The dynamics of image processing viewed as damped elastic deformation

Diffusion-type algorithms have been integrated in recent years successfully into the toolbox of image processing. We introduce a new more flexible and powerful family of parabolic-hyperbolic partial differential equations (PDEs) that somewhat resembles the structure of the parabolic diffusion equation, but incorporates the second order derivative in time. It is instructive to consider intuitively in this context the dynamics of image processing as the deformation of an `elastic sheet'. Indeed, our parabolic-hyperbolic PDE models elastic deformation. This analogy between a well-known physical system and process on one hand, and the dynamics of an image processing scheme on the other hand, contributes interesting and important insight about images and their processing. We explore and demonstrate the capabilities and advantages afforded by the application of the proposed family of equations in image enhancement. The problem of computational complexity is addressed, and efficient numeric schemes are also presented.