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We present a new approach to unsupervised shape correspondence learningbetween pairs of point clouds. We make the first attempt to adapt the classicallocally linear embedding algorithm (LLE) -- originally designed for nonlineardimensionality reduction -- for shape correspondence. The key idea is to finddense correspondences between shapes by first obtaining high-dimensionalneighborhood-preserving embeddings of low-dimensional point clouds andsubsequently aligning the source and target embeddings using locally lineartransformations. We demonstrate that learning the embedding using a newLLE-inspired point cloud reconstruction objective results in accurate shapecorrespondences. More specifically, the approach comprises an end-to-endlearnable framework of extracting high-dimensional neighborhood-preservingembeddings, estimating locally linear transformations in the embedding space,and reconstructing shapes via divergence measure-based alignment ofprobabilistic density functions built over reconstructed and target shapes. Ourapproach enforces embeddings of shapes in correspondence to lie in the sameuniversal/canonical embedding space, which eventually helps regularize thelearning process and leads to a simple nearest neighbors approach between shapeembeddings for finding reliable correspondences. Comprehensive experiments showthat the new method makes noticeable improvements over state-of-the-artapproaches on standard shape correspondence benchmark datasets covering bothhuman and nonhuman shapes.

Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations