Determinantal point processes (DPPs) are probabilistic models of configurations that favor 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.


  1. determinantal point processes
  2. repulsion
  3. subsampling
  4. image
  5. pixels
  6. patches
  7. stationarity
  8. shot noise
  9. inference

MSC codes

  1. 60G55
  2. 62M40
  3. 68U10
  4. 94A08

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Information & Authors


Published In

cover image SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Pages: 304 - 348
ISSN (online): 1936-4954


Submitted: 26 March 2020
Accepted: 8 September 2020
Published online: 1 March 2021


  1. determinantal point processes
  2. repulsion
  3. subsampling
  4. image
  5. pixels
  6. patches
  7. stationarity
  8. shot noise
  9. inference

MSC codes

  1. 60G55
  2. 62M40
  3. 68U10
  4. 94A08



Funding Information

Region Ile-de-France

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