Our model for tree crown extraction 1/2

Energy of the model

In a Bayesian framework the density of the configuration is divided into a prior term and a likelihood term :

• The prior term gives us a general aspect of the solution we desire by adding some constraints to the configurations that should fit the data. As we are working on plantations of poplars, we model the periodic pattern of the alignments. Thus, the prior density contains a repulsive term in order to avoid overlapping objects,and an attractive term which favours the alignments between the objets. These two relationships are described in Fig. (3).
  

  Figure 3: Left : two overlapping objects and the quality of the interaction. Right : the 4 neighbourhoods regions where alignments are favoured.



• The likelihood of the data $\mathcal{I}$ given a configuration $\mathbf{x}$ is a statistical model of the image. Considering that the data can be represented by some Gaussian mixture of two classes (the trees with some high grey value and the background with low grey value), each pixel is associated to one of these two classes :
  • ${\mathcal{C}}_{i}=\mathcal{N}(m_i,\sigma_i)$ for the pixels inside at least one of the objects of the configuration,
  • ${\mathcal{C}}_{o}=\mathcal{N}(m_o,\sigma_o)$ for the pixels outside.