A multi-layer 'gas of circles' Markov random field model for the extraction of overlapping near-circular objects.

We propose a multi-layer binary Markov random field (MRF) model that assigns high probability to object configurations in the image domain consisting of an unknown number of possibly touching or overlapping near-circular objects of approximately a given size. Each layer has an associated binary field that specifies a region corresponding to objects. Overlapping objects are represented by regions in different layers. Within each layer, long-range interactions favor connected components of approximately circular shape, while regions in different layers that overlap are penalized. Used as a prior coupled with a suitable data likelihood, the model can be used for object extraction from images, e.g. cells in biological images or densely-packed tree crowns in remote sensing images. We present a theoretical and experimental analysis of the model, and demonstrate its performance on various synthetic and biomedical images