2026-05-29原文

Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments

This paper audits evaluation protocols for training-free shape descriptors by introducing Diffused Geodesic Moments (DGM). Experiments show that Geometric Moment Shape Descriptor based on Heat Kernel Signature (GMSD-HKS) achieves the highest scores on FAUST-Reg and TOSCA, while Wave Kernel Signature (WKS) remains strong. DGM is valuable for sparse or non-spectral applications. The work provides a reproducible protocol-cascade analysis, cross-shape alignment diagnostic, and recommendations for designing and reporting training-free descriptors.

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Key points

Introduces Diffused Geodesic Moments (DGM) as a training-free descriptor for protocol audit
GMSD-HKS outperforms other methods on FAUST-Reg and TOSCA; WKS remains competitive
Offers protocol-cascade analysis, cross-shape alignment diagnostic, and best practices
Highlights the dominant role of input field and aggregation protocol over moment formula

Why it matters

This matters because introduces Diffused Geodesic Moments (DGM) as a training-free descriptor for protocol audit.

Technical impact

May affect research directions, evaluation methods, open-source reproduction, and productization paths.

[2605.29004] Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments

[Submitted on 27 May 2026]

Title:Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments

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Abstract: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.

Subjects:

Computer Vision and Pattern Recognition (cs.CV); Graphics (cs.GR)

Cite as: arXiv:2605.29004 [cs.CV]

(or arXiv:2605.29004v1 [cs.CV] for this version)

https://doi.org/10.48550/arXiv.2605.29004

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Zhicheng Du [view email] [v1] Wed, 27 May 2026 19:00:41 UTC (2,676 KB)

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