TY - JOUR
T1 - Images as embedded maps and minimal surfaces
T2 - Movies, color, texture, and volumetric medical images
AU - Kimmel, R.
AU - Malladi, R.
AU - Sochen, N.
N1 - Funding Information:
We thank Dr. David Adalsteinsson for his help in manipulating and rendering Fig. 6 on his powerful Mac, Dr. Sherif Makram-Ebeid for interesting discussions in person and over the net, and Dr. Yacov Hel-Or for his benchmark images. We also thank the anonymous reviewers for their detailed comments that helped us improve the presentation. This work is supported in part by the US-Israel Binational Science Foundation, in part by the Applied Mathematics Subprogram of the Office of Energy Research under DE-AC03-76SFOOO98, ONR grant under NOOO14-96-1-0381, and partially by the National Science Foundation under grant PHY-90-21139.
PY - 2000/9
Y1 - 2000/9
N2 - We extend the geometric framework introduced in Sochen et al. 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, 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.
AB - We extend the geometric framework introduced in Sochen et al. 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, 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.
UR - http://www.scopus.com/inward/record.url?scp=0034266690&partnerID=8YFLogxK
U2 - 10.1023/A:1008171026419
DO - 10.1023/A:1008171026419
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AN - SCOPUS:0034266690
SN - 0920-5691
VL - 39
SP - 111
EP - 129
JO - International Journal of Computer Vision
JF - International Journal of Computer Vision
IS - 2
ER -