Complex diffusion on scalar and vector valued image graphs

Abstract

Complex diffusion was introduced in the image processing literature as a means to achieve simultaneous denoising and enhancement of scalar valued images. In this paper, we present a novel geometric framework to achieve complex diffusion for color images represented by image graphs. In this framework, we develop a novel variational formulation that involves a modified harmonic map functional and is quite distinct from the Polyakov action described by Sochen et al. Our formulation provides a novel framework for simultaneous feature preserving denoising and enhancement. We also develop a quaternionic diffusion that can be applied to color image data represented by a quaternion in the image graph framework. In this framework, the real and imaginary parts can be interpreted as low and high-pass filtered data respectively. Finally, we suggest novel ways to use the imaginary part of complex diffusion toward image reconstruction. We present results of comparison between the complex diffusion, quaternionic diffusion and the well known Beltrami flow in the image graph framework. © 2009 Springer.