# Disparity Measure Construction for Comparison of 3D Objects’ Surfaces

### Natalya Dyshkant

#### 2009

#### Abstract

In this paper a problem of 3D objects’ surfaces comparison is considered. Each spatial object is given as a set of schlicht surfaces that are described by point clouds. This article discusses a proposed disparity measure to compare such objects and an algorithm to compute it. A method for comparison of mesh functions defined on different point sets is proposed. The theoretical base of the proposed approach is the piecewise-linear approximation of surfaces using Delaunay triangulations for initial point clouds. The presented approach uses Delaunay triangulations of each point clouds, general Delaunay triangulation for both clouds, function interpolation on basis of localization of triangulations in each other and function comparison on single cells of general triangulation. Localization is implemented on basis of minimum spanning trees. As the application of the proposed methodology a problem of 3D face models comparison is considered. It was experimentally verified that the proposed method is numerically efficient.

#### References

- Yu. I. Zhuravlev and V. V. Nikiforov, Recognition Algorithms Based on Estimate Evaluation, Kibernetika, No. 3, 111 (1971).
- Petrenko, D. A., S. A. Triangulation comparison using hash-functions (in russian). In Herald of Tomsk State University 280 (2003).
- Scvortsov, A. V. Delaunay triangulation and its applications (in Russian). Tomsk (2002).
- Ernst, M., I. S. Fast randomized point location without preprocessing in two- and threedimensional delauney triangulation. In Proceedings of the 11th Annual Symposium on Computational Geometry. Los Alamos, New Mexico (1996).
- Cheriton, D., Tarjan, R. Finding minimum spanning trees. In SIAM J.Comput. (1976).
- Fredman, M., Tarjan, R. Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, London (1989), 2nd edition.
- Tarjan, R. Fibonacci heaps and their uses in improved network optimization algorithms. In Journal of the ACM (1987).
- Mestetskiy, L., Tsarik, E. Delaunay triangulation: recursion without space division of vertices (in russian). In GraphiCon, International Conference on computer graphics. Moscow (2004).
- Dyshkant, N., Mestetskiy, E. Asymmetry estimation in 3D faces (in russian). In Intellectual Data Processing'08, pp.94-96, Simferopol (2008).
- P. Cignoni, C. Rocchini and R. Scopigno Metro: measuring error on simplified surfaces. Computer Graphics Forum, Blackwell Publishers, vol. 17(2), pp. 167-174, (1998).

#### Paper Citation

#### in Harvard Style

Dyshkant N. (2009). **Disparity Measure Construction for Comparison of 3D Objects’ Surfaces** . In *Proceedings of the 2nd International Workshop on Image Mining Theory and Applications - Volume 1: Workshop IMTA, (VISIGRAPP 2009)* ISBN 978-989-8111-80-7, pages 43-52. DOI: 10.5220/0001957300430052

#### in Bibtex Style

@conference{workshop imta09,

author={Natalya Dyshkant},

title={Disparity Measure Construction for Comparison of 3D Objects’ Surfaces},

booktitle={Proceedings of the 2nd International Workshop on Image Mining Theory and Applications - Volume 1: Workshop IMTA, (VISIGRAPP 2009)},

year={2009},

pages={43-52},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001957300430052},

isbn={978-989-8111-80-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Workshop on Image Mining Theory and Applications - Volume 1: Workshop IMTA, (VISIGRAPP 2009)

TI - Disparity Measure Construction for Comparison of 3D Objects’ Surfaces

SN - 978-989-8111-80-7

AU - Dyshkant N.

PY - 2009

SP - 43

EP - 52

DO - 10.5220/0001957300430052