Procesamiento topo-geom\'etrico de im\'agenes neuronales

Fruit of the relationship of our research group with the team coordinated by the biologist Miguel Morales (http://spineup.es), we have applied different topo-geometric techniques for neuronal image processing. The images, captured with a powerful confocal microscope, allow to study the evolution of synaptic density under the influence of various substances, with the aim of studying neurodegenerative diseases like Alzheimer. In the paper we make a brief review of the techniques that appear in our bioinformatic problems, including the calculation of ordinary and persistent homology (for which one can use the program Kenzo for symbolic computation in algebraic topology ) and classical problems of digital topology as skeleton location and path tracking. We focus on some particular cases of recent application, with which we will illustrate the previous techniques.