Editing Markov random field (section)

== Varied applications ==
Markov random fields find application in a variety of fields, ranging from [[computer graphics (computer science)|computer graphics]] to computer vision,<ref>{{Cite book |last1=Banf |first1=Michael |last2=Blanz |first2=Volker |chapter=Man made structure detection and verification of object recognition in images for the visually impaired |date=2013-06-06 |title=Proceedings of the 6th International Conference on Computer Vision / Computer Graphics Collaboration Techniques and Applications |chapter-url=https://dl.acm.org/doi/10.1145/2466715.2466732 |series=MIRAGE '13 |location=New York, NY, USA |publisher=Association for Computing Machinery |pages=1–8 |doi=10.1145/2466715.2466732 |isbn=978-1-4503-2023-8}}</ref> [[machine learning]] or [[computational biology]],<ref name="Kindermann-Snell80"/><ref>{{Cite journal|last1=Banf|first1=Michael|last2=Rhee|first2=Seung Y.|date=2017-02-01|title=Enhancing gene regulatory network inference through data integration with markov random fields|journal=Scientific Reports|volume=7|issue=1|pages=41174|doi=10.1038/srep41174|pmid=28145456|pmc=5286517|issn=2045-2322|bibcode=2017NatSR...741174B}}</ref> and [[information retrieval]].<ref>{{Cite conference | first1= Donald | last1 = Metzler | first2 = W.Bruce |last2=Croft| title=A Markov random field model for term dependencies | year = 2005 | conference = Proceedings of the 28th ACM SIGIR Conference| pages = 472–479 | publisher=ACM | location= Salvador, Brazil | doi=10.1145/1076034.1076115}}</ref> MRFs are used in image processing to generate textures as they can be used to generate flexible and stochastic image models. In image modelling, the task is to find a suitable intensity distribution of a given image, where suitability depends on the kind of task and MRFs are flexible enough to be used for image and texture synthesis, [[image compression]] and restoration, [[image segmentation]], 3D image inference from 2D images, [[image registration]], [[texture synthesis]], [[super-resolution]], [[Computer stereo vision|stereo matching]] and [[information retrieval]]. They can be used to solve various computer vision problems which can be posed as energy minimization problems or problems where different regions have to be distinguished using a set of discriminating features, within a Markov random field framework, to predict the category of the region.<ref>{{Cite journal |title = Automatic Identification of Window Regions on Indoor Point Clouds Using LiDAR and Cameras|last = Zhang & Zakhor|first = Richard & Avideh|date = 2014|journal = VIP Lab Publications|citeseerx = 10.1.1.649.303}}</ref>  Markov random fields were a generalization over the  Ising model and have, since then, been used widely in combinatorial optimizations and networks.