Learning shape correspondence with anisotropic convolutional neural networks

TL;DR

This paper introduces an anisotropic convolutional neural network architecture that effectively learns shape correspondences on non-Euclidean domains, especially under challenging deformations and noise, achieving state-of-the-art results.

Contribution

The paper proposes a novel ACNN architecture based on anisotropic diffusion kernels for intrinsic shape correspondence, generalizing convolutions to non-Euclidean domains.

Findings

Achieves state-of-the-art results on shape correspondence benchmarks.

Effectively handles non-isometric deformations and topological noise.

Demonstrates the effectiveness of anisotropic diffusion kernels in deep learning for geometry processing.

Abstract

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks.