Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments
Quick Take
The paper introduces Diffused Geodesic Moments (DGM) for training-free 3D shape retrieval, achieving high scores on FAUST-Reg and TOSCA benchmarks. It emphasizes the importance of input fields and aggregation protocols in descriptor evaluation, with GMSD-HKS achieving top mean average precision scores of 0.621/0.820 and 0.865/0.963 respectively.
Key Points
- DGM computes sparse implicit heat responses for shape descriptor evaluation.
- GMSD-HKS outperforms with mean average precision scores of 0.621/0.820 and 0.865/0.963.
- Wave Kernel Signature remains a strong classical signal in shape retrieval.
- The paper offers a reproducible protocol-cascade analysis for descriptor design.
- Input field and aggregation protocol can significantly influence moment formula outcomes.
Article Content
From source RSS / original summaryarXiv:2605. 29004v1 Announce Type: new 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.
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