A comparison of state-of-the-art diffusion imaging techniques for smoothing medical/non-medical image data

Partial differential equations (PDEs) have dominated image processing research. 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 PDEs in the level set framework using finite difference methods; and (3) their easy extension to a higher dimensional space. The paper is an attempt to summarize PDEs 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 non-linear image denoising. Examples covering both synthetic and real world images are presented.