---
license: apache-2.0
language:
- en
pretty_name: RESIDUALS — LiDAR DEM residual fingerprints
tags:
- lidar
- dem
- digital-elevation-model
- signal-processing
- wavelet
- morphological-filtering
- remote-sensing
- archaeology
- algorithm-fingerprinting
- umap
size_categories:
- 10K<n<100K
task_categories:
- image-classification
- feature-extraction
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*.parquet
dataset_info:
  features:
  - name: filename
    dtype: string
  - name: decomp_family
    dtype: string
  - name: decomp_params
    dtype: string
  - name: upsamp_method
    dtype: string
  - name: upsamp_params
    dtype: string
  - name: scale
    dtype: int32
  - name: category
    dtype: string
  - name: signature
    sequence: float32
    length: 40
  - name: umap_2d
    sequence: float32
    length: 2
  - name: umap_3d
    sequence: float32
    length: 3
  - name: image
    dtype: image
  splits:
  - name: train
    num_examples: 39716
---

# RESIDUALS — LiDAR DEM residual fingerprints

39,716 residual images extracted by applying **593 distinct decomposition configurations × 25 upsampling methods** to a single Fairfield County, Ohio LiDAR-derived Digital Elevation Model (1500×375 at 3.33 ft/px). Each row pairs a 256×256 PNG of the residual (rendered with the standard `RdBu_r` colormap, 99th-percentile symmetric clipping) with the algorithm and parameters that produced it, plus a 40-dim signature vector and pre-computed 2D/3D UMAP coordinates.

The companion source-code project is [RESIDUALS](https://github.com/bshepp/RESIDUALS); the rendered atlas / sweep videos / Blender flythrough that visualize this dataset are produced by the [residuals-visuals](https://github.com/bshepp/residuals-visuals) project.

## Why this dataset is interesting

- **Algorithm classification benchmark**: predict which decomposition algorithm produced a residual (24 family classes, or 593 fine-grained classes). A non-trivial visual task — many algorithm families produce visually similar outputs at certain parameter settings.
- **Algorithm fingerprinting / signal-processing forensics**: the included 40-dim signatures (radial-FFT power spectrum + statistical moments) cluster algorithm families clearly in UMAP space — useful as a reference for inverse-problem and provenance work.
- **Same scene, all algorithms**: every residual is a different mathematical lens on the *same* underlying terrain, making this an unusually clean substrate for studying what each algorithm preserves vs. destroys.
- **Reproducible**: source DEM hashes + RESIDUALS source code = full regeneration of the original 4.28 TB float64 outputs.

## Schema

| Column | Type | Description |
|---|---|---|
| `filename` | string | Original `.npy` filename in the source RESIDUALS exhaustive run |
| `decomp_family` | string | e.g. `gaussian`, `wavelet_biorthogonal`, `morphological_rect`, `anisotropic_diffusion` |
| `decomp_params` | string (JSON) | e.g. `{"sigma": 10}` or `{"wavelet": "bior3.5", "level": 3}` |
| `upsamp_method` | string | e.g. `bicubic`, `lanczos`, `fft_zeropad`, `sinc_hamming` |
| `upsamp_params` | string (JSON) | e.g. `{"scale": 2, "kernel_size": 8}` |
| `scale` | int32 | Upsampling factor: 2, 3, 4, 8, or 16 |
| `category` | string | Meta-category: `classical`, `edge_preserving`, `wavelet`, `morphological`, `trend_removal`, `multiscale` |
| `signature` | list<float32>[40] | 32-bin radial-FFT log-power spectrum + 8 statistical moments (mean, std, skew, kurtosis, p50\|abs\|, p99\|abs\|, edge density, lag-1 autocorrelation) |
| `umap_2d` | list<float32>[2] | 2D UMAP embedding of the signature |
| `umap_3d` | list<float32>[3] | 3D UMAP embedding of the signature |
| `image` | binary (PNG) | 256×256 PNG of the residual, RdBu_r colormap, 99th-pctile symmetric clip |

## Source data

- **DEM**: 1500×375 array, 3.33 ft/px resolution, derived from LiDAR tiles `BS000600.las` through `BS000603.las` covering ~1 mi² in Fairfield County, Ohio. Z range: 808.5–1034.4 ft. CRS: Ohio State Plane South (EPSG:3735).
- **Residual crop**: 640×640 region at scale=2 coordinates `(row=1600, col=400)`, normalized to 256×256. Region was selected for high feature density (sweeping diagonal stream channel, branching drainage, V-shaped linear feature, distinct ridge/embankment patterns).
- 15 of the original 39,731 files are excluded due to division-by-zero edge cases in signature computation (all `bicubic_16x_scale=16` outputs).

## Splits

Single `train` split with 39,716 rows. The dataset is small enough that downstream users typically define their own splits (e.g. by `decomp_family` for held-out generalization, or random for IID evaluation).

## Quick start

```python
from datasets import load_dataset

ds = load_dataset("bshepp/residuals-fingerprints")
print(ds)
print(ds["train"][0]["decomp_family"], ds["train"][0]["decomp_params"])
ds["train"][0]["image"]  # PIL.Image.Image, 256x256
```

## Citation

The canonical citation is the Zenodo archive (which contains the full data + visualizations + code snapshot):

```bibtex
@dataset{sheppard_residuals_2026,
  author    = {Sheppard, Brian},
  title     = {RESIDUALS: 39,731-residual exhaustive parameter sweep of
               decomposition × upsampling methods on a Fairfield County,
               Ohio LiDAR DEM},
  year      = 2026,
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.19903273},
  url       = {https://doi.org/10.5281/zenodo.19903273}
}
```

Or this Hugging Face dataset (rendered subset for ML use):

```bibtex
@dataset{sheppard_residuals_fingerprints_2026,
  author    = {Sheppard, Brian},
  title     = {RESIDUALS — LiDAR DEM residual fingerprints (39,716 rows)},
  year      = 2026,
  publisher = {Hugging Face},
  url       = {https://huggingface.co/datasets/bshepp/residuals-fingerprints}
}
```

Project page: https://residuals.briansheppard.com · Source code: https://github.com/bshepp/residuals-visuals · Source pipeline: https://github.com/bshepp/RESIDUALS

## License

Apache 2.0 — same as the source RESIDUALS project.

## Limitations and ethics

- **Single scene**: all 39,716 samples come from the same DEM. Models trained here may not generalize to other terrains. Treat as a fingerprinting benchmark, not a generic remote-sensing pretraining set.
- **Class imbalance**: family counts range from 201 (`polynomial`) to 5,346 (`wavelet`). Use stratified splits or balanced sampling if classification accuracy matters.
- **Known artifact**: the leftmost ~30 columns of the source DEM exhibit upsampling-boundary effects. The crop window dodges this entirely.
- **No PII / sensitive content**: terrain residuals only. The source LiDAR is publicly-available Ohio state data.