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'''Gradient ___domain image processing''', also called '''Poisson image editing''',<ref name="Perez2003"/> is a type of [[digital image processing]] that operates on the differences between neighboring pixels, rather than on the pixel values directly. Mathematically, an [[image gradient]] represents the [[derivative]] of an image, so the goal of gradient ___domain processing is to construct a new image by [[integral|integrating]] the gradient, which requires solving [[Poisson's equation]].<ref name="Bhat2010">Bhat, Pravin, et{{cite aljournal|doi=10. "Gradientshop1145/1731047.1731048|url=http://grail.cs.washington.edu/projects/gradientshop/demos/gs_paper_TOG_2009.pdf|title=Gradient A''Shop'' gradient-___domain|year=2010 optimization|last1=Bhat framework|first1=Pravin for|last2=Zitnick image|first2=C. andLawrence video|last3=Cohen filtering."|first3=Michael |last4=Curless |first4=Brian |journal=ACM Transactions on Graphics |volume=29. |issue=2 (2010):|pages=1–14 10.|s2cid=3097999 }}</ref>
== Overview ==
Processing images in the gradient ___domain is a two-step process. The first step is to choose an image gradient. This is often extracted from one or more images and then modified, but it can be obtained through other means as well. For example, some researchers have explored the advantages of users painting directly in the gradient ___domain,<ref>McCann,{{cite James, and [[Nancy Pollardjournal|Nancy Sdoi=10. Pollard]]1145/1360612. "1360692|url=http://graphics.cs.cmu.edu/nsp/papers/gradFinal.pdf|title=Real-time gradient-___domain painting |year=2008 |last1=McCann |first1=James |last2=Pollard |first2=Nancy S." |journal=ACM Transactions on Graphics. Vol. |volume=27. No. |issue=3. ACM,|pages=1–7 2008.}}</ref> while others have proposed sampling a gradient directly from a camera sensor.<ref>Tumblin,{{cite Jack,book|url=https://users.cs.northwestern.edu/~jet/docs/2005_1323GradCamFinal.pdf|doi=10.1109/CVPR.2005.374 Amit|chapter=Why Agrawal,I andWant Ramesha Raskar.Gradient "WhyCamera I|title=2005 wantIEEE aComputer gradientSociety camera."Conference on Computer Vision and Pattern Recognition, 2005. (CVPR'05) |year=2005. IEEE|last1=Tumblin Computer|first1=J. Society|last2=Agrawal Conference on|first2=A. Vol|last3=Raskar |first3=R. |volume=1. IEEE,|pages=103–110 2005.|isbn=0-7695-2372-2 |s2cid=1821571 }}</ref> The second step is to solve Poisson's equation to find a new image that can produce the gradient from the first step. An exact solution often does not exist because the modified gradient field is no longer [[Conservative vector field|conservative]], so an image is found that approximates the desired gradient as closely as possible...
== Image editing ==
For [[image editing]] purposes, the gradient is obtained from an existing image and modified. Various operators, such as [[finite difference]] or [[Sobel operator|Sobel]], can be used to find the gradient of a given image. This gradient can then be manipulated directly to produce a number of different effects when the resulting image is solved for. For example, if the gradient is scaled by a uniform constant it results in a simple sharpening filter. A better sharpening filter can be made by only scaling the gradient in areas deemed important.<ref name="Bhat2010" />
Other uses include seamless [[image stitching]],<ref>Levin,{{cite Anat, et albook|doi=10. "1007/978-3-540-24673-2_31|chapter-url=https://webee.technion.ac.il/people/anat.levin/papers/blendingTR.pdf|chapter=Seamless imageImage stitchingStitching in the gradientGradient ___domain."Domain |title=Computer Vision - ECCV 2004. Springer|series=Lecture BerlinNotes Heidelberg,in Computer Science |year=2004. 377|last1=Levin |first1=Anat |last2=Zomet |first2=Assaf |last3=Peleg |first3=Shmuel |last4=Weiss |first4=Yair |volume=3024 |pages=377–389 |isbn=978-389.3-540-21981-1 }}</ref> removal of unwanted details from an image,<ref name="Perez2003">Pérez,{{cite Patrick, Michel Gangnet, and Andrew Blakebook|doi=10. "1145/1201775.882269|chapter-url=https://www.cs.jhu.edu/~misha/Fall07/Papers/Perez03.pdf|chapter=Poisson image editing." |title=ACM TransactionsSIGGRAPH 2003 Papers on Graphics.- Vol.SIGGRAPH 22.'03 No.|year=2003 3.|last1=Pérez ACM,|first1=Patrick 2003.|last2=Gangnet |first2=Michel |last3=Blake |first3=Andrew |page=313 |isbn=1581137095 |s2cid=6541990 }}</ref> [[non-photorealistic rendering]] filters,<ref name="Bhat2010" /> image [[deblocking]],<ref name="Bhat2010" />
the ability to seamlessly clone one part of an image onto another in ways that are difficult to achieve with conventional image-___domain techniques,<ref name="Perez2003" /> and [[high-dynamic-range imaging]]<ref>Fattal, Raanan, Dani{{cite Lischinski, and Michael Wermanbook|doi=10. "1145/566570.566573|chapter-url=https://www.cs.huji.ac.il/~danix/hdr/hdrc.pdf|chapter=Gradient ___domain high dynamic range compression." ACM|title=Proceedings Transactionsof the 29th annual conference on Graphics.Computer Vol.graphics 21.and No.interactive 3.techniques ACM,- SIGGRAPH '02 |year=2002. |last1=Fattal |first1=Raanan |last2=Lischinski |first2=Dani |last3=Werman |first3=Michael |page=249 |isbn=1581135211 |s2cid=1650337 }}</ref>
These gradient ___domain editing techniques can also be extended to moving images by considering a video clip to be a cube of pixels and solving a 3d Poisson equation.<ref>Wang, Hongcheng, et{{cite aljournal|doi=10. "1016/j.gmod.2006.06.002|title=Videoshop: A new framework for spatio-temporal video editing in gradient ___domain." |year=2007 |last1=Wang |first1=Hongcheng |last2=Xu |first2=Ning |last3=Raskar |first3=Ramesh |last4=Ahuja |first4=Narendra |journal=Graphical modelsModels |volume=69.1 (2007):|pages=57–70 57-70.}}</ref>
== Seamless image cloning ==
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