Algebraic Geometry and Computer Vision: Polynomial Systems, Real andComplex Roots

Authors:
S. Petitjean
Affiliations:
LORIA-CNRS & INRIA Lorraine, Bâtiment LORIA, BP 239, 54506 Vandœuvre-les-Nancy cedex, France. petitjea@loria.fr
Venue:
Journal of Mathematical Imaging and Vision
Year:
1999

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Abstract

We review the different techniques known for doing exact computationson polynomial systems. Some are based on the use of Gröbner bases andlinear algebra, others on the more classical resultants and its moderncounterparts. Many theoretical examples of the use of these techniquesare given. Furthermore, a full set of examples of applications in thedomain of artificial vision, where many constraints boil down topolynomial systems, are presented. Emphasis is also put on very recentmethods for determining the number of (isolated) real and complexroots of such systems.