The dynamics of image processing viewed as deformation of elastic sheet
Vadim. Ratner, Yehoshua Y. Josh Zeevi · 2009
Diffusion-type algorithms have been integrated successfully into the toolbox used in image processing and computer vision. We introduce in the context of digital signal and image processing 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 intuitively to consider in this context the dynamics of image processing as the deformation of an dasiaelastic sheetpsila. 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. Efficient numeric schemes are also presented.