The Perspective-3-Point Problem When Using a Planar Mirror

The Perspective-3-Point problem (P3P) is a classical and fundamental problem in computer vision. All possible solution sets for the P3P problem are from 1 to 4 solutions. In this paper, we propose a very simple way to reduce the ambiguity of numbers of possible solutions in P3P using a planar mirror. For three reference points, if they and their reflections in a planar mirror are both observed, we may obtain two P3P problems: One is from the three original reference points, and the other is from their reflections. A trivial procedure may be suggested: Solve for each of the two P3P problems, and then find the intersections of the two solution sets. Different from the trivial case, we propose an efficient method which employs the ratio relations of the unknowns in the two P3P problems. The ratio relations are arise from mirror reflection, and can be easily determined before solving the two P3P problems. With the ratio relations, a system of 6 equations with 3 unknowns can be determined. To solve the over-constraint problem, we utilize an efficient algorithm by finding all local minima of least-squares residual. Experiments validate our approach.