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Random Cross Ratios

Kale Aastrom 1 Luce Morin 2, 3
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : 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.
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https://hal.inria.fr/inria-00590012
Contributor : Team Perception <>
Submitted on : Tuesday, May 3, 2011 - 9:06:19 AM
Last modification on : Friday, June 26, 2020 - 4:04:03 PM
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  • HAL Id : inria-00590012, version 1

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IMAG | CNRS | INRIA | UGA | LARA

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

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