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Images as embedding maps and minimal surfaces: Movies, color, texture, and volumetric medical images (2000)
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| Venue: | INT. J. COMPUT. VIS |
| Citations: | 111 - 24 self |
BibTeX
@ARTICLE{Kimmel00imagesas,
author = {R. Kimmel and R. Malladi and N. Sochen},
title = {Images as embedding maps and minimal surfaces: Movies, color, texture, and volumetric medical images},
journal = {INT. J. COMPUT. VIS},
year = {2000},
volume = {39},
number = {2},
pages = {111--129}
}
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Abstract
We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multi-channel edges or the orientation-dependent texture features in them. Images are treated as manifolds in a feature-space. This geometrical interpretation lead to a general way for grey level, color, movies, volumetric medical data, and color-texture image enhancement. We first review our framework in which the Polyakov action from high-energy physics is used to develop a minimization procedure through a geometric flow for images. Here we show that the geometric flow, based on manifold volume minimization, yields a novel enhancement procedure for color images. We apply the geometric framework and the general Beltrami flow to feature-preserving denoising of images in various spaces. Next, we introduce a new method for color and texture enhancement. Motivated by Gabor’s geometric image sharpening method (Gabor, Laboratory Investigation, 14(6):801–807, 1965), we present a geometric sharpening procedure for color images with texture. It is based on inverse diffusion across the multi-channel edge, and diffusion along the edge.
Keyphrases
minimal surface volumetric medical image multi-channel edge geometric flow color image geometric framework image enhancement new method laboratory investigation texture enhancement gabor geometric image geometrical interpretation lead image processing manifold volume minimization feature-preserving denoising orientation-dependent texture feature volumetric medical data general beltrami flow various space general way grey level inverse diffusion novel enhancement procedure minimization procedure polyakov action ieee trans high-energy physic geometric sharpening procedure color-texture image enhancement enhancement technique
