Frequency-Scale Saliency for Spectral Descriptor Analysis in 3D Shape Retrieval

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.

Large pretrained vision models have substantially improved appearance-based 3D shape retrieval, but they still confuse shapes that look similar while differing in geometry. Although geometry-aware features can reduce these errors, naive fusion of geometry and appearance may hurt retrieval when the two modalities are already well aligned. We propose GATE-3D, a lightweight query-adaptive reranking method that incorporates geometry without retraining the retrieval backbone. For each query, GATE-3D predicts how much a geometry-aware score should adjust the appearance-based ranking using features that capture disagreement between the two modalities. This selective design lets geometry contribute where it helps and stay silent where it would hurt. Experiments on three open-set 3D retrieval benchmarks show that GATE-3D improves over appearance-only retrieval and is more robust than always-on fusion. On the primary benchmark, it improves mAP@10 by 2.00 points over appearance-only retrieval (p=0.041); it also improves leave-one-category-out generalization and reduces geometric false positives by 10.8%. GATE-3D achieves competitive zero-shot results against DAC-based baselines. We further find that simple linear routing is more effective than a small MLP in the low-data regime, suggesting that cross-modal disagreement features matter more than model capacity for adaptive routing.

Sketch-based 3D shape retrieval (SBSR) aims to retrieve 3D shapes that are consistent with the category of the input hand-drawn sketch. The core challenge of this task lies in two aspects: existing methods typically employ simplified aggregation strategies for independently encoded 3D multi-view features, which ignore the geometric relationships between views and multi-level details, resulting in weak 3D representation. Simultaneously, traditional SBSR methods are constrained by visible category limitations, leading to poor performance in zero-shot scenarios. To address these challenges, we propose Multi-View Hierarchical Graph Neural Network (MV-HGNN), a novel framework for SBSR. Specifically, we construct a view-level graph and capture adjacent geometric dependencies and cross-view message passing via local graph convolution and global attention. A view selector is further introduced to perform hierarchical graph coarsening, enabling a progressively larger receptive field for graph convolution and mitigating the interference of redundant views, which leads to more discriminate discriminative hierarchical 3D representation. To enable category agnostic alignment and mitigate overfitting to seen classes, we leverage CLIP text embeddings as semantic prototypes and project both sketch and 3D features into a shared semantic space. We use a two-stage training strategy for category-level retrieval and a one-stage strategy for zero-shot retrieval under the same model architecture. Under both category-level and zero-shot settings, extensive experiments on two public benchmarks demonstrate that MV-HGNN outperforms state-of-the-art methods.