Convolutional neural networks have achieved extraordinary results in many computer vision and pattern recognition applications; however, their adoption in the computer graphics and geometry processing communities is limited due to the non-Euclidean structure of their data. In this paper, we propose Anisotropic Convolutional Neural Network (ACNN), a generalization of classical CNNs to non-Euclidean domains, where classical convolutions are replaced by projections over a set of oriented anisotropic diffusion kernels. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes, a fundamental problem in geometry processing, arising in a wide variety of applications. We tested ACNNs performance in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks.

Convolutional neural networks have achieved extraordinary results in many computer vision and pattern recognition applications; however, their adoption in the computer graphics and geometry processing communities is limited due to the non-Euclidean structure of their data. In this paper, we propose Anisotropic Con-volutional Neural Network (ACNN), a generalization of classical CNNs to non-Euclidean domains, where classical convolutions are replaced by projections over a set of oriented anisotropic diffusion kernels. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes, a fundamental problem in geometry processing, arising in a wide variety of applications. We tested ACNNs performance in challenging settings, achieving state-of-the-art results on recent correspondence benchmarks.

I believe the paper to be of a high technical quality. The calculations are sound and appear to not have any major flaws or mistakes (other than small inaccuracies outlined below). The experimental methods used to evaluate the proposed method seem to be appropriate. This work builds on the publication "Geodesic Convolutional Neural Networks on Riemannian Manifolds" and the idea of Anisotropic Diffusion Descriptors. It shares the foundational concepts and notation with these articles, but proposes a novel "fused" approach combining the strengths of these two prior publications.