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

arXiv: https://arxiv.org/abs/2605.29004 · HTML: https://mlsanity.com/paper/2605.29004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 13 of 13)

- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithms](https://mlsanity.com/paper/2411.03511/) (2024)
- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2407.08244/) (2024)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [Learning Significant Persistent Homology Features for 3D Shape Understanding](https://mlsanity.com/paper/2602.14228/) (2026)
- [Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity](https://mlsanity.com/paper/2511.02496/) (2025)
- [LiteGE: Lightweight Geodesic Embedding for Efficient Geodesics Computation and Non-Isometric Shape Correspondence](https://mlsanity.com/paper/2512.17781/) (2025)
- [Symmetry Informative and Agnostic Feature Disentanglement for 3D Shapes](https://mlsanity.com/paper/2601.14804/) (2026)
- [From Feature Learning to Spectral Basis Learning: A Unifying and Flexible Framework for Efficient and Robust Shape Matching](https://mlsanity.com/paper/2603.23383/) (2026)
- [A Persistent Homology Design Space for 3D Point Cloud Deep Learning](https://mlsanity.com/paper/2604.04299/) (2026)

## Abstract (arXiv)

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.