R. Kimmel et al., Images as embedded maps and minimal surfaces: Movies, color, texture, and volumetric medical images, INT J COM V, 39(2), 2000, pp. 111-129
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 pre
serving 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, mo
vies, 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 fl
ow for images. Here we show that the geometric flow, based on manifold volu
me minimization, yields a novel enhancement procedure for color images. We
apply the geometric framework and the general Beltrami flow to feature-pres
erving denoising of images in various spaces.
Next, we introduce a new method for color and texture enhancement. Motivate
d by Gabor's geometric image sharpening method (Gabor, Laboratory Investiga
tion, 14(6):801-807, 1965), we present a geometric sharpening procedure for
color images with texture. It is based on inverse diffusion across the mul
ti-channel edge, and diffusion along the edge.