Atlanta world: an expectation maximization framework for simultaneous low-level edge grouping and camera calibration in complex man-made environments

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Abstract
Edges in man-made environments, grouped according to vanishing point directions, provide single-view constraints that have been exploited before as a precursor to both scene understanding and camera calibration. A Bayesian approach to edge grouping was proposed in the "Manhattan World" paper by Coughlan and Yuille, where they assume the existence of three mutually orthogonal vanishing directions in the scene. We extend the thread of work spawned by Coughlan and Yuille in several significant ways. We propose to use the expectation maximization (EM) algorithm to perform the search over all continuous parameters that influence the location of the vanishing points in a scene. Because EM behaves well in high-dimensional spaces, our method can optimize over many more parameters than the exhaustive and stochastic algorithms used previously for this task. Among other things, this lets us optimize over multiple groups of orthogonal vanishing directions, each of which induces one additional degree of freedom. EM is also well suited to recursive estimation of the kind needed for image sequences and/or in mobile robotics. We present experimental results on images of "Atlanta worlds", complex urban scenes with multiple orthogonal edge-groups, that validate our approach. We also show results for continuous relative orientation estimation on a mobile robot.

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