THE ?GAS OF CIRCLES? MODEL AND ITS APPLICATION TO TREE CROWN EXTRACTION

We present the ?gas of circles? (GOC) model, which is a tool to describe a set of circles with an approximately fixed radius. The model is based on the recently introduced ?higher-order active contour?(HOAC) framework. For certain ranges of the parameters, the model creates stable circles with an approximately fixed radius instead of networks. We show how to determine this set of parameters. The general ?gas of circles? model has many potential applications in varied domains, but it suffers from a drawback: the local minima corresponding to circles can trap the gradient descent algorithm, thus producing phantom circles even with no supporting data. We solve the problem of phantom circles by calculating, via a Taylor expansion of the energy, parameter values that make the circles into inflection points rather than minima. It is possible to create an alternative formulation of HOAC models, based on the ?phase field? framework. We address the tree crown extraction problem by constructing a phase field model of a ?gas of circles?. The available images are color-infrared (CIR) and panchromatic images. We introduce two data models. The first describes the use of only one band of the three available bands. The model is based on the image gradient and on Gaussian distributions. Our second data model makes use of all three bands in the CIR images. Experiments show that the models outperform other traditional methods.