Paper:
Learning shape correspondence with anisotropic convolutional neural networks
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 nonEuclidean 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.

Review:
This paper proposes a novel model called Anisotropic Convolutional Neural Network (ACNN), which generalizes classical convolutional neural networks to non-Euclidean domains. This work builds on two methods, namely, the Geodesic Convolutional Neural Network ("Geodesic Convolutional Neural Networks on Riemannian Manifolds") and the concept of Anisotropic Diffusion Descriptors. While sharing many foundational ideas, it describes a new "fused" approach resembling the idea of the Geodesic Convolutional Neural Network, but using kernels of the anisotropic Laplacian operator and avoiding a construction of geodesic local patches (which, if I understand everything correctly, appears to be an artificial and inconvenient construct). The suggested approach is demonstrated to outperform other approaches when applied to the problems of full and partial mesh correspondence.
> Technical quality.  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.  > Novelty/originality.  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. While not entirely novel in its details, the combination of two approaches seems to be a successful idea and as such a promising "step in the right direction".  > Potential impact or usefulness.  This work proposes a model which shows a significantly improved performance compared to prior approaches and seems to show a potential of having a large impact in its specialized sub-field.  > Clarity and presentation.  The paper is well written. However, the clarity of the presentation is lacking, seemingly due to the fact that the authors expect the reader to be familiar with prior publications on Geodesic Convolutional Neural Networks and Anisotropic Diffusion Descriptors. Some of the minor inaccuracies/problems include: (a) the conductivity tensor defined in Eq. (2) should have an additional x-dependent multiplier; (b) in Eq. (7), D should have subscripts; (c) the subsection about the discretization of the anisotropic Laplacian operator should include at least some references (Anisotropic Diffusion Descriptors, ...?); (d) instead of "the solution of heat equation (1) at time t is obtained by applying the anisotropic heat operator ...", the sentence should read "the solution of heat equation (1) with D=D_{\alpha \theta} at time t is obtained by applying the anisotropic heat operator ..."; (e) although the meaning of the notation < a,b >_H should be clear for the majority of the readers, including a definition or a reference would improve the clarity of the article.