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Gradient domain image processing, also called Poisson image editing, 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 An image gradient is a directional change in the intensity or color in an image. The gradient of the image is one of the fundamental building blocks in image processing. For example, the Canny edge detector uses image gradient for edge detection. ...
represents the
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...
of an image, so the goal of gradient domain processing is to construct a new image by integrating the gradient, which requires solving
Poisson's equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with th ...
.


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, while others have proposed sampling a gradient directly from a camera sensor. 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, 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 Sobel is a surname. Notable people with the surname include: * Adam Sobel (born 1967), American climatologist * Alex Sobel (born 1975), British politician * Barry Sobel (born 1959), American actor and comedian * Bernard Sobel (1887–1964), Americ ...
, 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. Other uses include seamless
image stitching Image stitching or photo stitching is the process of combining multiple photographic images with overlapping fields of view to produce a segmented panorama or high-resolution image. Commonly performed through the use of computer software, most app ...
, removal of unwanted details from an image, non-photorealistic rendering filters, image
deblocking A deblocking filter is a video filter applied to decoded compressed video to improve visual quality and prediction performance by smoothing the sharp edges which can form between macroblocks when block coding techniques are used. The filter aims ...
, the ability to seamlessly clone one part of an image onto another in ways that are difficult to achieve with conventional image-domain techniques, and
high-dynamic-range imaging In photography and videography, multi-exposure HDR capture is a technique that creates extended or high dynamic range (HDR) images by taking and combining multiple exposures of the same subject matter at different exposure levels. Combining mu ...
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.


Seamless image cloning

Digital compositing Digital compositing is the process of digitally assembling multiple images to make a final image, typically for print, motion pictures or screen display. It is the digital analogue of optical film compositing. Mathematics The basic operation use ...
is a common task in image editing in which some or all of one photo is pasted into another photo. Traditionally this is done by pasting the pixel values from one image to the other. A well-trained artist can make a convincing composite using traditional techniques, but it usually requires time-consuming color correction and mask cutting to make it work. Alternatively, the pasting can be performed in the gradient domain: if the differences between pixels are pasted rather than the actual pixel values, there is sometimes much less user input needed to achieve a clean result. The following example demonstrates the use of gradient domain image processing to seamlessly paste from one image to another. HandPhoto.jpg, Input image A EyePhoto.jpg, Input image B ModifiedGradient.jpg, Modified gradient. This is the result of pasting the gradient of B onto the gradient of A. GradientDomainPaste.jpg, Reconstructed image. This is the result of solving Poisson's equation on the modified gradient. The seam between the two images is barely visible. ImageDomainPaste.jpg, Traditional image domain paste. This is the result of pasting the pixel values directly from B onto A. There is an obvious seam. Notice that both the hand and the eye shifted color slightly in the image reconstructed from the modified gradient. This happened because the solver was set to find the entire image. However, it is possible to add constraints so that only the pasted section is solved for, leaving the rest of the image unmodified. It is also worth noting that the gradient pictured above represents the derivative of only one
color channel Color digital images are made of pixels, and pixels are made of combinations of primary colors represented by a series of code. A channel in this context is the grayscale image of the same size as a color image, made of just one of these primary co ...
(red), and was rendered with colors representing the strength and direction of the gradient. In practice two grayscale gradient images are found per color channel, one representing the change in ''x'' and the other representing the change in ''y''. Each color channel is solved for independently when reconstructing the final image.


References

{{reflist Image processing