Quasi-Globally Optimal and Efficient Vanishing Point Estimation in Manhattan World

The image lines projected from parallel 3D lines intersect at a common point called the vanishing point (VP). Manhattan world holds for the scenes with three orthogonal VPs. In Manhattan world, given several lines in a calibrated image, we aim at clustering them by three unknownbut-sought VPs. The VP estimation can be reformulated as computing the rotation between the Manhattan frame and the camera frame. To compute this rotation, state-of-theart methods are based on either data sampling or parameter search, and they fail to guarantee the accuracy and efficiency simultaneously. In contrast, we propose to hybridize these two strategies. We first compute two degrees of freedom (DOF) of the above rotation by two sampled image lines, and then search for the optimal third DOF based on the branch-and-bound. Our sampling accelerates our search by reducing the search space and simplifying the bound computation. Our search is not sensitive to noise and achieves quasi-global optimality in terms of maximizing the number of inliers. Experiments on synthetic and real-world images showed that our method outperforms state-of-theart approaches in terms of accuracy and/or efficiency. Image plane Camera frame Manhattan frame (MF) 3D lines in Manhattan world Vanishing point (VP)