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

• URL: http://arxiv.org/abs/2605.29004v1
• Date: Wed, 27 May 2026 19:00:41 GMT
• Title: Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments
• Abstract summary: We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses.<n>DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects.
• Score: 17.990911601858482
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisation [39.05672576418673]
  TokenMatch is a new transformer-based unified model for estimating 3D shape correspondences.<n>Our feed-forward approach trained exclusively on BeCoS, a challenging non-isometric partial-to-partial shape-matching dataset, can generalise to matching full shapes without retraining or fine-tuning.<n>We evaluate TokenMatch on standard benchmarks for partial and full shape matching, including CP2P, PSMAL, BeCoS, FAUST, SCAPE, and SHREC'19.
  arXiv  Detail & Related papers  (2026-09-03T17:59:55Z)
• Structuring Semantic Embeddings for Principle Evaluation: A Prototype-Guided Contrastive Learning Approach [58.15427952222424]
  General-purpose text embeddings are widely deployed for such tasks, but broad semantic similarity can place semantically similar yet task-distinct examples.<n>We introduce Prototype-Guided Contrastive Learning (PGCL), a prototype-guided geometric regularization module built on top of frozen text embeddings.
  arXiv  Detail & Related papers  (2026-08-15T13:19:25Z)
• Beyond the Simplex: Balanced Prototype Geometry for Scorer-Agnostic Open-Set Recognition [2.9506547907695997]
  We give a theoretical account of simplex-ratio OSR that holds in every embedding dimension, including d C-1.<n>We show that the prototypes attain one-distance symmetry, behaving like a regular simplex, if and only if d >= C-1.<n>We further show the false-ratio rate decays exponentially in d under natural isotropy assumptions.
  arXiv  Detail & Related papers  (2026-06-01T08:28:24Z)
• Generative Stochastic Optimal Transport: Guided Harmonic Path-Integral Diffusion [0.0]
  We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Optimal Transport.<n>A low-dimensional guidance protocol shapes the trajectory ensemble while preserving analytic structure.<n>GH-PID generates geometry-aware, trust-aware trajectories that satisfy the prescribed terminal distribution.
  arXiv  Detail & Related papers  (2025-12-05T05:18:15Z)
• Knowledge Graphs as Structured Memory for Embedding Spaces: From Training Clusters to Explainable Inference [3.2945446636945963]
  Graph Memory (GM) is a structured non-parametric framework that augments embedding-based inference with a compact, relational memory over region-level prototypes.<n>By explicitly modeling reliability and relational structure, GM provides a principled bridge between local evidence and global consistency in non-parametric learning.
  arXiv  Detail & Related papers  (2025-11-18T23:02:59Z)
• Prototype-Driven Adaptation for Few-Shot Object Detection [9.557416198772673]
  Prototype-Driven Alignment (PDA) is a lightweight, plug-in metric head for DeFRCN.<n>PDA maintains support-only prototypes and applies prototype-conditioned RoI alignment to reduce mismatch.<n> Experiments on FSOD and GFSOD benchmarks show that PDA consistently improves novel-class performance with minimal impact on base classes and negligible computational overhead.
  arXiv  Detail & Related papers  (2025-10-29T09:32:42Z)
• Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches [11.450257794341052]
  We present a self-supervised learning approach for extracting geometric features from 3D surfaces.<n>Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features.
  arXiv  Detail & Related papers  (2025-03-05T21:15:14Z)
• KP-RED: Exploiting Semantic Keypoints for Joint 3D Shape Retrieval and Deformation [87.23575166061413]
  KP-RED is a unified KeyPoint-driven REtrieval and Deformation framework.<n>It takes object scans as input and jointly retrieves and deforms the most geometrically similar CAD models.
  arXiv  Detail & Related papers  (2024-03-15T08:44:56Z)
• Rethinking Few-shot 3D Point Cloud Semantic Segmentation [62.80639841429669]
  This paper revisits few-shot 3D point cloud semantic segmentation (FS-PCS) We focus on two significant issues in the state-of-the-art: foreground leakage and sparse point distribution. To address these issues, we introduce a standardized FS-PCS setting, upon which a new benchmark is built.
  arXiv  Detail & Related papers  (2024-03-01T15:14:47Z)
• Semi-DETR: Semi-Supervised Object Detection with Detection Transformers [105.45018934087076]
  We analyze the DETR-based framework on semi-supervised object detection (SSOD) We present Semi-DETR, the first transformer-based end-to-end semi-supervised object detector. Our method outperforms all state-of-the-art methods by clear margins.
  arXiv  Detail & Related papers  (2023-07-16T16:32:14Z)
• DyCo3D: Robust Instance Segmentation of 3D Point Clouds through Dynamic Convolution [136.7261709896713]
  We propose a data-driven approach that generates the appropriate convolution kernels to apply in response to the nature of the instances. The proposed method achieves promising results on both ScanetNetV2 and S3DIS. It also improves inference speed by more than 25% over the current state-of-the-art.
  arXiv  Detail & Related papers  (2020-11-26T14:56:57Z)
• Making Affine Correspondences Work in Camera Geometry Computation [62.7633180470428]
  Local features provide region-to-region rather than point-to-point correspondences. We propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. Experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times.
  arXiv  Detail & Related papers  (2020-07-20T12:07:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.