Gradient-domain image processing
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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 gradient-domain processing involves solving an integral to extract an image from the gradient, which requires solving Poisson's equation.[1]
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 an existing image 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.[2] 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 not possible 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 achieve 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.[1] Other uses include:
- seamless image stitching[3]
- removal of unwanted details from an image[4]
- non-photorealistic rendering filters[1]
- image deblocking[1]
- the ability to seamlessly clone one part of an image onto another in ways that are difficult to achieve with conventional image domain techniques.[4]
References
- ^ a b c d Bhat, Pravin, et al. "Gradientshop: A gradient-domain optimization framework for image and video filtering." ACM Transactions on Graphics (TOG) 29.2 (2010): 10.
- ^ McCann, James, and Nancy S. Pollard. "Real-time gradient-domain painting." ACM Transactions on Graphics (TOG). Vol. 27. No. 3. ACM, 2008.
- ^ Levin, Anat, et al. "Seamless image stitching in the gradient domain." Computer Vision-ECCV 2004. Springer Berlin Heidelberg, 2004. 377-389.
- ^ a b Pérez, Patrick, Michel Gangnet, and Andrew Blake. "Poisson image editing." ACM Transactions on Graphics (TOG). Vol. 22. No. 3. ACM, 2003.