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Authors: Alexander Naitsat 1 ; Emil Saucan 2 and Yehoshua Y. Zeevi 1

Affiliations: 1 Technion, Israel ; 2 Max Planck Institute for Mathematics in the Sciences, Germany

ISBN: 978-989-758-175-5

Keyword(s): Conformal Geometry, Isometric Distortion, Volume Parameterization, Volumetric Meshes, Geometric Computing, Computer Graphics.

Related Ontology Subjects/Areas/Topics: Computer Vision, Visualization and Computer Graphics ; Fundamental Methods and Algorithms ; Geometric Computing ; Geometry and Modeling ; Modeling and Algorithms

Abstract: The problem of measuring geometrical distortions is not trivial for volumetric domains. There exist intrinsic restrictions and constrains on higher dimensional mappings. Moreover, according to Liouville theorem, most existing techniques for 2D data can not be directly applied to volumetric objects. In this work we approximate continuous deformations by piecewise affine functions defined on tetrahedral meshes. Our aim is to study a few types of geometrical distortions that can be expressed as functions of singular values of a Jacobian. We employ the proposed methods of estimating conformal and isometric distortions to analyze volumetric data. In particular, we examine parametrization of tetrahedral models to a ball. Distortions produced by the resulting spatial mappings depict intrinsic structure of domains, and therefore can be employed in such tasks as detection of abnormalities and comparison (i.e. similarity assessment) between 3D objects. This geometric approach and results are hi ghly relevant to various applications in Computer Vision, Computer Graphics, 3D Printing and Medical Imaging. (More)

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Paper citation in several formats:
Naitsat, A.; Saucan, E. and Zeevi, Y. (2016). Geometric Approach to Estimation of Volumetric Distortions.In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, pages 105-112. DOI: 10.5220/0005778201030110

@conference{grapp16,
author={Alexander Naitsat. and Emil Saucan. and Yehoshua Y. Zeevi.},
title={Geometric Approach to Estimation of Volumetric Distortions},
booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)},
year={2016},
pages={105-112},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005778201030110},
isbn={978-989-758-175-5},
}

TY - CONF

JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)
TI - Geometric Approach to Estimation of Volumetric Distortions
SN - 978-989-758-175-5
AU - Naitsat, A.
AU - Saucan, E.
AU - Zeevi, Y.
PY - 2016
SP - 105
EP - 112
DO - 10.5220/0005778201030110

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