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.