Efficient Deformable Shape Correspondence via Kernel Matching

2017/07/25 by Zorah Lähner, Matthias Vestner, Lähner, Zorah +19 · 3 citations
Engineering · Computer Science · #3D Shape Modeling and Analysis #Advanced Image and Video Retrieval Techniques #Advanced Vision and Imaging

paper · pdf · doi:10.48550/arxiv.1707.08991

Abstract

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.

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• Divergence-Free Shape Interpolation and Correspondence
• Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach
• Sinkhorn Normalization of Diffusion Kernels

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