Correspondence Calculation for Non-isometric 3D Shape Collection via Coupled Maps
YANG Jun1,2, XUE Youzhong1
1. School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070; 2. Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070
Abstract：To address the issues of low accuracy and poor generalization ability in existing non-isometric 3D shape collection correspondence calculation methods, a correspondence calculation method for non-isometric 3D shape collection via coupled maps is proposed. First, DiffusionNet is employed to directly extract initial features from the 3D shape, and thus discriminative feature descriptors are obtained. Then, functional maps matrix and point-to-point maps matrix are computed using these descriptors. Structural regularization constraints and softmax normalization are applied to both matrices, respectively, to obtain an optimal coupled maps matrix. Finally, a shape collection matching module based on a virtual template takes the initial model features as input and employs a point classifier constructed with the coupled maps to directly predict the correspondence between the shapes and the virtual templates. The final correspondence for the non-isometric shape collection is obtained through Gumbel-Sinkhorn normalization. Experimental results demonstrate that the proposed method effectively handles topological noise within non-isometric shapes, achieves low geodesic error in correspondence calculation, provides accurate results, and exhibits strong generalization ability.
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2025, Vol. 38 
