Images as embedding maps and minimal surfaces: movies, color, and volumetric medical images

A general geometrical framework for image processing is presented. We consider intensity images as surfaces in the (x, I) space. The image is thereby a two dimensional surface in three dimensional space for gray level images. The new formulation unifies many classical schemes, algorithms, and measures via choices of parameters in "master" geometrical measure. More important, it is a simple and efficient tool for the design of natural schemes for image enhancement, segmentation, and scale space. Here we give the basic motivation and apply the scheme to enhance images. We present the concept of an image as a surface in dimensions higher than the three dimensional intuitive space. This will help us handle movies, color, and volumetric medical images.