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

Mariem Abaach; Hermine Biermé; Elena Di Bernardino

doi:10.1214/21-EJS1949

2021 Testing marginal symmetry of digital noise images through the perimeter of excursion sets

Mariem Abaach, Hermine Biermé, Elena Di Bernardino

Author Affiliations +

Electron. J. Statist. 15(2): 6429-6460 (2021). DOI: 10.1214/21-EJS1949

Abstract

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 auto-normalised 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.

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Mariem Abaach, Hermine Biermé, and Elena Di Bernardino "Testing marginal symmetry of digital noise images through the perimeter of excursion sets," Electronic Journal of Statistics 15(2), 6429-6460, (2021). https://doi.org/10.1214/21-EJS1949

Received: 1 February 2021; Published: 2021

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