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

2026-05-27

AI Summary

This work addresses the confounding factors in evaluating training-free 3D shape retrieval methods, which obscure the individual contributions of pipeline components. To disentangle these effects, the authors propose a protocol auditing framework that introduces Diffusion Geodesic Moments (DGM) as a controlled variable, enabling systematic isolation of the impacts from signal design, normalization, aggregation, and distance metrics. Innovatively reframing descriptor evaluation as a protocol cascade analysis, the study employs DGM as a non-spectral baseline and integrates sparse implicit heat responses, distance field transformations, and multi-seed, multi-scale low-order moment aggregation. Comprehensive comparisons with classical methods such as GMSD-HKS and WKS on FAUST-Reg and TOSCA benchmarks show that GMSD-HKS achieves state-of-the-art mAP and top-1 accuracy (0.621/0.820 and 0.865/0.963, respectively), underscoring the dominant influence of input field representation and aggregation protocol on retrieval performance.

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.

Problem

• 3D shape retrieval
• training-free descriptors
• evaluation protocol
• component isolation
• shape descriptor benchmarking

Innovation

• Diffused Geodesic Moments
• training-free shape retrieval
• protocol audit
• non-spectral descriptor
• shape descriptor evaluation