Assessment of Texture Stationarity using the Asymptotic Behavior of the Empirical Mean and Variance

Rémi Blanc (1) , Jean-Pierre da Costa (1) , Youssef Stitou (1) , Pierre Baylou (1) , Christian Germain (1)

1 IMS - Laboratoire de l'intégration, du matériau au système

Given textured images considered as realizations of 2-D stochastic processes, a framework is proposed to evaluate the stationarity of their mean and variance. Existing strategies focus on the asymptotic behavior of the empirical mean and variance (respectively EM and EV), known for some types of non deterministic processes. In this paper, the theoretical asymptotic behaviors of the EM and EV are studied for large classes of second order stationary ergodic processes, in the sense of the Wold decomposition scheme, including harmonic and evanescent processes. Minimal rates of convergence for the EM and the EV are derived for these processes; they are used as criteria for assessing the stationarity of textures. The experimental estimation of the rate of convergence is achieved using a non parametric block sub-sampling method. Our framework is evaluated on synthetic processes with stationary or non stationary mean and variance and on real textures. It is shown that anomalies in the asymptotic behavior of the empirical estimators allow detecting non stationarities of the mean and variance of the processes in an objective way.

Mots clés: Image Analysis; Stationarity; Texture; Wold Decomposition

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Rémi Blanc, Jean-Pierre da Costa, Youssef Stitou, Pierre Baylou, Christian Germain. Assessment of Texture Stationarity using the Asymptotic Behavior of the Empirical Mean and Variance. IEEE Transactions on Image Processing, 2008, 17 (9), pp.1481-1490. ⟨10.1109/TIP.2008.2001403⟩. ⟨hal-00321867⟩