2D markov-switching autoregressive (MS AR) models for image segmentation

Abstract

2D autoregressive (AR) models have been successfully used in several applications in signal and image processing. See [1], [2] and [3] for their use in image restoration, [6], [7] and [8] for their contribution to textural images analysis and synthesis. However, 2D AR models do not allow to describe spatial series with fundamental changes and structural breaks in the dynamic of the data. For instance, when the pixels grey levels of a richly textured image are observed the resulting spatial series exhibit an alternance of different spatial dynamics corresponding to texture regimes. To take into account structural breaks occurring across 2D data, we introduce in this work the 2D Markov-switching autoregressive model that allows for the possibility of sudden changes in the values of the parameters of a 2D AR process. This model can capture various key features of image data, such as similar properties of neighboring pixels, a mean level growth of regional volatility or regional asymmetry.