On the Reconstruction of the Center of a Projection by Distances and Incidence Relations

Abstract

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.