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Algebraic methods in computer vision and automatic generation of efficient algebraic solvers

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Many problems in computer vision can be formulated using systems of polynomial equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency when solving them. In the first talk, presented by Zuzana Kukelova, we will briefly discuss two algebraic methods for creating such efficient solvers for computer vision problems. One is based on Groebner basis methods for solving systems of polynomial equations and one on polynomial eigenvalue problems and resultants. In the second talk, presented by Martin Bujnak, we will introduce the automatic generator of such efficient Groebner basis solvers which could be used even by non-experts to solve problems resulting in systems of polynomial equations. We will present several methods for speeding up such solvers based on Groebner bases and action matrix eigenvalue computations. Finally we will show several new solutions to absolute and relative pose problems which we have created using the two presented methods.

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