Examining the Validity of the Fundamental Matrix Equation
Tayeb Basta · International Journal of Applied Physics and Mathematics · 2012
In stereo vision, two cameras are used to obtain two views of a scene from two different standpoints. The epipolar geometry describes the relation between the two views. When the intrinsic cameras parameters are known, the essential matrix is the algebraic representation of this geometry; otherwise the fundamental matrix is the representation of such geometry. A number of derivation methods of the essential and fundamental matrices are available in the computer vision literature. This paper questions the validity of the equations of these matrices and demonstrates that such equations are the result of an undefined vector operation. Index Terms—Essential Matrix, fundamental matrix, stereo vision, epipolar geometry, dot product. I. INTRODUCTION In stereo vision, two cameras are used to obtain two differing views (i.e., images) of a scene from two different standpoints. The cameras are supposed to satisfy the pinhole model assumption. In this context, a camera is described by intrinsic and extrinsic parameters. The former include coordinates of the principal points, pixel aspect ratio, and focal lengths. The latter are the position and orientation of the camera with respect to the world coordinate system. The epipolar geometry describes the relation between the two views. When the intrinsic cameras parameters are known, the essential matrix is the algebraic representation of this geometry. When none of the parameters are known, the fundamental matrix encapsulates all the information about the epipolar geometry. This geometry which is depicted in