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

Mariem Abaach (1) , Hermine Biermé (2) , Elena Di Bernardino (3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]
3 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Mots clés: Threshold procedure; Test of symmetry; Excursion sets; Crossings; Binary image; Threshold procedure

Domaines: Mathématiques [math]

Mariem Abaach, Hermine Biermé, Elena Di Bernardino. Testing marginal symmetry of digital noise images through the perimeter of excursion sets. 52èmes Journées de Statistiques de la Société Française, Jun 2021, NICE, France. ⟨hal-03349100⟩