# Geometric Approach to Estimation of Volumetric Distortions

### Alexander Naitsat, Emil Saucan, Yehoshua Y. Zeevi

#### 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 highly relevant to various applications in Computer Vision, Computer Graphics, 3D Printing and Medical Imaging.

#### References

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#### Paper Citation

#### in Harvard Style

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

#### in Bibtex Style

@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},

}

#### in EndNote Style

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