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.