Discrete determinantal point processes and some applications on images

Determinantal point processes are used to model the repulsion in certain sets of points. They capture negative correlations: the more similar two points are, the less likely they are to be sampled simultaneously. Therefore, these processes tend to generate sets of diverse or distant points. Unlike other repulsive processes, these have the advantage of being entirely determined by their kernel and there are exact algorithms to sample them. During this presentation, I will present the determinantal point processes in a general discrete framework and then in the one of the images: a 2D framework, stationary and periodic. We have studied the repulsion properties of such processes, in particular by using shot noise models, properties that are interesting for synthesizing microtextures. I will also present how the determinantal processes can be applied to the sub-sampling of an image in the patch space.