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The design of composition distribution of the gradient ceramic nozzle was carried out with the aim of partial relaxation of the stress resulting from external loadings by residual thermal stress.
Here, a gradient profile is essentially the distribution of the gradient magnitude along the gradient direction.
Xue and Mou [39] used the Weibull distribution of the wavelet decomposition, whereas Cheng and Cheng [40] used the Laplace distribution of the gradient image.
This criterion assumes that a well-contrasted and noise-free image has a distribution of the gradient magnitude histogram close to exponential and it attributes a mark from zero to one.
In order to assess the quality of their adaptive smoothing method for underwater image denoising, Arnold-Bos et al. [26] proposed a simple criterion based on a general result by Pratt [40]: for most well contrasted and noise free images, the distribution of the gradient magnitude histogram is closely exponential, except for a small peak at low gradients corresponding to homogeneous zones.
The eigenvalues (λ1, λ2, λ3) and corresponding eigenvectors (e1, e2,e3) of S indicate the local distribution of the gradient vectors.
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In [12], considering the histogram of gradients of y as the discretization of the pdf of gradient distribution of y, the gradient histogram of the original image x is found by solving argmin_{H_{x}}{|H_{y} - H_{x} otimes H_{v}|^{2}+ccdot R(H_{x})} (9).
Chen and Bovik [35] calculated sharpness using the distributions of the gradient and wavelet-decomposition values.
To estimate the distribution of the colour gradient magnitude, we construct a weighted local histogram of colour gradient magnitude responses within an image region, where weights are determined by a Gaussian windowing function (σ = 1°, i.e. 30 pixels) located at the centre of the region.
By genetically engineering AN3 mobility, we assessed each contribution of cell-to-cell movement and tissue growth to the distribution of the AN3 gradient.
The targeting maps are valuable for evaluation and comparison of setups and are also helpful for the design and the optimisation of a magnet system with an appropriate strength and distribution of the field gradient.
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