Isometric 3D Shape Partial Matching Using GD-DNA

Isometric 3D shape partial matching has attracted a great amount of interest, with a plethora of applications ranging from shape recognition to texture mapping. In this paper, we propose a novel isometric 3D shape partial matching algorithm using the geodesic disk Laplace spectrum (GD-DNA). It transforms the partial matching problem into the geodesic disk matching problem. Firstly, the largest enclosed geodesic disk extracted from the partial shape is matched with geodesic disks from the full shape by the Laplace spectrum of the geodesic disk. Secondly, Generalized Multi-Dimensional Scaling algorithm (GMDS) and Euclidean embedding are conducted to establish final point correspondences between the partial and the full shape using the matched geodesic disk pair. The proposed GD-DNA is discriminative for matching geodesic disks, and it can well solve the anchor point selection problem in challenging partial shape matching tasks. Experimental results on the Shape Retrieval Contest 2016 (SHREC'16) benchmark validate the proposed method, and comparisons with isometric partial matching algorithms in the literature show that our method has a higher precision.