Learning shape correspondence with anisotropic convolutional neural networks

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