Fast and Robust Algorithms Using Coplanar Constraints to Estimate Fundamental Matrices

Two uncalibrated perspective images of a single rigid object/scene are related by the so-called epipolar geometry, which can be described by a 3x3 fundamental matrix. In the literature, there are lots of techniques for estimating the fundamental matrix. Because of degeneracies, however, the coplanar problem about selecting corresponding point pairs may let the estimation of fundamental matrices lead to wrong results. In this paper, two fast and robust algorithms, such as the plane fitting and homography algorithms are proposed to overcome the coplanar problem. The methods combining bucketing techniques with plane fitting and homography constraints are used to deal with some translational and rotational cases. In this paper, some experimental results are shown. According to our experimental results, the performance of our two proposed methods is better than that of the traditional method. Furthermore, the method using homography is better than that using plane fitting. Finally, we apply our results to 3D reconstruction.