Gradient-___domain image processing: Difference between revisions

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{{AFC submission|t||ts=20140807204556|u=Smitty121981|ns=118}} <!--- Important, do not remove this line before article has been created. --->

'''Gradient- ___domain image processing''' is a relatively new type of [[digital image processing]] that operates on the differences between neighboring pixels, rather than on the pixel values directly. An [[image gradient]] represents the derivative of an image, so the goal of gradient- ___domain processing is to obtain an image by integrating the gradient, which requires solving [[Poisson's equation]].<ref name="Bhat2010">Bhat, Pravin, et al. "Gradientshop: A gradient-___domain optimization framework for image and video filtering." ACM Transactions on Graphics (TOG) 29.2 (2010): 10.</ref>

== Basics ==

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 anone existingor imagemore 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, James, and Nancy S. Pollard. "Real-time gradient-___domain painting." ACM Transactions on Graphics (TOG). Vol. 27. No. 3. ACM, 2008.</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 is often does not possibleexist, so an image is found that approximates the desired gradient as closely as possible.

== Image Processing ==

For image processing purposes, the gradient is obtained from an existing image and modified. Various methods, such as a [[Sobel operator]], can be used to find the gradient of a given image. This gradient can then be manipulated directly to achieveproduce 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, Anat, et al. "Seamless image stitching in the gradient ___domain." Computer Vision-ECCV 2004. Springer Berlin Heidelberg, 2004. 377-389.</ref>

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* 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" />

* [[High-dynamic-range imaging]]<ref>Fattal, Raanan, Dani Lischinski, and Michael Werman. "Gradient ___domain high dynamic range compression." ACM Transactions on Graphics (TOG). Vol. 21. No. 3. ACM, 2002.</ref>

==References==