Some Recent Advances in Multiscale Geometric Analysis of Point Clouds

We discuss recent work based on multiscale geometric analyis for the study of large data sets that lie in high-dimensional spaces but have low-dimensional structure. We present three applications: the first one to the estimation of intrinsic dimension of sampled manifolds, the second one to the construction of multiscale dictionaries, called Geometric Wavelets, for the analysis of point clouds, and the third one to the inference of point clouds modeled as unions of multiple planes of varying dimensions.

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