A New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery
This work addresses camera location recovery in computer vision, particularly for multi-view settings with limited data, representing an incremental improvement.
The paper tackles the problem of camera matrix estimation in structure from motion by introducing a novel rank constraint on multi-view fundamental matrices, showing that a stacked matrix has rank 6 with proper scaling, and uses this to improve fundamental matrix estimation and camera location recovery, especially with fewer images.
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.