A branching random evolution and a nonlinear hyperbolic equation
SIAM Journal on Applied Mathematics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Forward-and-backward diffusion processes for adaptive image enhancement and denoising
IEEE Transactions on Image Processing
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Diffusion-type algorithms have been integrated 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 intuitively to consider 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, and highlight the importance of incorporating the second derivative in time. The problem of computational complexity is addressed, and efficient numeric schemes are also presented.