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
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Multiscale Texture Enhancement
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
Image Enhancement Using Elastic Manifolds
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
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
Image segmentation and edge enhancement with stabilized inverse diffusion equations
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 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 '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. Efficient numeric schemes are also presented.