Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Testing hypotheses about contours in images

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider the problem of testing hypotheses about the contours in binary images observed on the regular grid. We propose a simple goodness-of-fit test of the hypothesis that a contour belongs to a given parametric family against a nonparametric alternative. We analyze the behavior of the test under the null hypothesis, and under the alternative separated from the null parametric family by a distance of order $n^{-1/2}$ ($n$ is the total number of observations and the distance is defined as the measure of symmetric difference between the sets whose boundaries are the contours of interest). Finally, we prove the lower bound showing that no test can be consistent if the distance between the hypothesis and the alternative is of the order smaller than $n^{-1/2}$.

Mots Clés: Parametric versus nonparametric hypotheses testing ; goodness-of-fit ; minimax rate of testing ; binary image model

Date: 1999-06-24

Prépublication numéro: PMA-512