Macroscopically, a neuron is composed of its cell body (soma) and of its cellular extensions (dendrites and axon). These extensions allows neurons to connect to each other, thus establishing networks that play an essential role in transmitting and storing information. The morphology of dendritic and axonal processes induces the connectivity between neurons and support informational processing. Therefore, neuronal morphology is tightly linked with the functional properties of the brain.

The accurate control of the growing and guidance of the neuronal extensions to their target is a very important step for the maturation of the nervous system. As a result, the dynamic study of this process is of paramount importance. To accomplish this, image sequence of 3D volumes containing a population of axons in the process of growing need to be processed and analyzed. These tasks require the development of new computational techniques. In particular, axonal extremities appears as bright spheres which must be automatically detected and tracked.

The selected detection method is Marked Point Process, a statistical framework which has been applied to the detection of objects in different image processing problems. Its main advantages are that the number of objects to detect can be unknown, and that geometric constraints on the objects can be modeled.

The problem is formalized as an energy minimization problem. The objective is to design this energy in a way such that it is minimized by the axonal extremities extraction. To accomplish this, the energy is divided into two terms: a data term, fitting the objects (spheres) onto the image, and a prior term constraining the configuration by, for example, forbidding overlaps between objects.

Due to the intricate nature of the energy function, usual minimization algorithms cannot be applied . Therefore, the solution will be obtained by optimizing the model with a recently proposed algorithm called multiple births and deaths dynamics. In this approach, multiple objects are added to the current configuration with a given probability (referred to as birth probability). Later on, a new configuration is obtained by removing (killing) some of the objects with a different probability (death probability). This process is repeated iteratively until convergence. In addition, the birth and death process is embedded in a simulated annealing scheme to improve its performance.

This algorithm has been proven to solve the object extraction problem and to outperform the convergence speed of other methods such as RJMCMC (Reversible Jump Markov Chain Monte Carlo). Moreover, the combination of these two approaches (marked point process and multiple birth and death) has already been successfully applied to the detection of different objects such as flamingos in aerial images.

This is a joint project between INRIA (teams ARIANA and SERPICO) and IBDC from the University of Nice Sophia Antipolis. It will be completed thanks to a strong partnership between neurobiologists, computer scientists and applied mathematicians from the different labs.