Geometry-Grounded Articulation and Test-Time Adaptation for Zero-Shot, Scalable Shape Matching in the Wild

Dense correspondence on in-the-wild 3D scans must handle severe non-isometric deformation, partial observations, topology artifacts, irregular discretization, and extreme resolution. Together, these conditions make shape matching both a robustness and scalability problem. Existing methods typically handle only part of this regime and often require expensive spectral or dense feature processing, repeated pairwise optimization, or dataset-specific training. To address the above issues, we present GAMMA, a zero-shot framework based on Geometry-Grounded Articulation. For each scan, GAMMA renders multiple views and uses a pretrained estimator with a category-specific parametric model to produce one template estimate per view. Because these estimates share a fixed vertex ordering, confidence-weighted consensus fuses them into one canonical template and establishes sparse matches across scans. We refine these matches on the input geometry to recover accurate dense correspondences. All core matching steps run at inference time and require neither target-dataset correspondence training nor costly Laplace--Beltrami operator (LBO) computation on the input scans. Each fused template is cached, so additional pair queries reuse the canonicalization. GAMMA obtains average geodesic errors of 2.9 on TOPKIDS and 2.4 on remeshed SMAL, reducing error relative to URSSM by 67% and 60%, respectively. Complementary evaluations report lower aggregate errors than the evaluated baselines on BeCoS-processed partial subsets and demonstrate stable matching accuracy from decimated FAUST meshes to raw scans with 160k--200k vertices. These results demonstrate accurate correspondence across complementary settings and collection-level scalability after per-shape caching.