Geodesic convolutional neural networks on Riemannian manifolds

01/26/2015 ∙ by Jonathan Masci, et al. ∙ 0

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.

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ShapeNet_data_preparation_toolbox

Scripts to prepare datasets for ShapeNet using the geodesic patch operator.


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shape_pre_tool

shapenet_data_preparation_toolbox


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