Geodesic Convolutional Neural Networks on Riemannian Manifolds
Abstract
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.
Cite
Text
Masci et al. "Geodesic Convolutional Neural Networks on Riemannian Manifolds." IEEE/CVF International Conference on Computer Vision Workshops, 2015. doi:10.1109/ICCVW.2015.112Markdown
[Masci et al. "Geodesic Convolutional Neural Networks on Riemannian Manifolds." IEEE/CVF International Conference on Computer Vision Workshops, 2015.](https://mlanthology.org/iccvw/2015/masci2015iccvw-geodesic/) doi:10.1109/ICCVW.2015.112BibTeX
@inproceedings{masci2015iccvw-geodesic,
title = {{Geodesic Convolutional Neural Networks on Riemannian Manifolds}},
author = {Masci, Jonathan and Boscaini, Davide and Bronstein, Michael M. and Vandergheynst, Pierre},
booktitle = {IEEE/CVF International Conference on Computer Vision Workshops},
year = {2015},
pages = {832-840},
doi = {10.1109/ICCVW.2015.112},
url = {https://mlanthology.org/iccvw/2015/masci2015iccvw-geodesic/}
}