Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916056571838464 |
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| author | Du, Zhicheng Liu, Changyue Xi, Wenji Xie, Zhaotian Deng, Zhuo Zhang, Ziheng Liu, Yang Ma, Lan |
| author_facet | Du, Zhicheng Liu, Changyue Xi, Wenji Xie, Zhaotian Deng, Zhuo Zhang, Ziheng Liu, Yang Ma, Lan |
| contents | Reported retrieval scores for training-free shape descriptors conflate local signal design, normalization, aggregation, codebook fitting, and metric choices, making isolated component evaluation difficult. This paper reframes descriptor evaluation as a {\em protocol audit}. We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses, converts them to distance-like fields, and summarizes each vertex by low-order moments across seeds and scales. DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects. On the registered FAUST benchmark split (FAUST-Reg) and the TOSCA shape collection, aggregation-matched experiments show that an independent Geometric Moment Shape Descriptor baseline built on Heat Kernel Signature features (GMSD-HKS) obtains the highest scores in this implementation ($0.621/0.820$ and $0.865/0.963$ mean average precision (mAP)/top-1), Wave Kernel Signature (WKS) remains a strong classical signal, and DGM is useful mainly when sparse solves, non-spectral deployment, or symmetry-informative seed frames are priorities. The broader finding is methodological: the input field and aggregation protocol can dominate the moment formula. The paper contributes a reproducible protocol-cascade analysis, a cross-shape alignment diagnostic for functional-map compatibility, and concrete recommendations for designing and reporting training-free shape descriptors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments Du, Zhicheng Liu, Changyue Xi, Wenji Xie, Zhaotian Deng, Zhuo Zhang, Ziheng Liu, Yang Ma, Lan Computer Vision and Pattern Recognition Graphics Reported retrieval scores for training-free shape descriptors conflate local signal design, normalization, aggregation, codebook fitting, and metric choices, making isolated component evaluation difficult. This paper reframes descriptor evaluation as a {\em protocol audit}. We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses, converts them to distance-like fields, and summarizes each vertex by low-order moments across seeds and scales. DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects. On the registered FAUST benchmark split (FAUST-Reg) and the TOSCA shape collection, aggregation-matched experiments show that an independent Geometric Moment Shape Descriptor baseline built on Heat Kernel Signature features (GMSD-HKS) obtains the highest scores in this implementation ($0.621/0.820$ and $0.865/0.963$ mean average precision (mAP)/top-1), Wave Kernel Signature (WKS) remains a strong classical signal, and DGM is useful mainly when sparse solves, non-spectral deployment, or symmetry-informative seed frames are priorities. The broader finding is methodological: the input field and aggregation protocol can dominate the moment formula. The paper contributes a reproducible protocol-cascade analysis, a cross-shape alignment diagnostic for functional-map compatibility, and concrete recommendations for designing and reporting training-free shape descriptors. |
| title | Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments |
| topic | Computer Vision and Pattern Recognition Graphics |
| url | https://arxiv.org/abs/2605.29004 |