Learning to Solve Hard Minimal Problems

作     者：Hruby, Petr Duff, Timothy Leykin, Anton Pajdla, Tomas 

作者机构：ETH Zurich Switzerland Department of Mathematics University ofWashington Washington School of Mathematics Georgia Tech in Atlanta USA Czech Institute of Informatics Robotics and Cybernetics of the Czech Technical University in Prague Czechia 

出 版 物：《IEEE Transactions on Pattern Analysis and Machine Intelligence》 (IEEE Trans Pattern Anal Mach Intell)

年 卷 期：2023年第PP卷

页      面：1-16页

核心收录：

学科分类：070207[理学-光学] 0808[工学-电气工程] 081203[工学-计算机应用技术] 08[工学] 0835[工学-软件工程] 0803[工学-光学工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：Horizon 2020 Framework Programme  H2020  (856994) 

主　　题：Optimization 

摘      要：We present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization problem into a minimal problem with many spurious solutions. Our approach avoids computing large numbers of spurious solutions. We design a learning strategy for selecting a starting problem-solution pair that can be numerically continued to the problem and the solution of interest. We demonstrate our approach by developing a RANSAC solver for the problem of computing the relative pose of three calibrated cameras, via a minimal relaxation using four points in each view. On average, we can solve a single problem in under 70 μs. We also benchmark and study our engineering choices on the very familiar problem of computing the relative pose of two calibrated cameras, via the minimal case of five points in two views. IEEE