This article presents a new global approach for detecting vanishing points and groups of mutually orthogonal vanishing directions using lines detected in images of man-made environments. These two multi-model fitting problems are respectively cast as Uncapacited Facility Location (UFL) and Hierarchical Facility Location (HFL) instances that are efficiently solved using a message passing inference algorithm. We also propose new functions for measuring the consistency between an edge and a putative vanishing point, and for computing the vanishing point defined by a subset of edges. Extensive experiments in both synthetic and real images show that our algorithms outperform the state-of-the-art methods while keeping computation tractable. In addition, we show for the first time results in simultaneously detecting multiple Manhattan-world configurations that can either share one vanishing direction (Atlanta world) or be completely independent.
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