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

A Markov random field model for extracting near-circular shapes

We propose a binary Markov random field (MRF) model that assigns high probability to regions in the image domain consisting of an unknown number of circles of a given radius. We construct the model by discretizing the `gas of circles' phase field model in a principled way, thereby creating an `equivalent'MRF. The behaviour of the resulting MRF model is analyzed, and the performance of the new model is demonstrated on various synthetic images as well as on the problem of tree crown detection in aerial images