Dense Point-to-Point Correspondences Between Genus-Zero Shapes Using Cubic Mapping and Horn-Schunck Optical Flow

Pejman Hashemibakhtiar, Pejman Hashemibakhtiar, Thierry Cresson, Thierry Cresson, Jacques De Guise, Jacques De Guise, Carlos Vázquez, Carlos Vázquez

2023

Abstract

Establishing correspondences is a fundamental and essential task in computer graphics for further processing of shapes. We have proposed an important modification to an existing method to remove several large matching errors in specific regions. The method uses the unit sphere and the regular spherical grid as parameterization spaces to perform registration and obtain the matching map between two three-dimensional genus-zero shapes, considering non-rigid and non-isometric deformations. Although the unit sphere is a suitable parameterization space for rigid alignment, mapping the sphere to a regular spherical grid for non-rigid registration makes the process unstable since it is not a distance-preserving projection. Therefore, it produces large detachments on the grid and for several regions. Replacing the regular spherical grid mapping with Cubic mapping results in smooth displacement and locality for all corresponding vertices on each cube face. Due to our enhancement, the Optical Flow faces a smooth flow field in the non-rigid registration process. Our modification results in the elimination of matches with significant normalized geodesic error and an increase in the accuracy of the correspondence map, compared to the base method and other recently published approaches.

Paper Citation

in Harvard Style

Hashemibakhtiar P., Cresson T., De Guise J. and Vázquez C. (2023). Dense Point-to-Point Correspondences Between Genus-Zero Shapes Using Cubic Mapping and Horn-Schunck Optical Flow. In Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 1: GRAPP; ISBN 978-989-758-634-7, SciTePress, pages 196-205. DOI: 10.5220/0011674900003417

in Bibtex Style

@conference{grapp23,
author={Pejman Hashemibakhtiar and Thierry Cresson and Jacques De Guise and Carlos Vázquez},
title={Dense Point-to-Point Correspondences Between Genus-Zero Shapes Using Cubic Mapping and Horn-Schunck Optical Flow},
booktitle={Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 1: GRAPP},
year={2023},
pages={196-205},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011674900003417},
isbn={978-989-758-634-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 1: GRAPP
TI - Dense Point-to-Point Correspondences Between Genus-Zero Shapes Using Cubic Mapping and Horn-Schunck Optical Flow
SN - 978-989-758-634-7
AU - Hashemibakhtiar P.
AU - Cresson T.
AU - De Guise J.
AU - Vázquez C.
PY - 2023
SP - 196
EP - 205
DO - 10.5220/0011674900003417
PB - SciTePress