Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations

TL;DR

This paper introduces a novel unsupervised method for shape correspondence using a locally linear embedding approach, achieving improved accuracy by aligning high-dimensional embeddings of point clouds.

Contribution

It adapts the classical LLE algorithm for shape correspondence, creating an end-to-end framework that learns neighborhood-preserving embeddings and aligns shapes in a canonical space.

Findings

Significant improvement over state-of-the-art methods on benchmark datasets.

Effective shape correspondence for both human and nonhuman shapes.

Robustness demonstrated through comprehensive experiments.

Abstract

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.