Patch similarity under non Gaussian noise

Many tasks in computer vision require to match image parts. While higher-level methods consider image features such as edges or robust descriptors, low-level approaches compare groups of pixels (patches) and provide dense matching. Patch similarity is a key ingredient to many techniques for image registration, stereo-vision, change detection or denoising. A fundamental difficulty when comparing two patches from "real" data is to decide whether the differences should be ascribed to noise or intrinsic dissimilarity. Gaussian noise assumption leads to the classical definition of patch similarity based on the squared intensity differences. When the noise departs from the Gaussian distribution, several similarity criteria have been proposed in the literature. We review seven of those criteria taken from the fields of image processing, detection theory and machine learning. We discuss their theoretical grounding and provide a numerical comparison of their performance under Gamma and Poisson noises.