Introduction to Isotropic Diffusion

The proposed model is a fusion of Maximum Likelihood Expectation Maximization (MLEM) with partial differential equation based anisotropic diffusion (AD) filter.

Then the noise of the resultant acceleration (vertical direction) signal is removed by the smoothing process of the anisotropic diffusion based on the partial differential equation.

The considered nonlinear second-order anisotropic diffusion model is then particularized for an image restoration task.

So, the second section describes the anisotropic diffusion models for image restoration based on nonlinear second-order parabolic and hyperbolic partial differential equations, proposed by us.

The goal of the proposed review paper is to comprise a collection of the knowledge of the last seven decades dealing with the following topics: • stress fields induced by edge and screw dislocation; a presentation of the most recent solution technique and discussion of previous solutions; • eigenstrains of carbon and hydrogen atoms placed in octahedral and tetrahedral sites; a selection of the values of reliable sources; • assembling of the interstitial atoms, acting as inclusions with a misfit eigenstrain state, in cylindrical representative volume elements; • eigenstrain states in cylindrical representative volume elements due to occupancy of interstitial atoms described by X1, X2 and X3; • eigenstress fields generated by eigenstrains in cylindrical representative volume elements; • formulation of the generalized chemical potential of interstitial atoms in the stressed bcc lattice; • anisotropic diffusion equations for interstitials in a stressed bcc lattice, accounting for elastodiffusion and the effect of occupancy of different types of interstitial sites.

Firstly, we propose advanced skeleton strength map (ASSM) algorithm to create the skeleton which computes the skeleton strength map by isotropic diffusion on the gradient vector field, selects critical points from the skeleton strength map and connects them by Kruskal's algorithm.

Amyloid-b-42 positively correlated with restricted isotropic diffusion in several white matter tracts.

Contrary to the conventional wisdom that apparent diffusion coefficient (ADC) negatively correlates with increased tumor cellularity, we demonstrate disagreement between ADC and histologically confirmed tumor cellularity in glioblastoma specimens, whereas DBSI-derived restricted isotropic diffusion fraction positively correlated with tumor cellularity in the same specimens.

First, to reduce noise, an improved curvature anisotropic diffusion filter is applied, which simultaneously stores edge information.

The evaluated filters were Coherence-Enhancing Diffusion (CED), Speckle Reducing Anisotropic Diffusion (SRAD), Detail-Preserving Anisotropic Diffusion (DPAD), and Anisotropic Diffusion Filter with Memory Based on Speckle (ADMSS).

We formulate the system in terms of a high-dimensional, time-dependent, anisotropic diffusion equation and employ matched asymptotic analysis to derive the effective trapping rate.

NCSF is especially useful when coupled with an anisotropic diffusion equation in noisy configurations.

This paper demonstrates a method to segment liver lesions automatically in CT abdomen images by using Anisotropic Diffusion filtering, Chan-Vese algorithm, K-means clustering, and morphological binary operations.

, nonlocal operators, anisotropic diffusion filtering).

The finite volume method considered here has been developed recently in [3] to approximate heterogeneous and anisotropic diffusion problems using a general class of nonconforming meshes.

Finite difference schemes and iterative methods of solving anisotropic diffusion problems governing multidimensional elliptic PDE with mixed derivatives are considered.

We present a new method to study position-dependent, anisotropic diffusion tensors inside spherically confined systems—a geometry that is common to many chemical nanoreactors.

The Smoluchowski equation for the many-particle probability distribution then acquires an anisotropic diffusion tensor.

The considered nonlinear second-order anisotropic diffusion model is then particularized for an image restoration task.

To characterize the progression of misfolded proteins across the brain, we combine the classical Fisher–Kolmogorov equation for population dynamics with an anisotropic diffusion model and simulate misfolding across a sagittal section and across the entire brain.

In this AI architecture, ultrasound images were segmented by the reaction diffusion level set model combined with the Gabor-based anisotropic diffusion algorithm.

Finally, the reconstructed cone beam CT image is repaired by an anisotropic diffusion algorithm, which can suppress artifacts.

More precisely, the method performs a PDE-based anisotropic diffusion along directions defined by local structures in the 4D ray space.

The transport processes considered here are either anisotropic diffusion along axonal bundles or discrete Laplacian transport along a network.

Many biological tissues inside the human body exhibit highly anisotropic diffusion properties; for example, tissues of the nervous system and white matter in the brain.

Owing to the systematic alignment and ordering of fatty acid and ceramide chains, lipid layers in biological membranes have strongly anisotropic diffusion properties.

We illustrate our technique on synthetic and real-world 3D data and compare our method with the median method, weighted least squares, L0 volume gradient minimization, and edge aware anisotropic diffusion method.

In order to study the processing method of speckle noise reduction, this paper takes the OCT fundus image as the research object, and uses the median filtering, wavelet threshold method, Wiener filtering and anisotropic diffusion method to denoise the OCT fundus image.

The results indicated two mobile "free" states of the N-terminal domain undergoing global diffusive motions, with isotropic diffusion coefficients of 0.

all coefficients anisotropic, is compared with both the case possessing isotropic diffusion coefficients and the case of partial anisotropy, i.

This PDE is based on anisotropic diffusion behavior by adding some constraints to the Weickert coherence enhancing diffusion tensor in order to control the diffusion process near edges and avoids tiny corners destruction.

The ab initio molecular dynamics simulations exhibit the anisotropic diffusion behaviors of Na ions on both o-ScC2 and o-ScN2 monolayers with low energy barriers of 0.

Using a single‐shot isotropic diffusion encoding (IDE) preparation, we eliminate signal confounds caused by anisotropic diffusion, including microscopic anisotropy, and acquire in vivo diffusion‐weighted images (DWIs) over a wide range of diffusion sensitizations.

Here we combine isotropic diffusion encoding with ultra-strong diffusion gradients (240 mT/m) to achieve high diffusion-weightings with high signal to noise ratio, while suppressing signal arising from anisotropic water compartments with significant mobility along at least one axis (e.

Therefore, in this work, a novel method of optimal anisotropic diffusion technique along with contrast limited adaptive histogram equalization (CLAHE), Otsu's optimal thresholding and morphological thinning operation are applied over the fractographs for edge enhancement, overcoming inhomogeneous illumination, edge segmentation and thinning, respectively, to detect voids, automatically.

Wavelet-based filters and anisotropic diffusion techniques have proven their worth in reducing both Gaussian additive noise and speckle noise.

It is based on a multi-scale anisotropic diffusion scheme.

It is based on a multi-scale anisotropic diffusion scheme.

Meanwhile, the diffusion filtering method with adaptive image structure is introduced into image registration, and the anisotropic diffusion function with the ability of feature preservation and consistency enhancement is defined as the regularization term of the model.

The median filter as a nonlinear operator utilized for an oriented anisotropic diffusion function to reduce noise and preserve the edges, is performed on medical images.