We present a multi-scale method for non-rigid point cloud registration based on the Laplace-Beltrami (LB) eigenmap and optimal transport. The registration is defined in distribution sense which provides both generality and flexibility. Point clouds sampled from manifolds are first transformed to new point clouds by the LB eigenmap, which is invariant under isometric transformation, using the first N leading eigenvalues and corresponding eigenfunctions of the LB operator. Then we develop computational models and algorithms for registration of the transformed point clouds using rotation-invariant sliced-Wasserstein distance to achieve computation efficiency and handle ambiguities introduced by the LB eigenmap. By going from smaller N, which provides a quick and robust registration in coarse scale as well as a good initial guess for registration in finer scale, to a larger N, our method provides an efficient and robust multi-scale non-rigid point cloud registration. This is a joint work with Rongjie Lai.
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