The goal of Poisson image editing is to perform seamless (gradient) blending (cloning) of an object or a texture from a source image (captured by a mask image) with a target image. We want to create a photomontage by pasting an image region onto a new background using Poisson image editing. The idea is from the SIGGRAPH 2003 paper, Poisson Image Editing, by Perez et al., which shows that blending using the image gradients produces much more realistic results.
The gradient of the source and output images in the masked region will be the same after seamless cloning is done. Moreover, the intensity of the target image and the output image at the masked region boundary will be the same. The following diagram shows how a source image patch g is integrated seamlessly with a target image f* (over the region Ω), with a new image patch f (over the region...