Testing marginal symmetry of digital noise images through the perimeter of excursion sets

In this paper we consider digital images for which the pixels values are given by a sequence of independent and identically distributed variables within an observation window. We proceed to the construction of an unbiased estimator for the perimeter without border effects. The study of the first and...

Full description

Saved in:
Bibliographic Details
Published in:Electronic journal of statistics 2021-01, Vol.15 (2), p.6429-6460
Main Authors: Abaach, Mariem, Biermé, Hermine, Di Bernardino, Elena
Format: Article
Language:English
Subjects:
Mathematics
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider digital images for which the pixels values are given by a sequence of independent and identically distributed variables within an observation window. We proceed to the construction of an unbiased estimator for the perimeter without border effects. The study of the first and second moments of the perimeter allows to prove autonormalised asymptotic normality results with an explicit covariance matrix consistently estimated. Theses Central Limit Theorems permit to built a consistent and empirical accessible test statistic to test the symmetry of the marginal distribution. Finally the asymptotic perimeter behaviour in large threshold limit regime is also explored. Several numerical studies are provided to illustrate the proposed testing procedures.
ISSN:1935-7524
1935-7524
DOI:10.1214/21-EJS1949