Image processing via the beltrami operator

We present a framework for enhancing images while preserving either the edge or the orientation-dependent texture information present in them. We do this by treating images as manifolds in a feature-space. This geometrical interpretation leads to a natural way for grey level, color, movies, volumetric medical data, and color-texture image enhancement. Following this, we invoke the Polyakov action from high-energy physics, and develop a minimization procedure through a geometric flow. This flow, based on manifold volume minimization yields a natural enhancement procedure. We apply this framework to edge preserving denoising of grey value and color images, for volumetric medical data, and orientation-preserving flows for grey level and color texture images.