Learning Canonical Embeddings for Unsupervised Shape Correspondence With Locally Linear Transformations

Journal Article · 05 September 2023 · IEEE Transactions on Pattern Analysis and Machine Intelligence

DOI:https://doi.org/10.1109/TPAMI.2023.3307592· OSTI ID:2377643

He, Pan; Emami, Patrick; Ranka, Sanjay; Rangarajan, Anand

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 probability 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.

• Research Organization: National Renewable Energy Laboratory (NREL), Golden, CO (United States)
• Sponsoring Organization: National Science Foundation (NSF)
• DOE Contract Number: AC36-08GO28308
• OSTI ID: 2377643
• Report Number(s): NREL/JA-2C00-90362; MainId:92140; UUID:85332e4e-c964-4433-99e3-3c8045b51e8e; MainAdminId:72941
• Journal Information: IEEE Transactions on Pattern Analysis and Machine Intelligence, Journal Name: IEEE Transactions on Pattern Analysis and Machine Intelligence Journal Issue: 12 Vol. 45
• Country of Publication: United States
• Language: English

Related Subjects

MATHEMATICS AND COMPUTING
deformation
image reconstruction
manifolds
point cloud compression
probability density function
shape
shape measurement