Projective Invariants Of Shapes

Abstract

A major goal of computer vision is object recognition, which involves matching of images of an object, obtained from different, unknown points of view. Since there are infinitely many points of view, one is faced with the problem of a search in a multidimensional parameter space. A related problem is the stereo reconstruction of 3-D surfaces from multiple 2-d images. The author proposes to solve these fundamental problems by using geometrical properties of the visible shape that are invariant to a change in the point of view. To obtain such invariants, he starts from classical theories for differential and algebraic invariants not previously used in image understanding. As they stand, these theories are not directly applicable to vision. He suggests extensions and adaptations of these methods to the needs of machine vision. He then studies general projective transformations, which include both perspective and orthographic projections as special cases.<>