Seamless cloning and Poisson image editing

The goal of Poisson image editing is to perform seamless blending (cloning) of an object or a texture from a source image (captured by a mask image) to a target image. We want to create a photomontage by pasting an image region onto a new background using Poisson image editing. This idea is from the SIGGRAPH 2003 paper, Poisson Image Editing, by Perez et alia. The problem is first expressed in the continuous domain as a constrained variational optimization problem (the Euler-Lagrange equation is used to find a solution), and then can be solved using a discrete Poisson solver. The main task of the discrete Poisson solver is to solve a huge linear system. The central insight in the paper is that working with image gradients, instead of image intensities, can produce much more realistic results. After seamless cloning, the gradient of the output image in the masked region is the same as the gradient of the source region in the masked region. Additionally...