Gradient-domain image processing

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.

Basics

The first step is to obtain an image gradient. This is often extracted from an existing image, but it can be created through any means. Some researchers have explored the advantages of users painting directly in the gradient domain. The next step is to solve Poisson's equation to find a new image that produces the desired gradient. An exact solution is often not possible so an image is found that approximates the desired gradient as closely as possible.

Image Processing

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. Other uses include

• seamless image stitching
• combining photographs of the same scene but with different lighting and exposure into one image
• removal of unwanted details from an image
• non-photorealistic rendering filters
• image deblocking
• the ability to seamlessly paste one part of an image onto another in ways that are difficult to achieve with conventional image domain techniques.