Partial differential equations (PDE?s) have dominated image processing research recently (see Suri et al. [1], [3], [5], [4] and Haker [6].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 P E?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 P E 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 P E. Finally, the paper presents the non-linear image denoising. Examples covering both synthetic and real world images are presented.