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This paper presents a region-based approach to segmentation of the satellite synthetic aperture radar (SAR) intensity imagery. The approach is based on a Voronoi tessellation, the Bayesian inference, and the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. By Voronoi tessellation, the approach partitions a SAR image into a set of polygons corresponding to the components of the segmented homogenous regions. Each polygon is assigned a label to indicate a homogeneous region. The labels for all the polygons form a label field, which is characterized by an improved Potts model. The intensities of pixels in each polygon are assumed to satisfy identical and independent gamma distributions in terms of their label. Following the Bayesian paradigm, the posterior distribution that characterizes the SAR image segmentation can be obtained up to the integration constant. Then, a RJMCMC scheme is designed to simulate the posterior distribution and estimate its parameters. Finally, an optimal segmentation is obtained by the maximum a posteriori algorithm. The results obtained on both real Radarsat-1/2 and simulated SAR intensity images show that our approach works well and is very promising.