PROJECTIVE RECONSTRUCTION AND INVARIANTS FROM MULTIPLE IMAGES

This correspondence investigates projective reconstruction of geometri c configurations seen in two or more perspective views, and the comput ation of projective invariants of these configurations from their imag es. A basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs. It is prove n that once the epipolar geometry is known, the configurations of many geometric structures (for instance sets of points or lines) are deter mined up to a collineation of projective 3-space rho3 by their project ion in two independent images. This theorem is the key to a method for the computation of invariants of the geometry. Invariants of six poin ts in rho3 and of four lines in rho3 are defined and discussed. An exa mple with real images shows that they are effective in distinguishing different geometrical configurations. Since the fundamental matrix is a basic tool in the computation of these invariants, new methods of co mputing the fundamental matrix from seven-point correspondences in two images or six-point correspondences in three images are given.