•The diffusion scheme based on Wiener filter is established.•The stopping method based on noise variance is researched in detail.•The algorithm can be considered as a discretization of adaptive heat ...equation.
In this paper, we propose an adaptive multiple steps local Wiener filter image denoising algorithm in the wavelet domain. This algorithm can be considered as a discretized implementation of adaptive heat diffusion equation, and is carried out by multiple successive steps. The denoised output from one iteration is taken as the input to the next. The proper iteration number is determined by total denoising amount which is measured by noise variance. The selected local window sizes are also relatively stable. The experimental results show the effectiveness of the proposed method.
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The heat diffusion distance and kernel have gained a central role in geometry processing and shape analysis. This paper addresses a novel discretization and spectrum-free computation of the diffusion ...kernel and distance on a 3D shape P represented as a triangle mesh or a point set. After rewriting different discretizations of the Laplace–Beltrami operator in a unified way and using an intrinsic scalar product on the space of functions on P, we derive a shape-intrinsic heat kernel matrix, together with the corresponding diffusion distances. Then, we propose an efficient computation of the heat distance and kernel through the solution of a set of sparse linear systems. In this way, we bypass the evaluation of the Laplacian spectrum, the selection of a specific subset of eigenpairs, and the use of multi-resolutive prolongation operators. The comparison with previous work highlights the main features of the proposed approach in terms of smoothness, stability to shape discretization, approximation accuracy, and computational cost.
Stability of the computation of the Chebyshev approximation of the heat diffusion distances on partially sampled surfaces. Display omitted
•Spectrum-free computation of the heat diffusion kernel and distances.•The computation is independent of the selected eigenpairs and prolongation operators.•The approximation accuracy is lower than 10−r (e.g., r≔5,7), r degree of the rational Chebyshev polynomial.•The approach is robust to surface discretization and free of user-defined parameters.
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Recent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, ...which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes.
Robustness of the biharmonic distance from a source (black) point, which has been computed using the linear FEM mass matrix as weight, with respect to (b) tiny and missing triangles, (c) noise, (d) holes of an irregularly sampled surface (a) with local shape artifacts. Display omitted
•We study the discretization of harmonic, Laplacian, diffusion maps and distances.•We generate spectral distances in a unified way.•We focus on different Laplacian matrices, initial conditions, and shapes.•The user can perform a large set of experiments on maps and spectral distances.
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The fractal heat-conduction problem via local fractional derivative is
investigated in this paper. The solution of the fractal heat-diffusion
equation is obtained. The characteristic equation method ...is proposed to find
the analytical solution of the partial differential equation in fractal
heat-conduction problem.
nema
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A theoretical approach based on thermomechanics of irreversible processes shows that the heat sources produced by a soda lime glass specimen under cyclic mechanical loading lead to temperature ...variations which can be detectable with a high resolution infrared camera. In order to validate this approach, experimental investigations are performed. For this purpose, a cyclic bending test is carried out and infrared measurements are performed. Temperature variations measured at the specimen surface are found to reach a few hundredths of a degree for a stress amplitude of the order of magnitude of 40MPa. Results are in a good agreement with theoretical predictions. These thermal measurements are then used for thermoelastic stress analysis and heat source calculation. The study demonstrates that such an experimental approach based on infrared thermography will improve the understanding of the thermomechanical behavior of inorganic glasses.
► Thermoelastic coupling in inorganic oxide glasses produces detectable heat source. ► Full temperature field measurements are performed by using infrared thermography. ► Temperature variations for cyclic bending reach a few hundredths of a degree. ► Temperature fields are processed to obtain stress and heat source fields. ► A new route in thermomechanics of inorganic glasses is opened.
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An ideal image edge detection scheme Zhang, Xiaochun; Liu, Chuancai
Multidimensional systems and signal processing,
10/2014, Volume:
25, Issue:
4
Journal Article
Peer reviewed
This paper introduces a scale-invariant and contrast-invariant multi-scale differential edge detector. The method is a direct consequence of two key discoveries: (1) a precise scale normalization ...method and (2) a formula to verify scale-invariant detectors. The new scale normalization method provides differential operators with respect to scale, among them the scale-invariant edge detectors. To investigate these differential detectors quantitatively, mathematical functions were used to represent the edges and to solve for the parameters, including position, width, contrast, offset, and orientation, in closed form. Noise is filtered as a low-contrast feature. The method has been tested with various kinds of synthesized edge functions and can extract edge features accurately. It is suitable for real-world images of several kinds of degradation.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
37.
Reliable computation with unreliable computers Brown, Andrew D; Mills, Rob; Dugan, Kier James ...
Chronic diseases and translational medicine,
07/2015, Volume:
9, Issue:
4
Journal Article
Peer reviewed
Open access
As computing systems continue their unquenchable rise towards and through million core architectures, two considerations that used to be unimportant become more and more dominant: power consumption ...(be it FLOPS/W or W/mm2) and reliability. This study is concerned with the latter: in a system of a million cores, it is unrealistic to expect 100% functionality on power-up; equally, operational availability degrades with time. Monitoring and maintaining the health of such a system using traditional techniques is costly, and most rely on the concept of some sort of central overseer or monitor to make a final judgement about system availability, giving a single point of failure. Large systems of the future will consist of hardware and software that work synergistically to cope with isolated points of failure, allowing the gross behaviour of the system to degrade gracefully and in a meaningful way in the face of faults. This study describes one such system: spiking neural network architecture is a million-core machine with layered fault-tolerance built in at many levels. The authors show how the system may be used to solve the canonical distributed heat diffusion equation, and how the quality of solution is modulated by the effects of partial system failure.
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This paper develops the immersed interface method (IIM) due to R.J. LeVeque, Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. ...Numer. Anal. 31 (1994) 1019–1044 for solving parabolic equations with singular own sources. New finite difference schemes are constructed to satisfy the discrete maximum principle. Convergence proof is provided. Numerical experiments show the efficiency of the proposed schemes.
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We consider the interesting smoothing method of global optimization recently proposed in Lau and Kwong (J Glob Optim 34:369–398, 2006) . In this method smoothed functions are solutions of an ...initial-value problem for a heat diffusion equation with external heat source. As shown in Lau and Kwong (J Glob Optim 34:369–398, 2006), the source helps to control global minima of the smoothed functions—they are not shifted during the smoothing. In this note we point out that for certain (families of) objective functions the proposed method unfortunately does not affect the functions, in the sense, that the smoothed functions coincide with the respective objective function. The key point here is that the Laplacian might be too weak in order to smooth out critical points.
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This paper presents a mathematical model for heat and moisture transfer through cloth. A two-dimensional mathematical model, which considers complicated heat and mass transfer is developed. The ...coupled partial differential equations are created based on integrations of porous medium equations and heat, diffusion equations. A non-linearized implicit finite-difference method is presented to find numerical solutions of the two-dimensional simulation model. Results obtained by the present method are found to agree satisfactorily with the experimental data available in the literature.
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