Globally Optimal and Efficient Vanishing Point Estimation in Atlanta World

Atlanta world holds for the scenes composed of a vertical dominant direction and several horizontal dominant directions. Vanishing point (VP) is the intersection of the image lines projected from parallel 3D lines. In Atlanta world, given a set of image lines, we aim to cluster them by the unknown-but-sought VPs whose number is unknown. Existing approaches are prone to missing partial inliers, rely on prior knowledge of the number of VPs, and/or lead to low efficiency. To overcome these limitations, we propose the novel mine-and-stab (MnS) algorithm and embed it in the branch-and-bound (BnB) algorithm. Different from BnB that iteratively branches the full parameter intervals, our MnS directly mines the narrow sub-intervals and then stabs them by probes. We simultaneously search for the vertical VP by BnB and horizontal VPs by MnS. The proposed collaboration between BnB and MnS guarantees global optimality in terms of maximizing the number of inliers. It can also automatically determine the number of VPs. Moreover, its efficiency is suitable for practical applications. Experiments on synthetic and real-world datasets showed that our method outperforms state-of-the-art approaches in terms of accuracy and/or efficiency.

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