A Comparison of State-of-the-Art Diffusion Imaging Techniques for Smoothing Medical/Non-Medical Image Data

Abstract Partial differential equations (PDE’s) have dominated image processing research recently (see Suri et al. [1], [2], [3], [4], [5], [6] and Haker [7]). The three main reasons for their success are: (1) their ability to transform a segmentation modeling problem into a partial differential equation framework and their ability to embed and integrate different regularizers into these models; (2) their ability to solve PDE’s in the level set framework using finite difference methods; and (3) their easy extension to a higher dimensional space. This paper is an attempt to summarize PDE’s and their solutions applied to image diffusion. The paper first presents the fundamental diffusion equation. Next, the multi-channel anisotropic diffusion imaging is presented, followed by tensor non-linear anisotropic diffusion. We also present the anisotropic diffusion based on PDE and the Tukey/Huber weight function for image noise removal. The paper also covers the recent growth of image denoising using the curve evolution approach and image denoising using histogram modification based on PDE. Finally, the paper presents the non-linear image denoising. Examples covering both synthetic and real world images are presented.