Numerically Computing Galois Groups of Minimal Problems
This work addresses a computational challenge in computer vision for researchers and practitioners, but it appears incremental as it builds on over five years of prior efforts.
The paper tackles the problem of solving multiple instances of parametric algebraic equation systems, which arises in computer vision for robust model-fitting like RanSaC, and aims to measure the intrinsic difficulty and develop practical solutions.
I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely "Random Sampling and Consensus", aka "RanSaC".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions.