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Algebraic Geometry & Computer Vision: Polynomial Systems, Real & Complex Roots

Sylvain Petitjean 1
1 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We review the different techniques known for doing exact computations on polynomial systems. Some are based on the use of Gröbner bases and linear algebra, others on the more classical resultants and its modern counterparts. Many theoretical examples of the use of these techniques are given. Furthermore, a full set of examples of applications in the domain of artificial vision, where many constraints boil down to polynomial systems, are presented. Emphasis is also put on very recent methods for determining the number of (isolated) real and complex roots of such systems.
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Submitted on : Tuesday, September 26, 2006 - 8:38:42 AM
Last modification on : Friday, February 4, 2022 - 3:21:57 AM


  • HAL Id : inria-00098796, version 1



Sylvain Petitjean. Algebraic Geometry & Computer Vision: Polynomial Systems, Real & Complex Roots. Journal of Mathematical Imaging and Vision, Springer Verlag, 1999, 10 (3), pp.191-220. ⟨inria-00098796⟩



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