Abstract
A new method for the deformation of curves is presented. It is based upon a decomposition of the linear elasticity problem into basic physical laws. Unlike other methods which solve the partial differential equation arising from the physical laws by numerical techniques, we encode the basic laws using computational algebraic topology. Conservative laws use exact global values while constitutive allow to make wise assumptions using some knowledge about the problem and the domain. The deformations computed with our approach have a physical interpretation. Furthermore, our algorithm performs with either 2D or 3D problems. We finally present an application of the model in updating road databases and results validating our approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.F. Auclair-Fortier, P. Poulin, D. Ziou, and M. Allili. Physics Based Resolution of Smoothing and Optical Flow: A Computational Algebraic Topology Approach. Technical Report 269, Département de mathématiques et d’informatique, Université de Sherbrooke, 2001.
L. Bentabet, S. Jodouin, D. Ziou, and J. Vaillancourt. Automated Updating of Road Databases from SAR Imagery: Integration of Road Databases and SAR Imagery information. In Proceedings of the Fourth International Conference on Information Fusion, volume WeA1, pages 3–10, 2001.
A.P. Boresi. Elasticity in Engineering Mechanics. Prentice Hall, 1965.
F. Cosmi. Numerical Solution of Plane Elasticity Problems with the Cell Method. to appear in Computer Modeling in Engineering and Sciences, 2, 2001.
S.F.F. Gibson and B. Mirtich. A Survey of Deformable Modeling in Computer Graphics. Technical report, Mitsubishi Electric Research Laboratory, 1997.
M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active Contour Models. The International Journal of Computer Vision, 1(4):321–331, 1988.
G. T. Mase and G. E. Mase. Continuum Mechanics for Engineers. CRC Press, 1999.
C. Mattiussi. The Finite Volume, Finite Difference, and Finite Elements Methods as Numerical Methods for Physical Field Problems. Advances in Imaging and Electron Physics, 113:1–146, 2000.
J. Montagnat, H. Delingette, N. Scapel, and N. Ayache. Representation, shape, topology and evolution of deformable surfaces. Application to 3D medical imaging segmentation. Technical Report 3954, INRIA, 2000.
S. Platt and N. Badler. Animating Facial Expressions. Computer Graphics, 15(3):245–252, 1981.
P. Poulin, M.-F. Auclair-Fortier, D. Ziou and M. Allili. A Physics Based Model for the Deformation of Curves: A Computational Algebraic Topology Approach. Technical Report 270, Département de mathématiques et d’informatique, Université de Sherbrooke, 2001.
S. Sclaroff and A. Pentland. Model Matching for Correspondance and Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(6):545–561, 1995.
E. Tonti. A Direct Discrete Formulation of Field Laws: The Cell Method. CMES-Computer Modeling in Engineering & Sciences, 2(2):237–258, 2001.
E. Tonti. Finite formulation of the electromagnetic field. Progress in Electromagnetics Research, PIER 32 (Special Volume on Geometrical Methods for Comp. Electromagnetics): 1–44, 2001.
D. Ziou. Finding Lines in Grey-Level Images. Technical Report 240, Département de mathématiques et d’informatique, Université de Sherbrooke, 1999.
D. Ziou and M. Allili. An Image Model with Roots in Computational Algebraic Topology: A Primer. Technical Report 264, Département de mathématiques et d’informatique, Université de Sherbrooke, April 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Auclair-Fortier, M.F., Poulin, P., Ziou, D., Allili, M. (2002). A Computational Algebraic Topology Model for the Deformation of Curves. In: Perales, F.J., Hancock, E.R. (eds) Articulated Motion and Deformable Objects. AMDO 2002. Lecture Notes in Computer Science, vol 2492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36138-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-36138-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00149-2
Online ISBN: 978-3-540-36138-1
eBook Packages: Springer Book Archive