3D Isometric Shape Correspondence

3D shape correspondence methods seek on two given shapes for pairs of surface points that are semantically equivalent. We present three automatic algorithms that address three different aspects of this problem: 1) coarse, 2) dense, and 3) partial correspondence. In 1), after sampling evenly-spaced base vertices on shapes, we formulate the problem of shape correspondence as combinatorial optimization over the domain of all possible mappings of bases, which then reduces within a probabilistic framework to a log-likelihood maximization problem that we solve via EM (Expectation Maximization) algorithm.

Due to computational limitations, we change this algorithm to a coarse-to-fine one (2) to achieve dense correspondence between all vertices. Our scale-invariant isometric distortion measure makes partial matching (3) possible as well.