image restoration has been an active research area. dierent formulations are eective in high qualityrecovery. partial dierential equations (pdes) have become an important tool in image processingand analysis. one of the earliest models based on pdes is perona-malik model that is a kindof anisotropic diusion (andi) lter. anisotropic diusion lter has become a valuable tool indierent elds...

We present two nonlinear di usion processes with timedependent di usion coeÆcients. Both processes converge to nontrivial solutions, eliminating the need to impose an arbitrary di usion stopping time, otherwise required in the implementation of most nonlinear diffusion processes. The two schemes employ nonlinear cooling mechanisms that preserve edges. One scheme is intended for general denoisin...

A novel local scale controlled piecewise linear di usion for selective smoothing and edge detection is presented. The di usion stops at the place and time determined by the minimum reliable local scale and a spatial variant, anisotropic local noise estimate. It shows nisotropic, nonlinear di usion equation using di usion coe cients/tensors that continuously depend on the gradient is not necessa...

A novel local scale controlled piecewise linear diffusion for selective smoothing and edge detection is presented. The di usion stops at the place and time determined by the minimum reliable local scale and a spatial variant, anisotropic local noise estimate. It shows nisotropic, nonlinear di usion equation using di usion coe cients/tensors that continuously depend on the gradient is not necess...

We present a uni ed anisotropic geometric di usion PDEmodel for smoothing (fairing) out noise both in triangulated 2-manifold surface meshes in IR and functions de ned on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic di usion tensor. We combine the C limit representation of Loop's subdivision for triangular surface meshes and vector functions o...

Transport theory's equation of transfer is a well-accepted model for wave scattering in a random medium. However, exact solutions are only available for a small class of special cases (isotropic scattering in in nite and semiin nite domains) and thus, analytic solutions for a wide variety of geometries and range of parameters which correspond to more physically relevant situations still remain ...

We employ a nonlinear anisotropic di usion operator like the ones used as a means of ltering and edge enhancement in image processing, in numerical methods for conservation laws. It turns out that algorithms currently used in image processing are very well suited for the design of nonlinear higher-order dissipative terms. In particular, we stabilize the well-known Lax-Wendro formula by means of...

A resolution enhancement scheme is presented. It consists of interpolation followed by processing with an adaptive nonlinear forward-and-backwarddi usion process that enhances edges while suppressing interpolation ringings and denoising smooth areas. keywords: super-resolution, image interpolation, anisotropic di usion, image enhancement, scale-space.

For strongly directed anisotropic di usion ltering it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic di usion. It applies recently discovered di erentiation lters with optimal rotation invariance [11], and comes down to an explicit scheme on a 5 5 stencil. By comparing it with severa...

Synopsis We describe a model-free method to quantify the spectrum of water mobilities in ៯�xed and live brain tissues. We eliminate confounds caused by anisotropic di៛�usion in brain tissues by measuring orientationally-averaged di៛�usion weighted images over a large range of b-values. Spectra of orientationally-averaged water di៛�usivities show clear distinctions between white matter, gray mat...