Learning shape correspondence with anisotropic convolutional neural\n networks

Abstract

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