Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images

  • Authors:

  • R. Kimmel;R. Malladi;N. Sochen

  • Affiliations:

  • Computer Science Department, Technion, Haifa 32000, Israel;Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA;Dept. of Applied Mathematics, School of Mathematical Science, Tel Aviv University, Tel Aviv 69978, Israel

  • Venue:
  • International Journal of Computer Vision - Special issue on computer vision research at the Technion
  • Year:
  • 2000

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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.