Images as embedding maps and minimal surfaces: a unified approachfor image diffusion

摘要

We introduce a new geometrical framework for image processing.This framework finds a seamless link between the TV-L₁ andthe L₂ norms that are often used in image processing, basedon the geometry of the image and its interpretation as a surface. Itunifies most of the current “scale space” models for imagesby a simple selection of one parameter, yet more important, it enablesone to introduce new methods to deal with images in a simple and naturalway. A functional called “Polyakov (1981) action”, borrowedfrom high energy physics, is shown to be useful for image enhancement incolor, texture, volumetric medical data, movies, and more