MIT Department of Electrical Engineering & Computer Science

E E C S

Images as Embedding Maps and Minimal Surfaces: A Unified Approach for Image Diffusion

Ron Kimmel
Lawrence Berkeley National Laboratory and University of California, Berkeley

Thursday, April 3, 1997
4:15 PM (4:00 refreshments)
Grier Room, Room 34-401A
EECS Special Seminar

Abstract

The speaker will 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 importantly, it enables introducion of new methods for dealing with images in a simple and natural way. A functional called "Polyakov action," borrowed from high energy physics, is shown to be useful for image enhancement in color, texture,volumetric medical data, movies, and more. The idea is to consider images as surfaces rather than functions and then minimize the area of the surface in a special way. E.g., a gray level image is consider to be a 2D surface given by the graph I(x,y) in the 3D space (x,y,I). Similarly, a color image is a 2D surface that is given by the three graphs: R(x,y), G(x,y), and B(x,y), in the 5D space (x,y,R,G,B). The results that will be presented in this talk are based on joint collaboration with Nir Sochen (Tel Aviv University, Israel) and Ravi Malladi (Lawrence Berkeley National Laboratory, University of California).

URL of this page: http://www-eecs.mit.edu/AY96-97/events/25.html
Created: Mar 12, 1997 | Modified: Jun 24, 1997
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