A Brute-Force Algorithm for Reconstructing a Scene from Two Projections

Is the real problem in finding the relative orientation of two viewpoints the correspondence problem? We argue that this is only one difficulty. Even with known correspondences, popular methods like the eight point algorithm and minimal solvers may break down due to planar scenes or small relative motions. In this paper, we derive a simple, brute-force algorithm which is both robust to outliers and has no such algorithmic degeneracies. Several cost functions are explored including maximizing the consensus set and robust norms like truncated least-squares. Our method is based on parameter search in a fourdimensional space using a new epipolar parametrization. In principle, we do an exhaustive search of parameter space, but the computations are very simple and easily parallelizable, resulting in an efficient method. Further speedups can be obtained by restricting the domain of possible motions to, for example, planar motions or small rotations. Experimental results are given for a va...

• Type: Journal
• Year: 2011
• Where: CVPR
• Authors: Olof Enqvist, Fangyuan Jiang, Fredrik Kahl
• Keywords: Algorithm, Computer Vision, CVPR 2011, Several Cost Functions, Small Relative Motions