Some Properties of the E Matrix in Two-View Motion Estimation

ACstract--In the eight-point linear algorithm for determining 3-D motion/structure from two perspective views using point correspondences, the E matrix occupies a central role. The E matrix is defined as a skew-symmetrical matrix (containing the translation components) postmultiplied by a rotation matrix. In this correspondence, we show that a necessary and sufficient condition for a 3 x 3 matrix to be so decomposable is that one of its singular values is zero and the other two are equal. Several other forms of this property are also presented. Finally, some applications are briefly described.