A Minimal Closed-form Solution for the Perspective Three Orthogonal Angles (P3oA) Problem: Application To Visual Odometry

We provide a simple closed-form solution to the Perspective three orthogonal angles (P3oA) problem: given the projection of three orthogonal lines in a calibrated camera, find their 3D directions. Upon this solution, an algorithm for the estimation of the camera relative rotation between two frames is proposed. The key idea is to detect triplets of orthogonal lines in a hypothesize-and-test framework and use all of them to compute the camera rotation in a robust way. This approach is suitable for human-made environments where numerous groups of orthogonal lines exist. We evaluate the numerical stability of the P3oA solution and the estimation of the relative rotation with synthetic and real data, comparing our results to other state-of-the-art approaches.