  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.
