Recognition of planar objects using the density of affine shape

In this paper, we will study the recognition problem for finite point confi gurations, in a statistical manner. We study the statistical theory of shap e for ordered finite point configurations, or otherwise stated, the uncerta inty of geometric invariants. Here, a general approach for defining shape a nd finding its density, expressed in the densities for the individual point s, is developed. No approximations are made, resulting in an exact expressi on of the uncertainty region. In particular, we will concentrate on the aff ine shape, where often analytical computations is possible. In this case co nfidence intervals for invariants can be obtained from a priori assumptions on the densities of the detected points in the images. However, the theory is completely general and can be used to compute the density of any invari ant (Euclidean, affine, similarity, projective, etc.) from arbitrary densit ies of the individual points. These confidence intervals can be used in suc h applications as geometrical hashing, recognition of ordered point configu rations, and error analysis of reconstruction algorithms. Finally, an examp le will be given, illustrating the theory for the problem of recognizing pl anar point configurations from images taken by an affine camera. This case is of particular importance in applications, where details on a conveyor be lt are captured by a camera, with image plane parallel to the conveyor belt and extracted feature points from the images are used to sort the objects. (C) 1999 Academic Press.