Images as embedded maps and minimal surfaces: Movies, color, texture, and volumetric medical images

R. Kimmel*, R. Malladi, N. Sochen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)111-129
Number of pages19
JournalInternational Journal of Computer Vision
Issue number2
StatePublished - Sep 2000


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