Images as embedding maps and minimal surfaces: movies, color, and volumetric medical images
- 22 November 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
Abstract
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.Keywords
This publication has 13 references indexed in Scilit:
- Partial differential equations and image processingPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Minimal surfaces: a geometric three dimensional segmentation approachNumerische Mathematik, 1997
- Intrinsic Scale Space for Images on Surfaces: The Geodesic Curvature FlowGraphical Models and Image Processing, 1997
- Image Processing: Flows under Min/Max Curvature and Mean CurvatureGraphical Models and Image Processing, 1996
- Invariance of edges and corners under mean-curvature diffusions of imagesPublished by SPIE-Intl Soc Optical Eng ,1995
- Nonlinear total variation based noise removal algorithmsPhysica D: Nonlinear Phenomena, 1992
- Scale-space and edge detection using anisotropic diffusionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1990
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulationsJournal of Computational Physics, 1988
- A note on the gradient of a multi-imageComputer Vision, Graphics, and Image Processing, 1986
- Quantum geometry of bosonic stringsPhysics Letters B, 1981