Computer Vision and Image Understanding
Robust Computation and Parametrization of Multiple View Relations
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Globally Optimal Estimates for Geometric Reconstruction Problems
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Multiple View Geometry and the L_"-norm
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Automatic Generator of Minimal Problem Solvers
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
A Column-Pivoting Based Strategy for Monomial Ordering in Numerical Gröbner Basis Calculations
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part IV
Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision
International Journal of Computer Vision
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Optimizing polynomial solvers for minimal geometry problems
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Robust fitting for multiple view geometry
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
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Numerous geometric problems in computer vision involve the solution of systems of polynomial equations. This is particularly true for so called minimal problems, but also for finding stationary points for overdetermined problems. The state-of-the-art is based on the use of numerical linear algebra on the large but sparse coefficient matrix that represents the original equations multiplied with a set of monomials. The key observation in this paper is that the speed and numerical stability of the solver depends heavily on (i) what multiplication monomials are used and (ii) the set of so called permissible monomials from which numerical linear algebra routines choose the basis of a certain quotient ring. In the paper we show that optimizing with respect to these two factors can give both significant improvements to numerical stability as compared to the state of the art, as well as highly compact solvers, while still retaining numerical stability. The methods are validated on several minimal problems that have previously been shown to be challenging with improvement over the current state of the art.