Gradient-domain image processing
Mathematics
Gradient domain image processing, also called Poisson image editing, is a type of digital image processing that operates directly on the differences between neighboring pixels, rather than on the pixel values. Mathematically, an image gradient represents the derivative 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.
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 also be obtained through other means. 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 approximating the desired gradient as closely as possible is found.
Image editing
The gradient is obtained from an existing image and modified for image editing purposes. Various operators, such as finite difference or Sobel, can be used to find the gradient of a given image.
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