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.
Type de document :
Rapport
[Technical Report] IMAG-RT - 92-088 ; LIFIA - 92-014, 1992, pp.8
Liste complète des métadonnées

Littérature citée [5 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00590012
Contributeur : Team Perception <>
Soumis le : mardi 3 mai 2011 - 09:06:19
Dernière modification le : samedi 21 avril 2018 - 01:26:56
Document(s) archivé(s) le : jeudi 4 août 2011 - 02:39:10

Fichier

10.1.1.139.8226.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : inria-00590012, version 1

Collections

IMAG | INRIA | UGA | LARA

Citation

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

Partager

Métriques

Consultations de la notice

236

Téléchargements de fichiers

117