Determinantal point processes for image processing

Claire Launay (1, 2) , Bruno Galerne (3) , Agnès Desolneux (4, 5, 6)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 UFR Mathématiques et informatique [Sciences] - Université Paris Cité
3 IDP - Institut Denis Poisson
4 CB - CB - Centre Borelli - UMR 9010
5 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
6 CNRS - Centre National de la Recherche Scientifique

Determinantal point processes (DPPs) are probabilistic models of configurations that favour diversity or repulsion. They have recently gained influence in the machine learning community, mainly because of their ability to elegantly and efficiently subsample large sets of data. In this paper, we consider DPPs from an image processing perspective, meaning that the data we want to subsample are pixels or patches of a given image. To this end, our framework is discrete and finite. First, we adapt their basic definition and properties to DPPs defined on the pixels of an image, that we call determinantal pixel processes (DPixPs). We are mainly interested in the repulsion properties of such a process and we apply DPixPs to texture synthesis using shot noise models. Finally, we study DPPs on the set of patches of an image. Because of their repulsive property, DPPs provide a strong tool to subsample discrete distributions such as that of image patches.

Mots clés: Inference; Shot noise; Stationarity; Patches; Subsampling; Image; Pixels; Determinantal point processes; Repulsion

Domaines: Mathématiques [math]; Traitement du signal et de l'image [eess.SP]; Probabilités [math.PR]

Claire Launay, Bruno Galerne, Agnès Desolneux. Determinantal point processes for image processing. 2020. ⟨hal-02611259v1⟩