A New Rank Constraint on Multi-View Fundamental Matrices, and Its Application to Camera Location Recovery

Soumyadip Sengupta, Tal Amir, Meirav Galun, Tom Goldstein, David W. Jacobs, Amit Singer, Ronen Basri; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp. 4798-4806

Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6. Moreover, this matrix forms the symmetric part of a rank 3 matrix whose factors relate directly to the corresponding camera matrices. We use this new characterization to produce better estimations of fundamental matrices by optimizing an L1-cost function using Iterative Re-weighted Least Squares and Alternate Direction Method of Multiplier. We further show that this procedure can improve the recovery of camera locations, particularly in multi-view settings in which fewer images are available.