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Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations

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posted on 2022-09-07, 20:25 authored by Pan HePan He

We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE)---originally designed for nonlinear dimensionality reduction---for shape correspondence. The key idea is to find dense correspondences between shapes by first obtaining high-dimensional neighborhood-preserving embeddings of low-dimensional point clouds and subsequently aligning the source and target embeddings using locally linear transformations. We demonstrate that learning the embedding using a new LLE-inspired point cloud reconstruction objective results in accurate shape correspondences. More specifically, the approach comprises an end-to-end learnable framework of extracting high-dimensional neighborhood-preserving embeddings, estimating locally linear transformations in the embedding space, and reconstructing shapes via divergence measure-based alignment of probabilistic density functions built over reconstructed and target shapes. Our approach enforces embeddings of shapes in correspondence to lie in the same universal/canonical embedding space, which eventually helps regularize the learning process and leads to a simple nearest neighbors approach between shape embeddings for finding reliable correspondences. Comprehensive experiments show that the new method makes noticeable improvements over state-of-the-art approaches on standard shape correspondence benchmark datasets covering both human and nonhuman shapes.


NSF CNS 1922782


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University of Florida

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  • United States of America