Random Cross Ratios
Kalle Åström, Luce Morin, 38 - Saint-Martin-d'Heres (France). Lab. d'Informatique Fondamentale et d'Intelligence Artificielle Informatique et Mathematiques Appliquees de Grenoble (IMAG), 38 - Grenoble (France). Lab. d'Informatique Fondamentale et d'Intelligence Artificielle (LIFIA) Institut National Polytechnique de Grenoble (INPG) · 1992
The main result of this paper is the derivation of the probability density function of the cross ratio c a d b k a b c d d a c b when the numbers a, b, c and d are independent stochastic variables with identical rectangular distribution. The probability density function of the cross ratio is needed to study the effectiveness of invariant based recognition systems. A short background into invariant based recognition is given. The use of the result is illustrated by examples and a short comment is given on generalizing the result to other distributions on a, b, c and d. Although theoretical, this result is useful in understanding algorithms based on the cross ratio, e.g. in autonomous vehicle navigation, object recognition and reconstruction from images. 1.