gradientdomain

Gradient domain, or gradient-domain processing, refers to techniques that operate on the gradient field of an image or signal rather than directly on pixel intensities. The gradient captures edge and texture information, and manipulating this field can yield edits that are difficult to achieve by altering pixel values alone. The core idea is to modify the gradient and then reconstruct the image by integrating the altered gradients, typically by solving a Poisson equation with appropriate boundary conditions.

In practice, gradients are computed from the image, edits are applied in the gradient domain (for example transferring gradients from one region to another, sharpening, or smoothing while preserving edges), and the final image is recovered by solving a Poisson problem so that the reconstructed image has the desired gradient field and matches the boundary pixels of a surrounding region.

Applications span several image editing tasks. Poisson image editing enables seamless cloning and compositing by blending gradient information across regions. Gradient-domain methods are also used in tone mapping and high dynamic range (HDR) processing, detail transfer, texture editing, and edge-preserving denoising.

Advantages include strong edge preservation, natural-looking composites, and reduced halo artifacts around edited regions. Limitations involve higher computational cost due to Poisson solvers, sensitivity to boundary conditions, and potential artifacts if the gradient field is inconsistently defined or requires careful handling of color channels and gamma correction.

Historically, gradient-domain techniques were popularized for image editing by Pérez, Gangnet, and Blake in 2003 with Poisson image editing. The approach builds on solving Poisson equations to reconcile modified gradients with boundary constraints, enabling flexible and visually coherent edits.