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...

Conventional grayscale error di usion halftoning produces worms and other objectionable artifacts. Tone dependent error di usion (Li and Allebach) reduces these artifacts by controlling the di usion of quantization errors based on the input graylevel. Li and Allebach optimize error lter weights and thresholds for each (input) graylevel based on a human visual system model. This paper extends to...

I develop an omnibus speci…cation test for di¤usion models based on the in…nitesimal operator instead of the already extensively used transition density. The in…nitesimal operatorbased identi…cation of the di¤usion process is equivalent to a "martingale hypothesis" for the new processes transformed from the original di¤usion process. The transformation is via the celebrated "martingale problems...

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

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...

Tritium behavior in plasma-facing components (PFCs) of future tokamak reactors such as ITER is an essential factor in evaluating and choosing the ideal plasma-facing materials (PFMs). One important parameter that in ̄uences tritium buildup and release in candidate materials is the e€ect of material porosity on tritium di€usion and retention. Di€usion in porous materials, for example, consists of...

A ®rm's ability to compete in new product markets is vital to its pro®tability and long-term survival. Therefore, it is important to understand the development and growth of these markets. Following a pioneering study by Bass (1969), di€usion models have traditionally provided this understanding in marketing. The great appeal of the Bass model is that it is a simple one that ®ts the data very w...

|The error di usion algorithm for digital halftoning is equivalent in form to a noise-shaping feedback coder, a class of delta-sigma modulator. The white noise assumption of the quantizer error is known to be false; in fact, the quantizer error is seen to be highly correlated with the input image. To account for this correlation, we use a gain model for the quantizer. This model accurately pred...

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 ...

A simple and e€ective numerical method is proposed for simulating the temporal di€usive mass transport process through a microstructure with arbitrary complexity described by a phase-®eld approach. The mass di€usion through a given microstructure is modeled by a di€usion equation with a variable di€usion coecient, which is solved by an ecient and accurate semi-implicit spectral method. It is ...