Correspondence Learning via Linearly-invariant Embedding

by   Riccardo Marin, et al.

In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead of using the Laplace-Beltrami eigenfunctions as done in virtually all previous works in this domain, we demonstrate that learning the basis from data can both improve robustness and lead to better accuracy in challenging settings. We interpret the basis as a learned embedding into a higher dimensional space. Following the functional map paradigm the optimal transformation in this embedding space must be linear and we propose a separate architecture aimed at estimating the transformation by learning optimal descriptor functions. This leads to the first end-to-end trainable functional map-based correspondence approach in which both the basis and the descriptors are learned from data. Interestingly, we also observe that learning a canonical embedding leads to worse results, suggesting that leaving an extra linear degree of freedom to the embedding network gives it more robustness, thereby also shedding light onto the success of previous methods. Finally, we demonstrate that our approach achieves state-of-the-art results in challenging non-rigid 3D point cloud correspondence applications.


page 8

page 18

page 19

page 20

page 21

page 22

page 23


DPFM: Deep Partial Functional Maps

We consider the problem of computing dense correspondences between non-r...

Learning Canonical Embedding for Non-rigid Shape Matching

This paper provides a novel framework that learns canonical embeddings f...

Scale-Invariant Fast Functional Registration

Functional registration algorithms represent point clouds as functions (...

Continuous and Orientation-preserving Correspondences via Functional Maps

We propose a method for efficiently computing orientation-preserving and...

REGTR: End-to-end Point Cloud Correspondences with Transformers

Despite recent success in incorporating learning into point cloud regist...

Point-wise Map Recovery and Refinement from Functional Correspondence

Since their introduction in the shape analysis community, functional map...

Correspondence Matrices are Underrated

Point-cloud registration (PCR) is an important task in various applicati...

Code Repositories