Block based Spectral Processing of Dense 3D Meshes using Orthogonal Iterations

Aris S. Lalos, Gerasimos Arvanitis, Anastasios Dimas, Kostantinos Moustakas

2018

Abstract

Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the density of the models increases. In this paper, we propose a novel approach for supporting fast and efficient spectral processing of dense 3D meshes, ideally suited for real time compression and denoising scenarios. To achieve that, we apply the problem of tracking graph Laplacian eigenspaces via orthogonal iterations, exploiting potential spectral coherences between adjacent parts. To avoid perceptual distortions when a fixed number of eigenvectors is used for all the individual parts, we propose a flexible solution that automatically identifies the optimal subspace size for satisfying a given reconstruction quality constraint. Extensive simulations carried out with different 3D meshes in compression and denoising setups, showed that the proposed schemes are very fast alternatives of SVD based spectral processing while achieving at the same time similar or even better reconstruction quality. More importantly, the proposed approach can be employed by several other state of the art denoising methods as a preprocessing step, optimizing both their reconstruction quality and their computational complexity.

Paper Citation

in Harvard Style

Lalos A., Arvanitis G., Dimas A. and Moustakas K. (2018). Block based Spectral Processing of Dense 3D Meshes using Orthogonal Iterations. In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 1: GRAPP; ISBN 978-989-758-287-5, SciTePress, pages 122-132. DOI: 10.5220/0006611401220132

in Bibtex Style

@conference{grapp18,
author={Aris S. Lalos and Gerasimos Arvanitis and Anastasios Dimas and Kostantinos Moustakas},
title={Block based Spectral Processing of Dense 3D Meshes using Orthogonal Iterations},
booktitle={Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 1: GRAPP},
year={2018},
pages={122-132},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006611401220132},
isbn={978-989-758-287-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 1: GRAPP
TI - Block based Spectral Processing of Dense 3D Meshes using Orthogonal Iterations
SN - 978-989-758-287-5
AU - Lalos A.
AU - Arvanitis G.
AU - Dimas A.
AU - Moustakas K.
PY - 2018
SP - 122
EP - 132
DO - 10.5220/0006611401220132
PB - SciTePress