Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.
@article{arxiv.1501.06297,
title = {Geodesic convolutional neural networks on Riemannian manifolds},
author = {Jonathan Masci and Davide Boscaini and Michael M. Bronstein and Pierre Vandergheynst},
journal= {arXiv preprint arXiv:1501.06297},
year = {2018}
}