Geodesic Convolutional Neural Networks on Riemannian Manifolds
Open accessAbstract
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 neural 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 ShapeNet to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.
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Under the MoNet framework, several existing approaches for manifolds and graphs can be generalized as special instances of MoNet by constructing nonparametric weight functions.
“Under the MoNet framework, several existing approaches for manifolds such as Geodesic CNN (GCNN) [90], Anisotropic CNN (ACNN) [91], Spline CNN [92], and for graphs such as GCN [22], DCNN [25] can be generalized as special instances of MoNet by constructing nonparametric weight functions.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [90]
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Background
- Authors
- Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P.
- Affiliations
- Università della Svizzera italiana (CH)
- École Polytechnique Fédérale de Lausanne (CH)
- Venue
- 2015 IEEE International Conference on Computer Vision Workshop (ICCVW)
- Publisher
- IEEE
- Published
- 2015-12
- Pages
- 832-840
- ISSN
- 2473-9936 (ISSN-L)
- OpenAlex
- W2240571584
- Cited by
- 721
- References
- 7
- Citations by year
- 2026: 10 · 2025: 35 · 2024: 34 · 2023: 71 · 2022: 62 · 2021: 93 · 2020: 133 · 2019: 118 · 2018: 95 · 2017: 48 · 2016: 21 · 2015: 1
- FWCI
- 101.10
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE International Conference on Computer Vision Workshops (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- Riemannian manifolds, non-Euclidean geometry, polar coordinates, shape correspondence, shape retrieval, shape description, shape segmentation, ShapeNet
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