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A Computational Algebraic Topology Model for the Deformation of Curves

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Articulated Motion and Deformable Objects (AMDO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2492))

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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.

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Author information

Authors and Affiliations

  1. DMI, Université de Sherbrooke, Sherbrooke, Canada, J1K 2R1

    M. F. Auclair-Fortier, P. Poulin & D. Ziou

  2. DCSM, Bishop’s University, Lennoxville, Canada, J1M 1Z7

    M. Allili

Authors
  1. M. F. Auclair-Fortier
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  2. P. Poulin
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  3. D. Ziou
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  4. M. Allili
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Maths, Computer Science Engineering School (EPS-UIB), C/Valldemossa km 7.5, PC 07071, Palma de Mallorca, Baleares, Spain

    Francisco José Perales (Director, Computer Graphics and Vision Group, Sub-Director) (Director, Computer Graphics and Vision Group, Sub-Director)

  2. Department of Computer Science, University of York, YO1 5DD, York, UK

    Edwin R. Hancock

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© 2002 Springer-Verlag Berlin Heidelberg

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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

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  • DOI: https://doi.org/10.1007/3-540-36138-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00149-2

  • Online ISBN: 978-3-540-36138-1

  • eBook Packages: Springer Book Archive

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