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Session S34 - Symbolic and Numerical Computation with Polynomials

Friday, July 16, 13:00 ~ 13:30 UTC-3

A complete error analysis on solving an overdetermined system in computer vision using linear algebra

Margaret H. Regan

Duke University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Many problems in computer vision are represented using a parametrized overdetermined system of polynomials which must be solved quickly and efficiently. Classical methods for solving these systems involve specialized solvers based on Groebner basis techniques or utilize randomization in order to create well-constrained systems for numerical techniques. We propose new methods in numerical linear algebra for solving such overdetermined polynomial systems and provide a complete error analysis showing that the numerical approach is stable. Examples will be provided to show the efficacy of the method and how the error in the data affects the error in the solution.

Joint work with Jonathan Hauenstein (University of Notre Dame, USA).

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