Skip to Main content Skip to Navigation
New interface
Reports (Technical report)

Random Cross Ratios

Kale Aastrom 1 Luce Morin 2, 3 
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, 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.
Document type :
Reports (Technical report)
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download
Contributor : Perception team Connect in order to contact the contributor
Submitted on : Tuesday, May 3, 2011 - 9:06:19 AM
Last modification on : Wednesday, October 26, 2022 - 8:13:58 AM
Long-term archiving on: : Thursday, August 4, 2011 - 2:39:10 AM

Files produced by the author(s)


  • HAL Id : inria-00590012, version 1



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



Record views


Files downloads