Image segmentation and labeling using the Polya urn model

We propose a segmentation method based on Polya's (1931) urn model for contagious phenomena. A preliminary segmentation yields the initial composition of an urn representing the pixel. The resulting urns are then subjected to a modified urn sampling scheme mimicking the development of an infection to yield a segmentation of the image into homogeneous regions. This process is implemented using contagion urn processes and generalizes Polya's scheme by allowing spatial interactions. The composition of the urns is iteratively updated by assuming a spatial Markovian relationship between neighboring pixel labels. The asymptotic behavior of this process is examined and comparisons with simulated annealing and relaxation labeling are presented. Examples of the application of this scheme to the segmentation of synthetic texture images, ultra-wideband synthetic aperture radar (UWB SAR) images and magnetic resonance images (MRI) are provided.