Projective reconstruction and invariants from multiple images

This correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views, and the computation of projective invariants of these configurations from their images. A basic tool in this investigation is the fundamental matrix that 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 projective 3-space 𝒫³ by their projection in two independent images. This theorem is the key to a method for the computation of invariants of the geometry. Invariants of six points in 𝒫³ and of four lines in 𝒫³ are defined and discussed. An example 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 computing the fundamental matrix from seven-point correspondences in two images or six-point correspondences in three images are given