Abstract
We consider the problem of surface comparison given as spatial point clouds that can be explicitly projected onto a plane. This problem can be reduced to comparison of mesh functions of two variables given on different grids. A general case when both grids are unstructured and have different density is of interest. A measure to compare such functions that allow to estimate difference on areas with nodes from both grids and an algorithm to compute it are proposed. Estimation for computational complexity of the algorithm is presented. Computing experiments on real data (3d face models) were carried out.
Chapter PDF
Similar content being viewed by others
Keywords
References
Artec Group — 3D Scanning Technologies, http://www.artec-group.com
Kolesov, A., Pavlova, O.: Surfer Package — Processing and Visualization of 2d Functions (in Russian). Computer Press (1999)
Dyshkant, N.: Disparity Measure Construction for Comparison of 3D Objects’ Surfaces. In: Proceedings of the 2nd International Workshop on Image Mining, Theory and Applications (IMTA-2-2009), pp. 43–52. INSTICC Press, Lisbon (2009)
Dzaraev, C., Persin, L., Porochin, A.: Using of 3d Scanners for Diagnostics of Dentoalveolar Anomalies (in Russian). In: Theoretical and Practical Forum ”Dental-Review”, Moscow (2010)
Gruen, A., Akca, D.: Squares 3D Surface and Curve Matching. ISPRS Journal of Photogrammetry and Remote Sensing 59, 151–174 (2005)
Cignoni, P., Roccini, C., Scopigno, R.: Metro: measuring error on simplified surfaces. In: Computer Graphics Forum, vol. 17, pp. 167–174. Blackwell Publishers, Malden (1998)
Fan, T., Medioni, G., Nevatia, R.: Recognizing 3D objects using surface descriptions. IEEE PAMI 11(11), 1140–1157 (1989)
Schenk, T.: Digital Photogrammetry. Terra-Science, Laurelville (1999)
Skvortsov, A.: A survey of algorithms for constructing a Delaunay triangulation (in Russian). In: Numerical Methods and Programming, vol. 3. RCC MSU Press (2002)
Mestetskiy, L.: Continuous Morphology of Binary Images: Figures, Skeletons and Circulars (in Russian). PHYSMATLIT Press, Moscow (2009)
Mestetskiy, L., Tsarik, E.: Delaunay triangulation: recursion without space division of vertices (in Russian). In: 14th International Conference on Computer Graphics and Vision GraphiCon 2004, pp. 267–270. CMC MSU Press, Moscow (2004)
Preparata, F., Shamos, M.: Computational Geometry: An Introduction. Springer, Heidelberg (1985)
Mestetskiy, L., Tsarik, E.: Merging od Unseparated Delaunay Triangulations. In: Complex Systems: Processing, Modelling and Optimization Od Information, vol. 2, pp. 216–231. Tver State University, Tver (2004)
Dyshkant, N., Mestetskiy, L.: Comparison of One-Sheet Surfaces Acquired by 3D Scanning (in Russian). In: 18th International Conference on Computer Graphics and Vision GraphiCon 2008, pp. 270–277. CMC MSU Press, Moscow (2008)
Cheriton, D., Tarjan, R.: Finding minimum spanning trees. SIAM J. Comput. 5(4), 724–742 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dyshkant, N. (2011). Measures for Surface Comparison on Unstructured Grids with Different Density. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2011. Lecture Notes in Computer Science, vol 6607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19867-0_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-19867-0_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19866-3
Online ISBN: 978-3-642-19867-0
eBook Packages: Computer ScienceComputer Science (R0)