Abstract—In computer stereo vision, the fundamental matrix is the algebraic representation of the epipolar geometry that relates two images of a scene observed from two different viewpoints. The most important feature of the fundamental matrix is its independence of the scene structure. Different methods have been proposed to derive the fundamental matrix equation. This paper reviews one of these methods and reveals that it is based on flawed statements to conclude the existence of a homography between the points on the two images. This derivation of the fundamental matrix equation is based on the existence of a homography between the two images.

Index Terms—computer vision, stereo vision, fundamental matrix, homography

Cite: Tayeb Basta, "Does the Fundamental Matrix Define a One-to-One Relation between the Corresponding Image Points of a Scene?," Journal of Image and Graphics, Vol. 1, No. 3, pp. 125-128, September 2013. doi: 10.12720/joig.1.3.125-128