用数值方法计算最小问题的伽罗瓦群，评估求解难度。
Numerically Computing Galois Groups of Minimal Problems
- 通过数值算法计算代数方程组的伽罗瓦群
- 揭示参数化方程组求解的内在复杂度
- 对计算机视觉中的鲁棒模型拟合有实际意义
我讨论了代数、数值计算与计算机视觉中看似不相关的主题的交汇。核心问题是求解参数化代数方程组（多项式或有理函数）的多个实例。这一问题对ISSAC参会者已具吸引力，但在计算机视觉领域当前采用的鲁棒模型拟合范式（即“随机采样与共识”，简称RanSaC）中尤为关键。本次报告将概述过去五年多的研究工作，旨在衡量此类参数化系统求解的内在难度，并在实用解决方案上取得进展。
原文摘要 · Abstract (English)
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.
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