Efficient Deformable Shape Correspondence via Kernel Matching
This addresses shape correspondence challenges in computer graphics and vision, but appears incremental as it builds on existing optimization techniques.
The paper tackles the problem of matching 3D shapes under non-isometric deformations, topology changes, and partiality by formulating it as a quadratic assignment problem with a continuity prior, and reports that the method converges to semantically meaningful and continuous mappings in most experiments while scaling well.
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.