely on 3D annotated data while being the state-of-the-art among methods relying only on 2D supervision.