A `Gas of Circles' Phase Field Model and its Application to Tree Crown Extraction

The problem of extracting the region in the image domain corresponding to an a priori unknown number of circular objects occurs in several domains. We propose a new model of a ‘gas of circles’, the ensemble of regions in the image domain composed of circles of a given radius. The model uses the phase field reformulation of higher-order active contours (HOACs). Phase fields possess several advantages over contour and level set approaches to region modelling, in particular for HOAC models. The reformulation allows us to benefit from these advantages without losing the strengths of the HOAC framework. Combined with a suitable likelihood energy, and applied to the tree crown extraction problem, the new model shows markedly improved performance, both in quality of results and in computation time, which is two orders of magnitude less than the HOAC level set implementation