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

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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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Petitjean, S. Algebraic Geometry and Computer Vision: Polynomial Systems, Real and Complex Roots. Journal of Mathematical Imaging and Vision 10, 191–220 (1999). https://doi.org/10.1023/A:1008348724781

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