ABSTRACT Establishing correspondences between 3D shapes under challenging conditions, such as mixed pose and non‐isometric deformations, is critical for applications like shape registration in computer vision and graphics. Existing methods, including geodesic‐based, orientation‐preserving, and deep learning approaches, often falter in handling intrinsic symmetries and significant deformations, as evidenced in benchmarks like SHREC’20 and TOSCA. We introduce TransLAP, a transformer‐based linear assignment solver that directly operates on hybrid geometric features (geodesic distances + Dirichlet‐to‐Neumann eigenfunctions) to produce bijective mappings in a CPU‐efficient manner. TransLAP estimates soft assignment matrices using stacked self‐ and cross‐attention layers with assurance‐based early stopping, followed by Jonker–Volgenant optimisation and the Voting‐Based Consensus Algorithm (VBCA) refinement. Evaluated on TOSCA, SHREC’20, SMAL, and DT4D datasets, our method achieves average geodesic errors of 0.0932, 0.1094, 0.0614, and 0.0663, respectively — outperforming state‐of‐the‐art approaches (e.g., SSL, ConsistFMaps, DGFM, FM‐Net and Diffusion‐Net) by up to 60%. Qualitative results demonstrate effective matching for non‐isometric pairs (e.g., human‐gorilla, pig‐dog). Ablation studies confirm the role of each component in our proposed method, with TransLAP contributing approximately 50% and the Mapping Modifier contributing over 20%. Our method runs on a CPU with less than 3 GB of memory, making it practical for low‐resource settings.
Amirfathiyan et al. (Thu,) studied this question.