Adaptive generalized metrics, distance maps and nearest neighbor transforms on gray tone images

This paper aims to introduce and study two novel metrics on gray tone images. These metrics are based on the General Adaptive Neighborhood Image Processing (GANIP) framework that enables to represent an image by spatial neighborhoods, named General Adaptive Neighborhoods (GAN) that fit to their local context. These metrics are generalized in the sense that they do not satisfy all the axioms of a standard mathematical metric. This notion of adaptive generalized metrics leads to the definition of relevant GAN distance maps and GAN nearest neighbor transforms used for image segmentation.