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

Sylvain Petitjean (1)

1 ISA - Models, algorithms and geometry for computer graphics and vision

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.

Mots clés: computer vision applications; systèmes polynomiaux; polynomial systems; symbolic computation; calcul symbolique; résultants; applications en vision par ordinateur

Domaines: Autre [cs.OH]

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