Cyclic optimization algorithms for simultaneous structure and motion recovery in computer vision

Abstract

With few exceptions, most previous approaches to the structure from motion (SFM) problem in computer vision have been based on a decoupling between motion and depth recovery, usually via the epipolar constraint. This article offers closed-form cyclic optimization algorithms for the simultaneous recovery of motion and depth in the discrete SFM problem. Cyclic coordinate descent (CCD) algorithms in which each stage admits closed-form solutions are developed for two widely used fitting criteria: the geometric error in one image, and the reprojection error criterion. As a by-product, analytic gradients that can be used in descent-based optimization methods are also obtained. The computational efficiency, statistical consistency, noise robustness, and accuracy of the algorithms are assessed via experiments with synthetic image data.