Random Cross Ratios

Kale Aastrom (1) , Luce Morin (2, 3)

1 Department of Mathematics [Lund University]
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
3 LIFIA - Laboratoire d'Informatique Fondamentale et d'Intelligence Artificielle

The main result of this paper is the derivation of the probability density function of the cross ratio k(a,b,c,d)=(c-a)(d-b)/(d-a)(c-b) when the numbers a, b, c and d are independent stoch astic 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.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Kale Aastrom, Luce Morin. Random Cross Ratios. [Technical Report] IMAG-RT - 92-088 ; LIFIA - 92-014, 1992, pp.8. ⟨inria-00590012⟩