Image Thresholding Using Two-Dimensional Tsallis Cross Entropy Based on Either Chaotic Particle Swarm Optimization or Decomposition

The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.

Two-Dimensional Entropy Method Based on Genetic Algorithm

Two dimensional(2 D) entropy method has to pay the price of time when applied to image segmentation. So the genetic algorithm is introduced to improve the computational efficiency of the 2 D entropy method. The proposed method uses both the gray value of a pixel and the local average gray value of an image. At the same time, the simple genetic algorithm is improved by using better reproduction and crossover operators. Thus the proposed method makes up the 2 D entropy method’s drawback of being time consuming, and yields satisfactory segmentation results. Experimental results show that the proposed method can save computational time when it provides good quality segmentation.

AUTOMATIC MULTILEVEL THRESHOLDING METHOD BASED ON MAXIMUM ENTROPY

In the multilevel thresholding segmentation of the image, the classification number is always given by the supervisor. To solve this problem, a fast multilevel thresholding algorithm considering both the threshold value and the classification number is proposed based on the maximum entropy, and the self-adaptive criterion of the classification number is given. The algorithm can obtain thresholds and automatically decide the classification number. Experimental results show that the algorithm is effective.

Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrodinger Equation

Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.

Comparison of different inversion methods of D-T_(2)two-dimensional nuclear magnetic resonance logging and applicability analysis

D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization methods)have been proposed successively,but most are limited to numerical simulations.This study focused on the applicability of different inversion methods for NMR logging data of various acquisition sequences,from which the optimal inversion method was selected based on the comparative analysis.First,the two-dimensional NMR logging principle was studied.Then,these inversion methods were studied in detail,and the precision and computational efficiency of CPMG and diffusion editing(DE)sequences obtained from oil-water and gas-water models were compared,respectively.The inversion results and calculation time of truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization were compared and analyzed through numerical simulations.The inversion method was optimized to process SP mode logging data from the MR Scanner instrument.The results showed that the TIST-regularization and LM-norm smoothing methods were more accurate for the CPMG and DE sequence echo trains of the oil-water and gas-water models.However,the LM-norm smoothing method was less time-consuming,making it more suitable for logging data processing.A case study in well A25 showed that the processing results by the LM-norm smoothing method were consistent with GEOLOG software.This demonstrates that the LM-norm smoothing method is applicable in practical NMR logging processing.

Mammogram Images Thresholding for Breast Cancer Detection Using Different Thresholding Methods

The purpose of this study is to apply different thresholding in mammogram images, and then we will determine which technique is the best in thresholding (extraction) malignant and benign tumors from the rest breast tissues. The used technique is Otsu method, because it is one of the most effective methods for most real world views with regard to uniformity and shape measures. Also, we present all the thresholding methods that used the concept of between class variance. We found from the experimental results that all the used thresholding techniques work well in detection normal breast tissues. But in abnormal tissues (breast tumors), we found that only neighborhood valley emphasis method gave best detection of malignant tumors. Also, the results demonstrate that variance and intensity contrast technique is the best in extraction the micro calcifications which represent the first signs of breast cancer.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

A New Regularized Minimum Error Thresholding Method

To overcome the shortcoming that the traditional minimum error threshold method can obtain satisfactory image segmentation results only when the object and background of the image strictly obey a certain type of probability distribution,one proposes the regularized minimum error threshold method and treats the traditional minimum error threshold method as its special case.Then one constructs the discrete probability distribution by using the separation between segmentation threshold and the average gray-scale values of the object and background of the image so as to compute the information energy of the probability distribution.The impact of the regularized parameter selection on the optimal segmentation threshold of the regularized minimum error threshold method is investigated.To verify the effectiveness of the proposed regularized minimum error threshold method,one selects typical grey-scale images and performs segmentation tests.The segmentation results obtained by the regularized minimum error threshold method are compared with those obtained with the traditional minimum error threshold method.The segmentation results and their analysis show that the regularized minimum error threshold method is feasible and produces more satisfactory segmentation results than the minimum error threshold method.It does not exert much impact on object acquisition in case of the addition of a certain noise to an image.Therefore,the method can meet the requirements for extracting a real object in the noisy environment.

THE CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPO SITION METHOD FOR SOLVING TWO-DIMENSIONAL ELLIPTIC EQUATION

This paper ix devoted to establishment of the Chebyshev pseudospectral domain de-composition scheme for solving two-dimensional elliptic equation. By the generalized equivalent variatiunal form, we can get the stability and convergence of this new scheme.

Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method

In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation

This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations

For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable.Numerical results indicate the effectiveness and accuracy of the method and con-firm the analysis.

A Context Sensitive Multilevel Thresholding Using Swarm Based Algorithms

In this paper, a comprehensive energy function is used to formulate the three most popular objective functions:Kapur's, Otsu and Tsalli's functions for performing effective multilevel color image thresholding. These new energy based objective criterions are further combined with the proficient search capability of swarm based algorithms to improve the efficiency and robustness. The proposed multilevel thresholding approach accurately determines the optimal threshold values by using generated energy curve, and acutely distinguishes different objects within the multi-channel complex images. The performance evaluation indices and experiments on different test images illustrate that Kapur's entropy aided with differential evolution and bacterial foraging optimization algorithm generates the most accurate and visually pleasing segmented images.

An Improved Double-Threshold Method Based on Gradient Histogram

This paper analyzes the characteristics of the output gradient histogram and shortages of several traditional automatic threshold methods in order to segment the gradient image better. Then an improved double-threshold method is proposed, which is combined with the method of maximum classes variance, estimating-area method and double-threshold method. This method can automatically select two different thresholds to segment gradient images. The computer simulation is performed on the traditional methods and this algorithm and proves that this method can get satisfying result. Key words gradient histogram image - threshold selection - double-threshold method - maximum classes variance method CLC number TP 391. 41 Foundation item: Supported by the National Nature Science Foundation of China (50099620) and the Project of Chenguang Plan in Wuhan (985003062)Biography: YANG Shen (1977-), female, Ph. D. candidate, research direction: multimedia information processing and network technology.

Study on the critical stress threshold of weakly cemented sandstone damage based on the renormalization group method

During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.

Optimal multilevel thresholding based on molecular kinetic theory optimization algorithm and line intercept histogram

Among all segmentation techniques, Otsu thresholding method is widely used. Line intercept histogram based Otsu thresholding method(LIH Otsu method) can be more resistant to Gaussian noise, highly efficient in computing time, and can be easily extended to multilevel thresholding. But when images contain salt-and-pepper noise, LIH Otsu method performs poorly. An improved LIH Otsu method(ILIH Otsu method) is presented, which can be more resistant to Gaussian noise and salt-and-pepper noise. Moreover, it can be easily extended to multilevel thresholding. In order to improve the efficiency, the optimization algorithm based on the kinetic-molecular theory(KMTOA) is used to determine the optimal thresholds. The experimental results show that ILIH Otsu method has stronger anti-noise ability than two-dimensional Otsu thresholding method(2-D Otsu method), LIH Otsu method, K-means clustering algorithm and fuzzy clustering algorithm.

Rational and Periodic Wave Solutions of Two-Dimensional Boussinesq Equation

Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.