Abstract

In 1981 Longuet-Higgins represented the world point by two vectors in the two camera reference frames and developed the essential matrix. Such a matrix is a relation between the corresponding image points on the two images of a world point on a rigid scene.<br /> The essential matrix is independent of the position and orientation of the cameras used to capture the two views.<br /> The calculation of the essential matrix requires the knowledge of at least five accurate pairs of corresponding points. The unavailability of a procedure that fulfills such a requirement led researchers to focus their attention on developing estimation methods of the essential matrix without questioning the mathematical correctness of its derivation.<br /> In this paper, we identify and expose flaws in Longuet-Higgins’ derivation of the essential matrix. These flaws are the result of mixing up between the scalar product of vectors in a single reference frame and the transformation of vectors from one reference frame to another.