Performing Image-like Convolution on Triangular Meshes

Tortorici, Claudio; Werghi, Naoufel; Berretti, Stefano

Performing Image-like Convolution on Triangular Meshes

Files

111-114.pdf (1.34 MB)

Date

2018

Authors

Tortorici, Claudio
Werghi, Naoufel
Berretti, Stefano

Publisher

The Eurographics Association

Abstract

Image convolution with a filtering mask is at the base of several image analysis operations. This is motivated by Mathematical foundations and by the straightforward way the discrete convolution can be computed on a grid-like domain. Extending the convolution operation to the mesh manifold support is a challenging task due to the irregular structure of the mesh connections. In this paper, we propose a computational framework that allows convolutional operations on the mesh. This relies on the idea of ordering the facets of the mesh so that a shift-like operation can be derived. Experiments have been performed with several filter masks (Sobel, Gabor, etc.) showing state-of-the-art results in 3D relief patterns retrieval on the SHREC'17 dataset. We also provide evidence that the proposed framework can enable convolution and pooling-like operations as can be needed for extending Convolutional Neural Networks to 3D meshes.

        @inproceedings{10.2312:3dor.20181060
,
booktitle = {Eurographics Workshop on 3D Object Retrieval
},
editor = {Telea, Alex and Theoharis, Theoharis and Veltkamp, Remco
},
title = {{Performing Image-like Convolution on Triangular Meshes
}},
author = {Tortorici, Claudio and 
Werghi, Naoufel and 
Berretti, Stefano
},
year = {2018
},
publisher = {The Eurographics Association
},
ISSN = {1997-0471
},
ISBN = {978-3-03868-053-6
},
DOI = {10.2312/3dor.20181060
}
}