Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. II. Continuous-wave results

We investigate the performance of the method proposed in Part I of this paper in several situations of interest in diffuse optical imaging of biological tissues. Monte Carlo simulations were extensively used to validate the approximate scaling relationship between higher-order and first-order self moments of the generalized temporal point-spread function in semi-infinite and slab geometry. More specifically we found that in a wide range of cases the scaling parameters c1, c2, c3 [see Eq. (36) of Part I] lie in the intervals (1.48, 1.58), (3.1, 3.7), and (8.5, 11.5), respectively. The scaling relationships between higher-order and first-order self moments are useful for the calculation of the perturbation of a single defect in a straightforward way. Although these relationships are more accurate for inclusions of linear size less than approximately 6mm, their performance is also studied for larger inclusions. A good agreement, to within approximately 10%, was found between the perturbations of single and multiple defects calculated with the proposed method and those obtained by Monte Carlo simulations. We also provide formulas for the calculation of the moments up to the fourth order for which it is clear how lower-order moments can be used for the calculation of higher-order moments.     

Multidistortion-invariant image recognition with radial harmonic Fourier moments

We propose radial harmonic Fourier moments, which are shifting, scaling, rotation, and intensity invariant. Compared with Chebyshev-Fourier moments, the new moments have superior performance near the origin and better ability to describe small images in terms of image-reconstruction errors and noise sensitivity. A multidistortion-invariant pattern-recognition experiment was performed with radial harmonic Fourier moments.     

Recognition of Polynomial Plane Curves Under Affine Transformations

 We present a new method to decide if two algebraic plane curves are (or are not) affine equivalent. The method is based on describing the curves by means of local parametrizations around related points. To that end we introduce a new type of parametrizations, called Ancochea parametrizations, which are canonical under affine transformations. Received: February 1, 2001; revised version: February 8, 2002     

Aberration extraction in the hartmann test by use of spatial filters

Using a computer, we generated a set of filters to aid in the retrieval of aberration functions from Hartmanngrams. These filters consist of discrete two-dimensional data points, like the Hartmanngrams themselves, and are orthogonalized by the Gram-Schmidt procedure. The aberration coefficients are obtained by calculation of the scalar product of the Hartmanngram and each orthogonal filter.     

Multimodal medical image fusion based on discrete Tchebichef moments and pulse coupled neural network

Multimodal medical image fusion plays a vital role in clinical diagnoses and treatment planning. In many image fusion methods‐based pulse coupled neural network (PCNN), normalized coefficients are used to motivate the PCNN, and this makes the fused image blur, detail loss, and decreases contrast. Moreover, they are limited in dealing with medical images with different modalities. In this article, we present a new multimodal medical image fusion method based on discrete Tchebichef moments and pulse coupled neural network to overcome the aforementioned problems. First, medical images are divided into equal‐size blocks and the Tchebichef moments are calculated to characterize image shape, and energy of blocks is computed as the sum of squared non‐DC moment values. Then to retain edges and textures, the energy of Tchebichef moments for blocks is introduced to motivate the PCNN with adaptive linking strength. Finally, large firing times are selected as coefficients of the fused image. Experimental results show that the proposed scheme outperforms state‐of‐the‐art methods and it is more effective in processing medical images with different modalities. © 2017 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 27, 57–65, 2017     

Optimal processors for images with an arbitrary number of gray levels

We present a new group of processors, optimal in a maximum-likelihood sense, for target location in images with a discrete number of gray levels. The discrete gray-level distribution can be of any arbitrary form. We compare the performance of the processor derived for five discrete levels with the performance of a processor derived for a continuous Gaussian distribution and show that there are cases when only the processor derived for discrete levels will exhibit satisfactory performance. We give an explanation of this difference based on moment analysis and show how the correlation orders are related to statistical moments of the input scene.     

基于Gabor滤波系数高阶矩的图像检索

在分析Gabor滤波器进行图像纹理特征提取的基础上,提出了利用多尺度和多方向Gabor滤波系数的高阶矩提取图像特征进行CBIR的方法,利用滤波系数的方差给出了基于Gabor滤波组提取的图像纹理特征的平滑度和纹理一致性算法,并采用四个尺度和六个方向的滤波系数的能量、方差、峰态、平滑度和一致性组成了CBIR特征向量.采用Brodatz纹理库和Corel图像库中的典型图像进行了对比实验.实验证明,提出的方法比传统的Gabor滤波进行CBIR具有更高的查准率.     

Numerical simulation of acoustic band gaps in homogenized elastic composites

The dispersion of acoustic or elastodynamic waves in elastic composites are studied using the homogenized model. We consider heterogeneous periodic structures consisting of soft but heavy inclusions embedded in a stiffer matrix. By virtue of the asymptotic homogenization technique in conjunction with an appropriate scaling of the elasticity coefficients in the inclusions, the limit model exhibits the band gaps in wave propagation due to the negative effective mass. This phenomenon can be revealed by studying guided waves in discrete mass-spring structures with scale-dependent parameters. The main purpose of the paper is to justify the applicability of the homogenized model of the heterogeneous elastic continuum for prediction of the band gaps in structures featured by a finite scale of heterogeneities. We show the band gaps numerical identification and discus aspects of anisotropy, microstructure geometry and material contrast between the constituents in the context of the long wave dispersion.     

Minimax Analysis for Finite-horizon Inventory Models

We consider stochastic finite-horizon inventory models with discrete distributions that are incompletely specified by selected moments, percentiles, or a combination of moments and percentiles. The objective is to determine an inventory policy that minimizes the maximum expected cost over the class of demand distributions satisfying the specifications described above. We show that many inventory models of this form can be solved by a sequence of linear programs.     

Determining cracks in gears using adaptive wavelet transform approach

A new family of biorthogonal wavelets used to identify fault in gears is dealt with. The fault detection analyses and methods presented in this paper are based on signals created by a faultless gear and by a gear with a crack in the tooth root, caused through operating conditions. The new wavelets are a generalization of biorthogonal wavelet systems. In the analysis, smoothness is controlled independently and discrete finite variation is used to optimise the synthesis bank. The procedure measure dispenses with a measure of differentiability, requiring a large number of vanishing wavelet moments in favour of a smoothness measure that is based on the fact that, in most practical applications, only a finite depth of the filter bank tree is involved.     

涉及离散变量的函数统计矩点估计法

点估计法对于仅包含连续随机变量的函数和系统的随机分析具有原理简洁清晰、操作简单易行的优点,并可以直接给出除均值和标准差之外的其他低阶统计矩。然而,对于客观存在的或者是需处理为的涉及离散随机变量的系统,现有的点估计法无能为力。为解决这一问题,该文基于一般随机系统的形式解析解,导出了涉及离散变量函数和系统的统计矩估计的理论表达式;然后,将其与现有的点估计法相结合,给出了涉及离散变量的函数和系统的低阶矩估计的点估计法;最后,通过理论推导和算例分析两种方式验证了建议方法的合理性和有效性,且指出该方法对包含离散变量的一般工程随机系统分析的适用性。     

Ordered moments and relation to Radon transform of Wigner quasiprobability

Abstract

It is shown that the symmetrically ordered moments of boson operators for a single boson mode can be reconstructed from the corresponding moments of the Radon transform of the Wigner quasiprobability for discrete sets of equidistant inequivalent angles which solve the circle division problem. This reconstruction is sometimes simpler than the corresponding reconstruction of the normally ordered moments where one first has to multiply the Radon transform with Hermite polynomials in comparison to power functions for symmetrically ordered moments and then to integrate. The connection to the reconstruction for the general class of s-ordered moments is established. The transition from discrete sets of angles to integration over angles via averaging over the discrete angles is made. The results are applied to displaced squeezed thermal states. It is shown how the ordered moments for these states can be explicitly found from the calculated Radon transform of the Wigner quasiprobability. The obtained formulae for these moments possess independent interest since they contribute to the discussion of the properties of the most general class of states with quasiprobabilities of Gaussian form with many possible special cases as, for example, squeezed coherent states and squeezed thermal states.     

Multiscale analysis of the intensity fluctuation in a time series of dynamic speckle patterns

We propose the application of a method based on the discrete wavelet transform to detect, identify, and measure scaling behavior in dynamic speckle. The multiscale phenomena presented by a sample and displayed by its speckle activity are analyzed by processing the time series of dynamic speckle patterns. The scaling analysis is applied to the temporal fluctuation of the speckle intensity and also to the two derived data sets generated by its magnitude and sign. The application of the method is illustrated by analyzing paint-drying processes and bruising in apples. The results are discussed taking into account the different time organizations obtained for the scaling behavior of the magnitude and the sign of the intensity fluctuation.     

Minimum-mean-square-error filters for detecting a noisy target in background noise

A minimum-mean-square-error filter is proposed to detect a noisy target in spatially nonoverlapping background noise. In this model, both the background noise that is spatially nonoverlapping with the target and the noise that is additive to the target and the input image are considered. The criterion used to design the filter is to minimize the mean-square-error between the filter output and a delta function located at the target position in the presence of the noise. Computer-simulation results for a number of noisy input images are presented, and the performance of the filter is determined. We also test the filter discrimination against undesired objects and tolerance to target distortions, such as rotation and scaling.     

Convergent optical correlator aligment based on frequency filtering

The convergent correlator is widely used but it presents the drawback of the alignment requirements: fine focusing of the input scene Fourier transform on the filter plane, filter centering, scaling the scene Fourier transform to match the filter size, and azimuth matching of the filter with the input scene. We propose a set of tests to obtain a precise alignment of the convergent correlator. These methods are based on frequency filtering properties and they are applicable either for amplitude input or for phase-encoded input. The tests we present allow us to fulfill all the alignment requirements. The theory on which these tests are based is explained. The experimental results obtained during the alignment procedure are presented. We show some additional verifications of the correct alignment of the convergent correlator.     

On the existence of maximum entropy distributions with four and more assigned moments

It is known that the probability distribution satisfy the Maximum Entropy Principle (MEP) if the available data consist in four moments of probability density function. Two problems are typically associated with use of MEP: the definition of the range of acceptable values for the moments M_i; the evaluation of the coefficients a_j. Both problems have already been accurately resolved by analytical procedures when the first two moments of the distribution are known.

In this work, the analytical solution in the case of four known moments is provided and a criterion for confronting the general case (whatever the number of known moments) is expounded. The first four moments are expressed in nondimensional form through the expectation and the coefficients of variation, skewness and kurtosis. The range of their acceptable values is obtained from the analytical properties of the differential equations which govern the problem and from the Schwarz inequality.     

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. I. Theory

We approach the perturbative solution to the diffusion equation for the case of absorbing inclusions embedded in a heterogeneous scattering medium by using general properties of the radiative transfer equation and the solution of the Fredholm equation of the second kind given by the Neumann series. The terms of the Neumann series are used to obtain the expression of the moments of the generalized temporal point-spread function derived in transport theory. The moments are calculated independently by using Monte Carlo simulations for validation of the theory. While the mixed moments are correctly derived from the theory by using the solution of the diffusion equation in the geometry of interest, in order to obtain the self moments we should reframe the problem in transport theory and use a suitable solution of the radiative transfer equation for the calculation of the multiple integrals of the corresponding Neumann series. Since the rigorous theory leads to impractical formulas, in order to simplify and speed up the calculation of the self moments, we propose a heuristic method based on the calculation of only a single integral and some scaling parameters. We also propose simple quadrature rules for the calculation of the mixed moments for speeding up the computation of perturbations due to multiple defects. The theory can be developed in the continuous-wave domain, the time domain, and the frequency domain. In a companion paper [J. Opt. Soc. Am. A23, 2119 (2006)] we discuss the conditions of applicability of the theory in practical cases found in diffuse optical imaging of biological tissues.     

On the use of sectional techniques for the solution of depolymerization population balances: Results on a discrete-continuous mesh

To study the discrete bond-breaking phenomena of depolymerization, the use of a fully continuous Population Balance Equation (PBE) is inadequate to embody all the inherent characteristics of the process, thus resulting in the need for a discrete-continuous mesh. Here, the performance of the fixed pivot technique (FPT) and the cell average technique (CAT) in approximating discrete depolymerization was extensively compared and evaluated. Both methods show different accuracy depending on the breakage mechanisms. For chain-end scission, the FPT and the CAT solutions coincide and satisfactorily predict the population densities and moments. We identified a previously-not-reported issue of a precipitous drop in the number density at the boundary of discrete and continuous region specifically for chain-end scission. We fixed this problem by modifying the particle allocation functions at the boundary points. For random scission, by introducing modifications that mimic the inherently discrete bond-breaking depolymerization process, both techniques predict the population densities and moments accurately at a very coarse mesh, even though the performance of the CAT pales in comparison with the FPT. In all assessed cases, the FPT is more computationally efficient and easily implemented. The assessments in this present work intend to provide a clear-cut direction to efficient and economical modelling of depolymerization processes.     

Image analysis by fast improved radial harmonic-Fourier moments algorithm

Radial harmonic-Fourier moments (RHFMs) are popular for image reconstruction and invariant pattern recognition due to their properties of translation, scaling and rotation invariant. RHFMs possess lower computation complexity as compared to Zernike moments and Bessel-Fourier moments. However, they always suffer from discontinuity, numerical instability near the center of image, and reconstruction error, especially have a rise for higher order of moments. In this paper, an improvement of radial harmonic-Fourier moments (IRHFMs) is proposed for effectively avoiding the above-mentioned problems.In this paper, a 2D fast Fourier transform algorithm also is applied to the image matrix to obtain the IRHFMs. Simulation experimental results demonstrate the proposed IRHFMs perform better than traditional RHFMs and other classic orthogonal moments including the latest image moments, for example, polar harmonic Fourier moments in terms of the image reconstruction capability and rotation invariant recognition accuracy in noise-free and noisy conditions.     

Discrete Wavelet Transform Signal Analyzer

This paper addresses the problem of processing biological data, such as cardiac beats in the audio and ultrasonic range, and on calculating wavelet coefficients in real time, with the processor clock running at a frequency of present application-specified integrated circuits and field programmable gate array. The parallel filter architecture for discrete wavelet transform (DWT) has been improved, calculating the wavelet coefficients in real time with hardware reduced up to 60%. The new architecture, which also processes inverse DWT, is implemented with the Radix-2 or the Booth-Wallace constant multipliers. One integrated circuit signal analyzer in the ultrasonic range, including series memory register banks, is presented.