minimum cross entropy thresholding abstract the threshold selection problem is solved by minimizing the cross entropy between the image and its segmented version the cross entropy is formulated in a pixel to pixel basis between the two images and a computationally attractive algorithm employing the histogram is developed without making a priori assumptions about the population distribution this method provides an unbiased estimate of a binarized version of the image in an information theoretic sense

image thresholding based on the em algorithm and the generalized gaussian distribution in this paper a novel parametric and global image histogram thresholding method is presented it is based on the estimation of the statistical parameters of object and background classes by the expectation maximization em algorithm under the assumption that these two classes follow a generalized gaussian gg distribution the adoption of such a statistical model as an alternative to the more common gaussian model is motivated by its attractive capability to approximate a broad variety of statistical behaviors with a small number of parameters since the quality of the solution provided by the iterative em algorithm is strongly affected by initial conditions which if inappropriately set may lead to unreliable estimation a robust initialization strategy based on genetic algorithms gas is proposed experimental results obtained on simulated and real images confirm the effectiveness of the proposed method

a simple weighted thresholding method for the segmentation of pigmented skin lesions in macroscopic images this work proposes a simple and yet effective thresholding method to segment pigmented skin lesions in macroscopic photographs automatically segmentation is one of the first steps in computer aided diagnosis of skin cancers therefore an accurate segmentation may play an important clinical role we develop an algorithm that searches for a thin rectangular shaped region near the image borders that is likely to contain mostly skin pixels segmentation is obtained by adapting otsu s thresholding method by combining independent threshold estimates computed from histograms of different parts of a new intensity image designed to discriminate lesions from background skin the proposed approach exploits the fact that the object of interest is approximately centered in the input photograph a cross diagonal sampling scheme helps to balance the size of the classes when the area of the lesion and the area of the surrounding skin are very different a post processing stage that includes morphological filtering and a weighted scheme to select the most salient object follows the experimental results suggest that the method potentially can be used successfully to segment atypical nevi and melanomas in lesions with a highly heterogeneous background skin the proposed algorithm is of interest for use in clinical settings as part of a cad system highlightsa simple and yet effective segmentation method for skin lesions is proposed a novel intensity map helps to discriminate lesions from background skin a multiple thresholding scheme helps to balance the contribution of the classes segmentation relies on a modified version of otsu s functional the proposed method may be used in clinical settings as part of cad system

thresholding based on variance and intensity contrast a new thresholding criterion is formulated for segmenting small objects by exploring the knowledge about intensity contrast it is the weighted sum of within class variance and intensity contrast between the object and background theoretical bounds of the weight are given for the uniformly distributed background and object followed by the procedure to estimate the weight from prior knowledge tests against two real and two synthetic images show that small objects can be extracted successfully irrespective of the complexity of background and difference in class sizes

a generalized multiclass histogram thresholding approach based on mixture modelling this paper presents a new approach to multi class thresholding based segmentation it considerably improves existing thresholding methods by efficiently modeling non gaussian and multi modal class conditional distributions using mixtures of generalized gaussian distributions mogg the proposed approach seamlessly 1 extends the standard otsu s method to arbitrary numbers of thresholds and 2 extends the kittler and illingworth minimum error thresholding to non gaussian and multi modal class conditional data moggs enable efficient representation of heavy tailed data and multi modal histograms with flat or sharply shaped peaks experiments on synthetic data and real world image segmentation show the performance of the proposed approach with comparison to recent state of the art techniques highlightsgeneralizing thresholding to multi modal class segmentation classes are modeled using mixtures of generalized gaussian distributions formulation of thresholding based on maximum likelihood estimation application to image foreground segmentation

bounds on eigenvalues of the hadamard product and the fan product of matrices we prove an upper bound for the spectral radius of the hadamard product of nonnegative matrices and a lower bound for the minimum eigenvalue of the fan product of m matrices these improve two existing results

generalized icm for image segmentation based on tsallis statistics abstract in this paper the iterated conditional modes optimization method of a markov random field technique for image segmentation is generalized based on tsallis statistics it is observed that for some q entropic index values the new algorithm performs better segmentation than the classical one the proposed algorithm also does not have a local minimum problem and reaches a global minimum energy point although the number of iterations remains the same as icm based on the findings of the new algorithm it can be expressed that the new technique can be used for the image segmentation processes in which the objects are gaussian or nearly gaussian distributed

m tensors and nonsingular m tensors abstract the m matrix is an important concept in matrix theory and has many applications recently this concept has been extended to higher order tensors 18 in this paper we establish some important properties of m tensors and nonsingular m tensors an m tensor is a z tensor we show that a z tensor is a nonsingular m tensor if and only if it is semi positive thus a nonsingular m tensor has all positive diagonal entries an m tensor regarding as the limit of a sequence of nonsingular m tensors has all nonnegative diagonal entries we introduce even order monotone tensors and present their spectral properties in matrix theory a z matrix is a nonsingular m matrix if and only if it is monotone this is no longer true in the case of higher order tensors we show that an even order monotone z tensor is an even order nonsingular m tensor but not vice versa an example of an even order nontrivial monotone z tensor is also given

on polynomial matrix spectral factorization by symmetric extraction we revise the 1963 davis algorithm 2 for the spectral factorization of a para hermitian nonnegative polynomial matrix phi by symmetric factor extraction this algorithm is careless about zeros at infinity by introducing the notion of diagonal reducedness of phi we obtain an easy sufficient test for the absence of zeros at infinity we show then how to get phi diagonally reduced by diagonal excess reduction steps similar to the oono and yasuura steps removing all zeros at infinity and then how to remove synunetrically finite zeros while keeping el diagonally reduced hence free of zeros at infinity this results in a revised symmetric extraction spectral factorization algorithm with monotone degree control an example shows the didactical conceptual simplicity of the method appropriate symmetric extraction is discovered by revising and discovering important particular one sided factor extraction properties of polynomial matrices

information measures in scale spaces this article investigates renyi s 1976 generalized entropies under linear and nonlinear scale space evolutions of images scale spaces are useful computer vision concepts for both scale analysis and image restoration we regard images as densities and prove monotony and smoothness properties for the generalized entropies the scale space extended generalized entropies are applied to global scale selection and size estimations finally we introduce an entropy based fingerprint description for textures

new lower bounds on eigenvalue of the hadamard product of an m matrix and its inverse abstract some new lower bounds for the minimum eigenvalue of the hadamard product of an m matrix and its inverse are given these bounds improve the results of h b li t z huang s q shen h li lower bounds for the minimum eigenvalue of hadamard product of an m matrix and its inverse linear algebra appl 420 2007 235 247

t tests f tests and otsu s methods for image thresholding otsu s binarization method is one of the most popular image thresholding methods student s t test is one of the most widely used statistical tests to compare two groups this paper aims to stress the equivalence between otsu s binarization method and the search for an optimal threshold that provides the largest absolute student s t statistic it is then naturally demonstrated that the extension of otsu s binarization method to multi level thresholding is equivalent to the search for optimal thresholds that provide the largest f statistic through one way analysis of variance anova furthermore general equivalences between some parametric image thresholding methods and the search for optimal thresholds with the largest likelihood ratio test statistics are briefly discussed

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

an image thresholding method using a minimum weighted squared distortion criterion we present a new thresholding method for image segmentation in which thresholds are selected on the basis of a minimum weighted squared distortion criterion an iterative algorithm which is named a supervised lloyd algorithm to satisfy the criterion is derived in order to achieve reliable segmentation we discuss how the weight coefficients of the criterion must be tuned by a supervisor two supervised approaches based on a probabilistic histogram model and typical images in processing images are treated in detail

threshold selection using renyi s entropy image segmentation is an important and fundamental task in many digital image processing systems image segmentation by thresholding is the simplest technique and involves the basic assumption that objects and background in the digital image have distinct gray level distributions in this paper we present a general technique for thresholding of digital images based on renyi s entropy our method includes two of the previously proposed well known global thresholding methods the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

a novel numerical method to determine the algebraic multiplicity of nonlinear eigenvalues we generalize the algebraic multiplicity of the eigenvalues of nonlinear eigenvalue problems neps to the rational form and give the extension of the argument principle in addition we propose a novel numerical method to determine the algebraic multiplicity of the eigenvalues of the neps in a given region by the contour integral method finally some numerical experiments are reported to illustrate the effectiveness of our method

a medial axis transformation for grayscale pictures blum s medial axis transformation mat for binary pictures yields medial axis points that lie midway between opposite borders of a region or along angle bisectors this note discusses a generalization of the mat in which a score is computed for each point p of a grayscale picture based on the gradient magnitudes at pairs of points that have p as their midpoint these scores are high at points that lie midway between pairs of antiparallel edges or along angle bisectors so that they define a mat like skeleton which we may call the gradmat however this skeleton is rather sensitive to the presence of noise edges or to irregularities in the region edges and it also is subject to artifacts created by pairs of edges belonging to different objects

template matching of binary targets in grey scale images a nonparametric approach this paper introduces a nonparametric similarity measure based on the kolmogorov smirnov ks statistic to be used in template matching problems where a target of binary characteristics is to be located in a grey scale image ks statistic yields the best expected value for a binary domain similarity measure if the threshold selection to binarize the image had been optimized to take into account the geometric constraints of the template there is however no need to actually binarize the image some good properties of a ks based similarity measure are exposed and compared with the corresponding properties of normalized correlation a practical algorithm to implement a template matching procedure based on the ks statistic is shown and its computing time is compared with normalized correlation a ks based similarity measure proves to be usually much faster computationally that normalized correlation finally some experimental results are shown

numerical methods for finding multiple eigenvalues of matrices depending on parameters let a alpha lambda be a square matrix dependent on parameters alpha and lambda of which we choose lambda as the eigenvalue parameter many computational problems are equivalent to finding a point alpha lambda such that a alpha lambda has a multiple eigenvalue lambda lambda at alpha alpha an incomplete qr decomposition of a matrix dependent on several parameters is proposed based on the developed theory two new algorithms are presented for computing multiple eigenvalues of a alpha lambda with geometric multiplicity m ge 2 a third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity m 1 but which also appears to have local quadratic convergence to semi simple eigenvalues convergence analyses of these methods are given several numerical examples are presented which illustrate the behaviour and applications of our methods

analysis of fuzzy thresholding schemes abstract fuzzy thresholding schemes preserve the structural details embedded in the original gray distribution in this paper various fuzzy thresholding schemes are analysed in detail thresholding scheme based on fuzzy clustering has been extended to a possibilistic framework the characteristic difference for assignment of membership of fuzzy algorithms and their correspondence with conventional hard thresholding schemes have been investigated a possible direction towards unifying a number of hard and fuzzy thresholding schemes has been presented

sensitivity analysis of the largest dependent eigenvalue functions of eigensystems this paper presents and discusses the first order sensitivity of the largest eigenvalue functions of eigensystems the analysis is based on investigating the entries of the matrices associated with the finite element formulations these entries are continuously differentiable functions but the dependent eigenvalue functions may be continuous nondifferentiable the main emphasis of this contribution is the derivation and the investigation of this analysis under the assumption that the generalized dependent eigenvalue functions are continuous nondifferentiable

some characterizations of m tensors via digraphs abstract for a tensor a a i 1 i m c n n the associated digraph of a has the vertex set v a 1 n and the arc set of a is e a i j a i i 2 i m 0 j i 2 i m i i in this paper we give some characterizations of m tensors and h tensors by using the associated digraph of a tensor

on some properties of three different types of triangular blocked tensors abstract we define and study three different types of upper and lower triangular blocked tensors which are all generalizations of the triangular blocked matrices and are also generalizations of reducible or weakly reducible tensors we study some common properties as well as different properties of these three types of triangular blocked tensors we obtain the formulas for the determinants characteristic polynomials and spectra of the first and second type triangular blocked tensors and give an example to show that these formulas no longer hold for the third type triangular blocked tensors we prove that the product of any two n 1 n r upper or lower triangular blocked tensors of the first or second or third type is still an n 1 n r upper or lower triangular blocked tensor of the same type we also prove that if an n 1 n r upper triangular blocked tensor of the first or second or third type has a left k inverse then its unique left k inverse is still an n 1 n r upper triangular blocked tensor of all the three types also if it has a right k inverse then all of its right k inverses are still n 1 n r upper triangular blocked tensors of all the three types by showing that the left k inverse if any of a weakly irreducible nonsingular m tensor is a positive tensor we show that the left k inverse if any of a first or second or third type normal n 1 n r upper triangular blocked nonsingular m tensor is an n 1 n r upper triangular blocked tensor of all the three types all of whose diagonal blocks are positive tensors we also show that every order m dimension n tensor is permutation similar to some third type normal upper triangular blocked tensor all of whose diagonal blocks are irreducible we give an example to show that this is not true for the first type normal upper triangular blocked tensor

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

efficient circular thresholding otsu s algorithm for thresholding images is widely used and the computational complexity of determining the threshold from the histogram is o n where n is the number of histogram bins when the algorithm is adapted to circular rather than linear histograms then two thresholds are required for binary thresholding we show that surprisingly it is still possible to determine the optimal threshold in o n time the efficient optimal algorithm is over 300 times faster than traditional approaches for typical histograms and is thus particularly suitable for real time applications we further demonstrate the usefulness of circular thresholding using the adapted otsu criterion for various applications including analysis of optical flow data indoor outdoor image classification and non photorealistic rendering in particular by combining circular otsu feature with other colour texture features a 96 9 correct rate is obtained for indoor outdoor classification on the well known iitm scid2 data set outperforming the state of the art result by 4 3

noise driven anisotropic diffusion filtering of mri a new filtering method to remove rician noise from magnetic resonance images is presented this filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for mri as the speckle reducing anisotropic diffusion did for ultrasound images the parameters of the filter are automatically chosen from the estimated noise this property improves the convergence rate of the diffusion while preserving contours leading to more robust and intuitive filtering the partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations this new filter combines volumetric planar and linear components of the local image structure the numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented in the experiments the new filter leads to the best results

multilevel image thresholding based on 2d histogram and maximum tsallis entropy a differential evolution approach multilevel thresholding amounts to segmenting a gray level image into several distinct regions this paper presents a 2d histogram based multilevel thresholding approach to improve the separation between objects recent studies indicate that the results obtained with 2d histogram oriented approaches are superior to those obtained with 1d histogram based techniques in the context of bi level thresholding here a method to incorporate 2d histogram related information for generalized multilevel thresholding is proposed using the maximum tsallis entropy differential evolution de a simple yet efficient evolutionary algorithm of current interest is employed to improve the computational efficiency of the proposed method the performance of de is investigated extensively through comparison with other well known nature inspired global optimization techniques such as genetic algorithm particle swarm optimization artificial bee colony and simulated annealing in addition the outcome of the proposed method is evaluated using a well known benchmark the berkley segmentation data set bsds300 with 300 distinct images

an eigenvalue method for testing positive definiteness of a multivariate form in this paper we present an eigenvalue method for testing positive definiteness of a multivariate form this problem plays an important role in the stability study of nonlinear autonomous systems via lyapunov s direct method in automatic control at first we apply the d andrea dickenstein version of the classical macaulay formulas of the resultant to compute the symmetric hyperdeterminant of an even order supersymmetric tensor by using the supersymmetry property we give detailed computation procedures for the bezoutians and specified ordering of monomials in this approach we then use these formulas to calculate the characteristic polynomial of a fourth order three dimensional supersymmetric tensor and give an eigenvalue method for testing positive definiteness of a quartic form of three variables some numerical results of this method are reported

on minimum cross entropy thresholding over last few years several papers have been written on entropy based thresholding some of these methods use the gray level histogram while others use entropy associated with the two dimensional histogram or the co occurrence matrix recently li and lee proposed a thresholding scheme that is aimed to minimize the cross entropy this note first points out a certain conceptual problem and then proposes two algorithms which are free from that problem the proposed schemes are tested on several data sets the results are encouraging

on kublanovskaya s approach to the solution of the generalized latent value problem for functional lambda matrices in siam j numer anal 7 1970 pp 532 537 kublanovskaya proposed a quadratically convergent algorithm for computing the eigenvalues of the generalized latent value problem for lambda matrices in this contribution we show that kublanovskaya s algorithm does not constitute a newton iteration though it can be justified through its equivalence with the generalized rayleigh quotient an alternative iteration scheme that can provide a higher order of convergence is proposed

optimal threshold selection for tomogram segmentation by projection distance minimization grey value thresholding is a segmentation technique commonly applied to tomographic image reconstructions many procedures have been proposed to optimally select the grey value thresholds based on the tomogram data only e g using the image histogram in this paper a projection distance minimization pdm method is presented that uses the tomographic projection data to determine optimal thresholds these thresholds are computed by minimizing the distance between the forward projection of the segmented image and the measured projection data an important contribution of the current paper is the efficient implementation of the forward projection method which makes the use of the original projection data as a segmentation criterion feasible simulation experiments applied to various phantom images show that our proposed method obtains superior results compared to established histogram based projection data methods

application of the conditional population mixture model to image segmentation the problem of image segmentation is considered in the context of a mixture of probability distributions the segments fall into classes a probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function a numerical example is given choice of the number of classes using akaike s information criterion aic for model identification is illustrated

a novel image thresholding method based on parzen window estimate image segmentation is one of the most important and fundamental tasks in image processing and techniques based on image thresholding are typically simple and computationally efficient however the image segmentation results depend heavily on the chosen image thresholding methods in this paper histogram is integrated with the parzen window technique to estimate the spatial probability distribution of gray level image values and a novel criterion function is designed by optimizing the criterion function an optimal global threshold is obtained the experimental results for synthetic real world and images demonstrate the success of the proposed image thresholding method as compared with the otsu method the met method and the entropy based method

multilevel minimum cross entropy threshold selection based on particle swarm optimization thresholding is one of the popular and fundamental techniques for conducting image segmentation many thresholding techniques have been proposed in the literature among them the minimum cross entropy thresholding mcet have been widely adopted although the mcet method is effective in the bilevel thresholding case it could be very time consuming in the multilevel thresholding scenario for more complex image analysis this paper first presents a recursive programming technique which reduces an order of magnitude for computing the mcet objective function then a particle swarm optimization pso algorithm is proposed for searching the near optimal mcet thresholds the experimental results manifest that the proposed pso based algorithm can derive multiple mcet thresholds which are very close to the optimal ones examined by the exhaustive search method the convergence of the proposed method is analyzed mathematically and the results validate that the proposed method is efficient and is suited for real time applications

some inequalities on the minimum h eigenvalue of the fan product of z tensors abstract in this paper some bounds on the minimum h eigenvalue of a z tensor and the fan product of z tensors are given by applying the bounds we obtain some criteria for m tensors and the positive definiteness of the fan product of z tensors and give some properties for the determinant of the fan product of m tensors

optimum image thresholding via class uncertainty and region homogeneity thresholding is a popular image segmentation method that converts a gray level image into a binary image the selection of optimum thresholds has remained a challenge over decades besides being a segmentation tool on its own often it is also a step in many advanced image segmentation techniques in spaces other than the image space we introduce a thresholding method that accounts for both intensity based class uncertainty a histogram based property and region homogeneity an image morphology based property a scale based formulation is used for region homogeneity computation at any threshold intensity based class uncertainty is computed by fitting a gaussian to the intensity distribution of each of the two regions segmented at that threshold the theory of the optimum thresholding method is based on the postulate that objects manifest themselves with fuzzy boundaries in any digital image acquired by an imaging device the main idea here is to select that threshold at which pixels with high class uncertainty accumulate mostly around object boundaries to achieve this a threshold energy criterion is formulated using class uncertainty and region homogeneity such that at any image location a high energy is created when both class uncertainty and region homogeneity are high or both are low finally the method selects that threshold which corresponds to the minimum overall energy the method has been compared to a maximum segmented image information method superiority of the proposed method was observed both qualitatively on clinical medical images as well as quantitatively on 250 realistic phantom images generated by adding different degrees of blurring noise and background variation to real objects segmented from clinical images

some new bounds on eigenvalues of the hadamard product and the fan product of matrices abstract let a and b be nonsingular m matrices a lower bound on the minimum eigenvalue q b a 1 for the hadamard product of a 1 and b and a lower bound on the minimum eigenvalue q a b for the fan product of a and b are given in addition an upper bound on the spectral radius a b of nonnegative matrices a and b is also obtained these bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices a and b

dynamic context cooperative quantum behaved particle swarm optimization based on multilevel thresholding applied to medical image segmentation this paper proposes a dynamic context cooperative quantum behaved particle swarm optimization algorithm the proposed algorithm incorporates a new method for dynamically updating the context vector each time it completes a cooperation operation with other particles we first explain how this leads to enhanced search ability and improved optimization over previous methods and demonstrate this empirically with comparative experiments using benchmark test functions we then demonstrate a practical application of the proposed method by showing how it can be applied to optimize the parameters for otsu image segmentation for processing medical images comparative experimental results show that the proposed method outperforms other state of the art methods from the literature

proof of a conjecture of fiedler and markham let a be an n n nonsingular m matrix for the hadamard product a a 1 m fiedler and t l markham conjectured in linear algebra appl 10l 1988 1 that q a a 1 2 n where q a a 1 is the smallest eigenvalue in modulus of a a 1 we considered this conjecture in linear algebra appl 288 1999 259 having observed an incorrect proof in linear algebra appl 144 1991 171 and obtained that q a a 1 2 n n 1 n the present paper gives a proof for this conjecture

thresholding using relaxation if a picture contains dark objects on a light background or vice versa the objects can be extracted by thresholding i e by classifying the pixels into light and dark classes if the picture is noisy so that the object and background gray level populations overlap there will be errors in the thresholded output a relaxation process can be used to reduce these errors we classify the pixels probabilistically and then adjust the probabilities for each pixel based on its neighbors probabilities with light reinforcing light and dark dark when this adjustment process is iterated the dark probabilities become very high for pixels that belong to dark regions and vice versa so that thresholding becomes trivial

on some new bounds for eigenvalues of the hadamard product and the fan product of matrices abstract let a and b be nonnegative matrices a new upper bound on the spectral radius a b is obtained meanwhile a new lower bound on the smallest eigenvalue q a b for the fan product and a new lower bound on the minimum eigenvalue q b a 1 for the hadamard product of b and a 1 of two nonsingular m matrices a and b are given these bounds improve some results of li et al 9 and generalize some corresponding results the new estimating formulae are only depending on the entries of matrices a and b therefore they are easy to calculate

a technique of three level thresholding based on probability partition and fuzzy 3 partition thresholding is a commonly used technique in image segmentation selecting the correct thresholds is a critical issue in this paper the relationship between a probability partition pp and a fuzzy c partition fp in thresholding is given this relationship and the entropy approach are used to derive a thresholding technique to select the best fuzzy c partition the measure of the selection quality is the compatibility between the fp and the pp generated by the problem an entropy function defined by the pp and fp is used to measure the compatibility a necessary condition of the entropy function arriving at a maximum is derived based on this condition an efficient algorithm for three level thresholding is deduced experiments to verify the efficiency of the proposed method and comparison to some existing techniques are also presented the experiment results show that our proposed method gives the best performance in three level thresholding using fuzzy c partition

performance analysis for a class of iterative image thresholding algorithms a performance analysis procedure that analyses the properties of a class of iterative image thresholding algorithms is described the image under consideration is modeled as consisting of two maximum entropy primary images each of which has a quasi gaussian probability density function three iterative thresholding algorithms identified to share a common iteration architecture are employed for thresholding 4595 synthetic images and 24 practical images the average performance characteristics including accuracy stability speed and consistency are analysed and compared among the algorithms both analysis and practical thresholding results are presented

solving polynomial eigenvalue problems by means of the ehrlich aberth method abstract given the n n matrix polynomial p x i 0 k p i x i we consider the associated polynomial eigenvalue problem this problem viewed in terms of computing the roots of the scalar polynomial det p x is treated in polynomial form rather than in matrix form by means of the ehrlich aberth iteration the main computational issues are discussed namely the choice of the starting approximations needed to start the ehrlich aberth iteration the computation of the newton correction the halting criterion and the treatment of eigenvalues at infinity we arrive at an effective implementation which provides more accurate approximations to the eigenvalues with respect to the methods based on the qz algorithm the case of polynomials having special structures like palindromic hamiltonian symplectic etc where the eigenvalues have special symmetries in the complex plane is considered a general way to adapt the ehrlich aberth iteration to structured matrix polynomials is introduced numerical experiments which confirm the effectiveness of this approach are reported

maximum likelihood thresholding based on population mixture models maximum likelihood thresholding methods are presented on the basis of population mixture models it turns out that the standard thresholding proposed by otsu which is based on a discriminant criterion and also minimizes the mean square errors between the original image and the resultant binary image is equivalent to the maximization of the likelihood of the conditional distribution in the population mixture model under the assumption of normal distributions with a common variance it is also shown that kittler and illingworth s thresholding which minimizes a criterion related to the average classification error rate assuming normal distribution with different variances is equivalent to the maximization of the likelihood of the joint distribution in the population mixture model a multi thresholding algorithm based on dynamic programming is also presented

an inequality for the hadamard product of an m matrix and an inverse m matrix abstract an estimate from below the smallest eigenvalue q a c of the hadamard product a c of an m matrix a and an inverse m matrix c is proved in particular if a is an m matrix of order n we obtain the inequality q a a 1 1 n

efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization the fuzzy c partition entropy has been widely adopted as a global optimization technique for finding the optimized thresholds for multilevel image segmentation however it involves expensive computation as the number of thresholds increases and often yields noisy segmentation results since spatial coherence is not enforced in this paper an iterative calculation scheme is presented for reducing redundant computations in entropy evaluation the efficiency of threshold selection is further improved through utilizing the artificial bee colony algorithm as the optimization technique finally instead of performing thresholding for each pixel independently the presented algorithm oversegments the input image into small regions and uses the probabilities of fuzzy events to define the costs of different label assignments for each region the final segmentation results is computed using graph cut which produces smooth segmentation results the experimental results demonstrate the presented iterative calculation scheme can greatly reduce the running time and keep it stable as the number of required thresholds increases quantitative evaluations over 20 classic images also show that the presented algorithm outperforms existing multilevel segmentation approaches

a thresholding method based on two dimensional renyi s entropy in this paper we present a new thresholding technique based on two dimensional renyi s entropy the two dimensional renyi s entropy was obtained from the two dimensional histogram which was determined by using the gray value of the pixels and the local average gray value of the pixels this new method extends a method due to sahoo et al pattern recognition 30 1997 71 and includes a previously proposed global thresholding method due to abutaleb pattern recognition 47 1989 22 further our method extends a global thresholding method due to chang et al ieee trans image process 4 1995 370 to the two dimensional setting the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

multiple region segmentation without supervision by adaptive global maximum clustering in this paper we propose a new method of segmenting an image into several sets of pixels with similar intensity values called regions a multiple region segmentation problem is unstable because the result considerably depends on the number of regions given a priori therefore one of the most important tasks in solving the problem is automatically finding the number of regions the method we propose is able to find the reasonable number of distinct regions not only for clean images but also for noisy ones our method is made up of two procedures first we develop the adaptive global maximum clustering in this procedure we deal with an image histogram and automatically obtain the number of significant local maxima of the histogram this number indicates the number of different regions in the image second we derive a simple and fast calculation to segment an image composed of distinct multiple regions then we split an image into multiple regions according to the previous procedure finally we show the efficiency of our method by comparing it with other previous methods

thresholding of digital images using two dimensional entropies abstract thresholding is an important form of image segmentation and is a first step in the processing of images for many applications the selection of suitable thresholds is ideally an automatic process requiring the use of some criterion on which to base the selection one such criterion is the maximization of the information theoretic entropy of the resulting background and object probability distributions most processes using this concept have made use of the one dimensional 1d grey level histogram of the image in an effort to use more of the information available in the image the present approach evaluates two dimensional 2d entropies based on the 2d grey level local average grey level histogram or scatterplot the 2d threshold vector that maximizes both background and object class entropies is selected

a gaussian mixture based image segmentation algorithm this paper focuses on the formulation development and evaluation of an autonomous segmentation algorithm which can segment targets in a wide class of highly degraded images a segmentation algorithm based on a gaussian mixture model of a two class image is selected because it has the potential for effective segmentation provided that the histogram of the image approximates a gaussian mixture and the parameters of the model can be estimated accurately a selective sampling approach based on the laplacian of the image is developed to transform the histogram of any image into an approximation of a gaussian mixture and a new estimation method which uses information derived from the tails of the mixture density is formulated to estimate the model parameters the resulting selective sampling gaussian mixture parameter estimation segmentation algorithm is tested and evaluated on a set of real degraded target images and the results show that the algorithm is able to accurately segment diverse images

convergence factors of newton methods for nonlinear eigenvalue problems abstract consider a complex sequence k k 0 convergent to c with order p n the convergence factor is typically defined as the fraction c k k 1 k p in the limit k in this paper we prove formulas characterizing c k in the limit k for two different newton type methods for nonlinear eigenvalue problems the formulas are expressed in terms of the left and right eigenvectors the two treated methods are called the method of successive linear problems mslp and augmented newton and are widely used in the literature we prove several explicit formulas for c k for both methods formulas for both methods are found for simple as well as double eigenvalues in some cases we observe in examples that the limit c k as k does not exist for cases where this limit does not appear to exist we prove other limiting expressions such that a characterization of c k in the limit is still possible

improving consistency and reducing ambiguity in stochastic labeling an optimization approach we approach the problem of labeling a set of objects from a quantitative standpoint we define a world model in terms of transition probabilities and propose a definition of a class of global criteria that combine both ambiguity and consistency a projected gradient algorithm is developed to minimize the criterion we show that the minimization procedure can be implemented in a highly parallel manner results are shown on several examples and comparisons are made with relaxation labeling techniques

some properties of strong h tensors and general h tensors abstract h matrices matrices whose comparison matrix is an m matrix are well studied in matrix theory and have numerous applications e g linear complementarity problems and iterative methods for solving systems of linear equations in this article we establish some properties of their tensor counterparts strong h tensors and general h tensors

a multilevel image thresholding using the honey bee mating optimization image thresholding is an important technique for image processing and pattern recognition many thresholding techniques have been proposed in the literature among them the maximum entropy thresholding met has been widely applied in this paper a new multilevel met algorithm based on the technology of the honey bee mating optimization hbmo is proposed this proposed method is called the maximum entropy based honey bee mating optimization thresholding mehbmot method three different methods such as the particle swarm optimization pso the hybrid cooperative comprehensive learning based pso algorithm hcoclpso and the fast otsu s method are also implemented for comparison with the results of the proposed method the experimental results manifest that the proposed mehbmot algorithm can search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method in comparison with the other three thresholding methods the segmentation results using the mehbmot algorithm is the best and its computation time is relatively low furthermore the convergence of the mehbmot algorithm can rapidly achieve and the results validate that the proposed mehbmot algorithm is efficient

a diary on information theory foreword on the mathematical notion of information games of chance and probability theory notes on the teaching of probability theory variations on a theme by fibonacci the mathematical theory of trees

segmentation of images having unimodal distributions a gradient relaxation method based on maximizing a criterion function is studied and compared to the nonlinear probabilistic relaxation method for the purpose of segmentation of images having unimodal distributions although both methods provide comparable segmentation results the gradient method has the additional advantage of providing control over the relaxation process by choosing three parameters which can be tuned to obtain the desired segmentation results at a faster rate examples are given on two different types of scenes

a relative entropy based approach to image thresholding abstract in this paper we present a new image thresholding technique which uses the relative entropy also known as the kullback leiber discrimination distance function as a criterion of thresholding an image as a result a gray level minimizing the relative entropy will be the desired threshold the proposed relative entropy approach is different from two known entropy based thresholding techniques the local entropy and joint entropy methods developed by n r pal and s k pal in the sense that the former is focused on the matching between two images while the latter only emphasized the entropy of the co occurrence matrix of one image the experimental results show that these three techniques are image dependent and the local entropy and relative entropy seem to perform better than does the joint entropy in addition the relative entropy can complement the local entropy and joint entropy in terms of providing different details which the others cannot as far as computing saving is concerned the relative entropy approach also provides the least computational complexity

stability analysis of time delay systems using a contour integral method in this paper we propose a contour integral method for computing the rightmost characteristic roots of systems of linear time delay differential equations ddes these roots are very important in the context of stability analysis of the time delay systems the effectiveness of the proposed method is illustrated by some numerical experiments

fast pyramidal algorithms for image thresholding in this paper we present fast pyramidal versions of three sequential algorithms for the thresholding of images consisting of n grey levels for each of the sequential algorithms having complexities between o n time and o n2 time we propose a parallel version which runs in o lg n time on a pyramidal machine with an n n base

on a conjecture of fiedler and markham abstract for the hadamard product a a 1 of an m matrix a and its inverse a 1 fiedler and markham conjectured that q a a 1 2 n see m fiedler and t l markham linear algebra appl 101 1988 1 8 where q a a 1 is the smallest eigenvalue in modulus of a a 1 the present paper studies this conjecture an incorrect proof is given in li ching and chen ji cheng linear algebra appl 144 1991 171 178 and establishes q a a 1 2 n n 1 n for some special matrices the conjecture is proved

a new criterion for automatic multilevel thresholding a new criterion for multilevel thresholding is proposed the criterion is based on the consideration of two factors the first one is the discrepancy between the thresholded and original images and the second one is the number of bits required to represent the thresholded image based on a new maximum correlation criterion for bilevel thresholding the discrepancy is defined and then a cost function that takes both factors into account is proposed for multilevel thresholding by minimizing the cost function the classification number that the gray levels should be classified and the threshold values can be determined automatically in addition the cost function is proven to possess a unique minimum under very mild conditions computational analyses indicate that the number of required mathematical operations in the implementation of our algorithm is much less than that of maximum entropy criterion finally simulation results are included to demonstrate their effectiveness

some inequalities for the hadamard product and the fan product of matrices abstract if a and b are nonsingular m matrices a sharp lower bound on the smallest eigenvalue a b for the fan product of a and b is given and a sharp lower bound on a b 1 for the hadamard product of a and b 1 is derived in addition we also give a sharp upper bound on the spectral radius a b for nonnegative matrices a and b