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Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation
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Proposes SAUCD, an analytic 3D mesh metric that compares Laplace-Beltrami spectra via AUC difference (plus a learned per-band weighting), validated against a new 868-subject human study dataset, Shape Grading.
Problem
Existing 3D mesh shape metrics (Chamfer distance, IoU, F-score, UHD, learned SSFID) are insensitive to local details and do not align well with human perception of mesh quality.
Approach
Transform meshes to the spectrum domain using a revised, positive semidefinite discrete Laplace-Beltrami operator and Fourier transform, normalize spectrum AUC to 1, and measure the area between spectra so that all frequency bands count; the extension learns a 20-dimensional frequency-band weight from human scores.
Key results
- SAUCD achieves overall PLCC 0.567, SROCC 0.598, KROCC 0.445 on Shape Grading, versus 0.363 PLCC for the best prior baseline (SSFID).
- The human-adjusted SAUCD raises overall PLCC to 0.598, SROCC to 0.611, and KROCC to 0.453.
- Using only the frequency band [0, 0.001) gives PLCC 0.434, showing low-frequency bands carry much human-aligned signal; the full metric is best.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SAUCD instead of SSFID | 3D mesh evaluation · Shape Grading | PLCC: 0.363 -> 0.567 | Helped |
| learn frequency-band weights for SAUCD | SAUCD · Shape Grading | PLCC: 0.567 -> 0.598 | Helped |
| use the revised DLBO instead of Topology Laplacian (ablation) | SAUCD · Shape Grading | PLCC: 0.298 -> 0.567 | Helped |
| use the revised DLBO instead of the original Cotan formula (ablation) | SAUCD · Shape Grading | PLCC: 0.417 -> 0.567 | Helped |
| use amplitude difference instead of energy difference (ablation) | SAUCD · Shape Grading | PLCC: 0.268 -> 0.567 | Helped |
| add AUC normalization (ablation) | SAUCD · Shape Grading | PLCC: 0.257 -> 0.567 | Helped |
| use AUC normalization instead of spatial normalization (ablation) | SAUCD · Shape Grading | PLCC: 0.269 -> 0.567 | Helped |
| change noise-pruning portion from 0.1% to 0% (ablation) | SAUCD · Shape Grading | PLCC: 0.567 -> 0.513 | Hurt |
| change noise-pruning portion from 0.1% to 1% (ablation) | SAUCD · Shape Grading | PLCC: 0.567 -> 0.554 | No clear effect |
| change noise-pruning portion from 0.1% to 10% (ablation) | SAUCD · Shape Grading | PLCC: 0.567 -> 0.517 | Hurt |
| change noise-pruning portion from 0.1% to 20% (ablation) | SAUCD · Shape Grading | PLCC: 0.567 -> 0.503 | Hurt |
| use only frequency band [0, 0.001) instead of all frequencies (ablation) | SAUCD · Shape Grading | PLCC: 0.567 -> 0.434 | Hurt |
Surprising findings
- Chamfer Distance, which ranks Mesh B (smoothed, missing wrinkles) better than Mesh A (small pose error), contradicts human judgment.
- Using energy difference instead of amplitude difference lowers consistency with human scores (PLCC 0.268 vs 0.567).
Limitations
- Weighted version learned from only 12 ground-truth objects, so generalization is limited by dataset size.
- Correlations are moderate (best PLCC about 0.6), and the method underperforms on some objects, such as object 12 (SAUCD SROCC 0.24).
Experimental setup
Datasets: Shape Grading
Benchmarks: Shape Grading
Metrics: PLCC SROCC KROCC
Baselines: Chamfer Distance Point-to-Surface Normal Difference IoU F-score SSFID UHD
Builds on: Chamfer Distance Cotan formula SSFID
Closest papers by meaning
- Multistable Shape from Shading Emerges from Patch Diffusion (NeurIPS 2024 · similarity 0.80)
- Evaluate Geometry of Radiance Fields with Low-Frequency Color Prior (AAAI 2024 · similarity 0.80)
- Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · similarity 0.80)
- HybridMQA: Exploring Geometry-Texture Interactions for Colored Mesh Quality Assessment (CVPR 2025 · similarity 0.80)
- Joint2Human: High-Quality 3D Human Generation via Compact Spherical Embedding of 3D Joints (CVPR 2024 · similarity 0.79)
- Coupled Laplacian Eigenmaps for Locally-Aware 3D Rigid Point Cloud Matching (CVPR 2024 · similarity 0.79)
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