Learning to Solve Hard Minimal Problems
This addresses the problem of efficient and accurate geometric optimization for computer vision practitioners, though it appears incremental as it builds on existing RANSAC frameworks.
The paper tackles the challenge of solving hard geometric optimization problems in RANSAC by avoiding spurious solutions through a learning strategy for selecting starting problem-solution pairs, achieving an average solve time of under 70 μs for a three-camera relative pose problem.
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.