Invariants of Points Seen in Multiple Images

This paper investigates projective invariants of geometric configurations in 3 dimensional projective space P, and most particularly the computation of invariants from two or more independent images. A basic tool in this investigation is the essential matrix defined by Longuet-Higgins ([10]), for this matrix describes the epipolar correspondence between image pairs. It is proven that once the epipolar geometry is known, the configurations of many geometric structures (for instance sets of points or lines) are determined up to a collineation of Pby their projection in two independent images. This theorem is the key to a method for the computation of invariants of the geometry. Invariants of 6 points in Pand of four lines in Pare defined and discussed in detail. An example with real images shows that they are effective in distinguishing different geometrical configurations. Since the essential matrix is a fundamental tool in the computation of these invariants, new methods of computing the essential matrix from 7 point correspondences in two images, 6 point correspondences in 3 images or 13 line correspondences in three images are described.