Is the Fundamental Matrix Really Independent of the Scene Structure?
Tayeb Basta · International Journal of Signal Processing Image Processing and Pattern Recognition · 2014
In stereo vision, two images of a 3D scene are acquired from two viewpoints.One of the objectives of stereo vision work is to recover the 3D structure of the scene.Epipolar geometry describes the relationship between the images, and the essential and fundamental matrices are the algebraic representations of this geometry.The most important feature of these matrices that is emphasized in the literature is that they are independent of the scene structure.This article illustrates-empirically and theoretically-that the fundamental matrix depends on the scene structure and demonstrates that the matrix in 0 l r Fm m not only represents a relationship between corresponding points of the two views but also represents a relationship between other non-corresponding points.Furthermore, we show empirically that the equationdoes not hold for any pair of corresponding points.In scenes with objects of different depths, the value of l r Fm m depends on the depths of the 3D points and increases proportionally with an increasing baseline.