A higher-order active contour model of a `gas of circles' and its application to tree crown extraction

Many image processing problems involve identifying the region in the image domain occupied by a given entity in the scene. Automatic solution of these problems requires models that incorporate significant prior knowledge about the shape of the region. Many methods for including such knowledge run into difficulties when the topology of the region is unknown a priori, for example when the entity is composed of an unknown number of similar objects. Higher-order active contours (HOACs) represent one method for the modelling of non-trivial prior knowledge about shape without necessarily constraining region topology, via the inclusion of non-local interactions between region boundary points in the energy defining the model. The case of an unknown number of circular objects arises in a number of domains, e.g. medical, biological, nanotechnological, and remote sensing imagery. Regions composed of an a priori unknown number of circles may be referred to as a `gas of circles'. In this report, we present a HOAC model of a `gas of circles'. In order to guarantee stable circles, we conduct a stability analysis via a functional Taylor expansion of the HOAC energy around a circular shape. This analysis fixes one of the model parameters in terms of the others and constrains the rest. In conjunction with a suitable likelihood energy, we apply the model to the extraction of tree crowns from aerial imagery, and show that the new model outperforms other techniques.