ABSTRACT
Variational PDE (Partial Differential Equation) methods have emerged recently as alternatives to traditional statistical and fast transform-based methodologies in image processing. Examples are the Perona-Malik anisotropic diffusion model [27], the total variation restoration method by Rudin, Osher and Fatemi [29], the axiomatic derived fundamental PDE due to Alvarez, Guichard, Lions and Morel [1], the Mumford-Shah segmentation model [25] and various active con tour models for object detection. These PDE models offer a systematic way to treat geometric properties of images, as well as to properly handle singularities (e.g., edges), by using PDE concepts, such as gradients, jum ps, diffusion, cur vature and level sets. Also, these models treat images as continuous functions. Through these models, the vast arsenal of PDE and CFD (Com putational Fluid Dynamics) techniques can be brought to bear on image processing problems. The methods are often variational, the associated Euler-Lagrange equations give the PDE model.
