Our model
The configuration which minimizes the energy U(x) of the process will be the seeked tree crown extraction. The simulation and the optimization of this stochastic process is made thanks to a Reversible Jump Markov Chain Monte Carlo algorithm embedded in a Simulated Annealing
. In order to find a good extraction result, we should first model the energy to minimize it with the best configuration of objects.
The energy of the model is the sum of a regularizing term and a data term :

regularizing term : all the knowledge we have about the interaction between the trees in the stand (alignments, non overlapping, ...).
data term : fitting the objects into the image. The data energy of the configuration is the sum of the data energy of its objects. A negative data energy corresponds to "good objects", while a positive data energy is given to "bad objects".
The data energy computation takes into account the fact that the trees have a high reflectance in the near infrared band, and that we can detect them with their shadow (all around or just in one direction, depending on the image). We calculate the Bhattacharya distance between the distribution of the pixels inside the object and in the shadow area (different between the 2D model and in the 3D model), and give negative energy to high values of that distance, while small values are penalized.
