Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Regularized Shock Filters and Complex Diffusion
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Complex Diffusion Processes for Image Filtering
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
A general framework for low level vision
IEEE Transactions on Image Processing
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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.