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

We introduce a new geometrical framework for image processing. This framework finds a seamless link between the TV-L₁ and the L₂ norms that are often used in image processing, based on the geometry of the image and its interpretation as a surface. It unifies most of the current “scale space” models for images by a simple selection of one parameter, yet more important, it enables one to introduce new methods to deal with images in a simple and natural way. A functional called “Polyakov (1981) action”, borrowed from high energy physics, is shown to be useful for image enhancement in color, texture, volumetric medical data, movies, and more