robust spatially constrained fuzzy c means algorithm for brain mr image segmentation abstract objective accurate brain tissue segmentation from magnetic resonance mr images is an essential step in quantitative brain image analysis and hence has attracted extensive research attention however due to the existence of noise and intensity inhomogeneity in brain mr images many segmentation algorithms suffer from limited robustness to outliers over smoothness for segmentations and limited segmentation accuracy for image details to further improve the accuracy for brain mr image segmentation a robust spatially constrained fuzzy c means rscfcm algorithm is proposed in this paper method firstly a novel spatial factor is proposed to overcome the impact of noise in the images by incorporating the spatial information amongst neighborhood pixels the proposed spatial factor is constructed based on the posterior probabilities and prior probabilities and takes the spatial direction into account it plays a role as linear filters for smoothing and restoring images corrupted by noise therefore the proposed spatial factor is fast and easy to implement and can preserve more details secondly the negative log posterior is utilized as dissimilarity function by taking the prior probabilities into account which can further improve the ability to identify the class for each pixel finally to overcome the impact of intensity inhomogeneity we approximate the bias field at the pixel by pixel level by using a linear combination of orthogonal polynomials the fuzzy objective function is then integrated with the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain mr images simultaneously results to demonstrate the performances of the proposed algorithm for the images with without skull stripping the first group of experiments is carried out in clinical 3t weighted brain mr images which contain quite serious intensity inhomogeneity and noise then we quantitatively compare our algorithm to state of the art segmentation approaches by using jaccard similarity on benchmark images obtained from ibsr and brainweb with different level of noise and intensity inhomogeneity the comparison results demonstrate that the proposed algorithm can produce higher accuracy segmentation and has stronger ability of denoising especially in the area with abundant textures and details conclusion in this paper the rscfcm algorithm is proposed by utilizing the negative log posterior as the dissimilarity function introducing a novel factor and integrating the bias field estimation model into the fuzzy objective function this algorithm successfully overcomes the drawbacks of existing fcm type clustering schemes and em type mixture models our statistical results mean and standard deviation of jaccard similarity for each tissue on both synthetic and clinical images show that the proposed algorithm can overcome the difficulties caused by noise and bias fields and is capable of improving over 5 segmentation accuracy comparing with several state of the art algorithms

geometry of free loci and factorization of noncommutative polynomials abstract the free singularity locus of a noncommutative polynomial f is defined to be the sequence of hypersurfaces z n f x m n k g det f x 0 the main theorem of this article shows that f is irreducible if and only if z n f is eventually irreducible a key step in the proof is an irreducibility result for linear pencils arising from this is a free singularity locus nullstellensatz for noncommutative polynomials apart from consequences to factorization in a free algebra the paper also discusses its applications to invariant subspaces in perturbation theory and linear matrix inequalities in real algebraic geometry

power monoids a bridge between factorization theory and arithmetic combinatorics abstract we extend a few fundamental aspects of the classical theory of non unique factorization as presented in geroldinger and halter koch s 2006 monograph on the subject to a non commutative and non cancellative setting in the same spirit of baeth and smertnig s work on the factorization theory of non commutative but cancellative monoids baeth and smertnig 2015 5 then we bring in power monoids and applying the abstract machinery developed in the first part we undertake the study of their arithmetic more in particular let h be a multiplicatively written monoid the set p fin h of all non empty finite subsets of h is naturally made into a monoid which we call the power monoid of h and is non cancellative unless h is trivial by endowing it with the operation x y x y x y x y power monoids are in disguise one of the primary objects of interest in arithmetic combinatorics and here for the first time we tackle them from the perspective of factorization theory proofs lead to consider various properties of finite subsets of n that can or cannot be split into a sumset in a non trivial way giving rise to a rich interplay with additive number theory

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

a realization theorem for sets of distances abstract let h be an atomic monoid the set of distances h of h is the set of all d n with the following property there are irreducible elements u 1 u k v 1 v k d such that u 1 u k v 1 v k d but u 1 u k cannot be written as a product of l irreducible elements for any l n with k l k d it is well known and easy to show that if h is nonempty then min h gcd h in this paper we show conversely that for every finite nonempty set n with min gcd there is a finitely generated krull monoid h such that h

simultaneous parameter estimation and segmentation of gibbs random fields using simulated annealing an adaptive segmentation algorithm is developed which simultaneously estimates the parameters of the underlying gibbs random field grf and segments the noisy image corrupted by additive independent gaussian noise the algorithm which aims at obtaining the maximum a posteriori map segmentation is a simulated annealing algorithm that is interrupted at regular intervals for estimating the grf parameters maximum likelihood ml estimates of the parameters based on the current segmentation are used to obtain the next segmentation it is proven that the parameter estimates and the segmentations converge in distribution to the ml estimate of the parameters and the map segmentation with those parameter estimates respectively due to computational difficulties however only an approximate version of the algorithm is implemented the approximate algorithm is applied on several two and four region images with different noise levels and with first order and second order neighborhoods

statistical models of partial volume effect statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived the models assume either gaussian system sampling noise or intrinsic material variances with gaussian or poisson statistics in particular a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing or the material could have nondistinct values with a poisson distribution as might be the case in nuclear medicine images general forms of the probability density functions are presented for the n material cases and particular forms for two and three material cases are derived these models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component

stochastic and deterministic networks for texture segmentation several texture segmentation algorithms based on deterministic and stochastic relaxation principles and their implementation on parallel networks are described the segmentation process is posed as an optimization problem and two different optimality criteria are considered the first criterion involves maximizing the posterior distribution of the intensity field given the label field maximum a posteriori estimate the posterior distribution of the texture labels is derived by modeling the textures as gauss markov random fields gmrfs and characterizing the distribution of different texture labels by a discrete multilevel markov model a stochastic learning algorithm is proposed this iterated hill climbing algorithm combines fast convergence of deterministic relaxation with the sustained exploration of the stochastic algorithms but is guaranteed to find only a local minimum the second optimality criterion requires minimizing the expected percentage of misclassification per pixel by maximizing the posterior marginal distribution and the maximum posterior marginal algorithm is used to obtain the corresponding solution all these methods implemented on parallel networks can be easily extended for hierarchical segmentation results of the various schemes in classifying some real textured images are presented

factorizations of matrices over semirings in this paper as a generalization of prime boolean matrices and prime fuzzy matrices we study semiprime matrices over chain semirings using the relationship between semiprime matrices and their row spaces we show that a nonmonomial matrix with full semiring rank can be expressed as a product of elementary matrices and semiprime matrices furthermore we show that a nonmonomial regular matrix with full semiring rank can be expressed as a product of elementary matrices

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

positive periodic solutions for a class of neutral delay gause type predator prey system abstract by using a continuation theorem based on coincidence degree theory we establish easily verifiable criteria for the existence of positive periodic solutions for neutral delay gause type predator prey system x t x t r t a t x t 1 x t 2 t x t y t 1 t y t y t d t h t x t 2 t in addition our results are applicable to neutral delay predator prey systems with different types of functional responses such as holling type ii and ivlev type

factorization theory from commutative to noncommutative settings abstract we study the non uniqueness of factorizations of non zero divisors into atoms irreducibles in noncommutative rings to do so we extend concepts from the commutative theory of non unique factorizations to a noncommutative setting several notions of factorizations as well as distances between them are introduced in addition arithmetical invariants characterizing the non uniqueness of factorizations such as the catenary degree the invariant and the tame degree are extended from commutative to noncommutative settings we introduce the concept of a cancellative semigroup being permutably factorial and characterize this property by means of corresponding catenary and tame degrees also we give necessary and sufficient conditions for there to be a weak transfer homomorphism from a cancellative semigroup to its reduced abelianization applying the abstract machinery we develop we determine various catenary degrees for classical maximal orders in central simple algebras over global fields by using a natural transfer homomorphism to a monoid of zero sum sequences over a ray class group we also determine catenary degrees and the permutable tame degree for the semigroup of non zero divisors of the ring of n n upper triangular matrices over a commutative domain using a weak transfer homomorphism to a commutative semigroup

detection and inpainting of facial wrinkles using texture orientation fields and markov random field modeling facial retouching is widely used in media and entertainment industry professional software usually require a minimum level of user expertise to achieve the desirable results in this paper we present an algorithm to detect facial wrinkles imperfection we believe that any such algorithm would be amenable to facial retouching applications the detection of wrinkles imperfections can allow these skin features to be processed differently than the surrounding skin without much user interaction for detection gabor filter responses along with texture orientation field are used as image features a bimodal gaussian mixture model gmm represents distributions of gabor features of normal skin versus skin imperfections then a markov random field model is used to incorporate the spatial relationships among neighboring pixels for their gmm distributions and texture orientations an expectation maximization algorithm then classifies skin versus skin wrinkles imperfections once detected automatically wrinkles imperfections are removed completely instead of being blended or blurred we propose an exemplar based constrained texture synthesis algorithm to inpaint irregularly shaped gaps left by the removal of detected wrinkles imperfections we present results conducted on images downloaded from the internet to show the efficacy of our algorithms

on the atomicity of monoid algebras abstract let m be a commutative cancellative monoid and let r be an integral domain the question of whether the monoid ring r x m is atomic provided that both m and r are atomic dates back to the 1980s in 1993 roitman gave a negative answer to the question for m n 0 he constructed an atomic integral domain r such that the polynomial ring r x is not atomic however the question of whether a monoid algebra f x m over a field f is atomic provided that m is atomic has been open since then here we offer a negative answer to this question first we exhibit for any infinite cardinal a torsion free atomic monoid m of rank satisfying that the monoid domain r x m is not atomic for any integral domain r then for every n 2 and for each field f of finite characteristic we find a torsion free atomic monoid m of rank n such that f x m is not atomic finally we construct a torsion free atomic monoid m of rank 1 such that z 2 x m is not atomic

an extension of the standard mixture model for image segmentation standard gaussian mixture modeling gmm is a well known method for image segmentation however the pixels themselves are considered independent of each other making the segmentation result sensitive to noise to reduce the sensitivity of the segmented result with respect to noise markov random field mrf models provide a powerful way to account for spatial dependences between image pixels however their main drawback is that they are computationally expensive to implement and require large numbers of parameters based on these considerations we propose an extension of the standard gmm for image segmentation which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard gmm the proposed model is easy to implement and compared with mrf models requires lesser number of parameters we also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log likelihood based on the gradient method experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness accuracy and effectiveness of the proposed model in image segmentation as compared to other methods based on standard gmm and mrf models

a generalized em algorithm for 3 d bayesian reconstruction from poisson data using gibbs priors a generalized expectation maximization gem algorithm is developed for bayesian reconstruction based on locally correlated markov random field priors in the form of gibbs functions and on the poisson data model for the m step of the algorithm a form of coordinate gradient ascent is derived the algorithm reduces to the em maximum likelihood algorithm as the markov random field prior tends towards a uniform distribution three different gibbs function priors are examined reconstructions of 3 d images obtained from the poisson model of single photon emission computed tomography are presented

number theory of matrix semigroups abstract unlike factorization theory of commutative semigroups which are well studied very little literature exists describing factorization properties in noncommutative semigroups perhaps the most ubiquitous noncommutative semigroups are semigroups of square matrices and this article investigates the factorization properties within certain subsemigroups of m n z the semigroup of n n matrices with integer entries certain important invariants are calculated to give a sense of how unique or non unique factorization is in each of these semigroups

expectation maximization algorithms null spaces and map image restoration a computationally efficient easily implementable algorithm for map restoration of images degraded by blur and additive correlated gaussian noise using gibbs prior density functions is derived this algorithm is valid for a variety of complete data spaces the constraints upon the complete data space arising from the gaussian image formation model are analyzed and a motivation is provided for the choice of the complete data based upon the ease of computation of the resulting em algorithms the overlooked role of the null space of the blur operator in image restoration is introduced an examination of this role reveals an important drawback to the use of the simulated annealing algorithm in maximizing a specific class of functionals an alternative iterative method for computing the nullspace component of a vector is given the ability of a simple gibbs prior density function to enable partial recovery of the component of an image within the nullspace of the blur operator is demonstrated

factorizations in upper triangular matrices over information semialgebras abstract an integral domain or a commutative cancellative monoid is atomic if every nonzero nonunit element factors into atoms and it satisfies the accp if every ascending chain of principal ideals eventually stabilizes the interplay between these two properties has been investigated since the 1970s an atomic domain or monoid satisfies the finite factorization property ffp if every element has only finitely many factorizations and it satisfies the bounded factorization property bfp if for each element there is a bound for the number of atoms in each of its factorizations these two properties have been systematically studied since they were introduced by anderson anderson and zafrullah in 1990 noetherian domains satisfy the bfp while dedekind domains satisfy the ffp it is well known that for commutative cancellative monoids and in particular for multiplicative monoids of integral domains ffp bfp accp atomic for n 2 we show that each of these four properties transfers back and forth between an information semialgebra s certain commutative cancellative semiring and the multiplicative monoid t n s consisting of n n upper triangular matrices over s we also show that a similar transfer behavior takes place if one replaces t n s by its submonoid u n s consisting of upper triangular matrices with units along their main diagonals as a consequence we find that the atomic chain ffp bfp accp atomic also holds for the two classes comprising the noncommutative monoids t n s and u n s finally we construct various rational information semialgebras to verify that in general none of the established implications is reversible

arithmetic of seminormal weakly krull monoids and domains abstract we study the arithmetic of seminormal v noetherian weakly krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes these monoids include seminormal orders in holomorphy rings in global fields the crucial property of seminormality allows us to give precise arithmetical results analogous to the well known results for krull monoids having finite class group and prime divisors in each class this allows us to show for example that unions of sets of lengths are intervals and to provide a characterization of half factoriality

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

multiple resolution segmentation of textured images a multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior in addition an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions both algorithms use a causal gaussian autoregressive model to describe the mean variance and spatial correlation of the image textures together the algorithms can be used to perform unsupervised texture segmentation the multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified this method results in accurate segmentations and requires significantly less computation than some previously known methods the field containing the classification of each pixel in the image is modeled as a markov random field segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint at each resolution the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks the unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the aic information criterion clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters concurrently the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached

a spatially constrained mixture model for image segmentation gaussian mixture models gmms constitute a well known type of probabilistic neural networks one of their many successful applications is in image segmentation where spatially constrained mixture models have been trained using the expectation maximization em framework in this letter we elaborate on this method and propose a new methodology for the m step of the em algorithm that is based on a novel constrained optimization formulation numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach

turbo segmentation of textured images we consider the problem of semi supervised segmentation of textured images existing model based approaches model the intensity field of textured images as a gauss markov random field to take into account the local spatial dependencies between the pixels classical bayesian segmentation consists of also modeling the label field as a markov random field to ensure that neighboring pixels correspond to the same texture class with high probability well known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion but these techniques are usually computationally intensive because they require a large number of iterations to converge in this paper we propose a new bayesian framework by modeling two dimensional textured images as the concatenation of two one dimensional hidden markov autoregressive models for the lines and the columns respectively a segmentation algorithm which is similar to turbo decoding in the context of error correcting codes is obtained based on a factor graph approach the proposed method estimates the unknown parameters using the expectation maximization algorithm

likelihood calculation for a class of multiscale stochastic models with application to texture discrimination a class of multiscale stochastic models based on scale recursive dynamics on trees has previously been introduced theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale e g 1 f processes as well as 1d markov processes and 2d markov random fields moreover efficient optimal estimation algorithms have been developed for these models by exploiting their scale recursive structure the authors exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation they illustrate one possible application to texture discrimination and demonstrate that likelihood based methods using the algorithm achieve performance comparable to that of gaussian markov random field based techniques which in general are prohibitively complex computationally

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a class adaptive spatially variant mixture model for image segmentation we propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model according to this model the pixel labels are random variables and a smoothness prior is imposed on them the main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models these gauss markov random field based priors allow all their parameters to be estimated in closed form via the maximum a posteriori map estimation using the expectation maximization methodology thus it is possible to introduce priors with multiple parameters that adapt to different aspects of the data numerical experiments are presented where the proposed map algorithms were tested in various image segmentation scenarios these experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model based segmentation

regularized constrained total least squares image restoration in this paper the problem of restoring an image distorted by a linear space invariant lsi point spread function psf that is not exactly known is formulated as the solution of a perturbed set of linear equations the regularized constrained total least squares rctls method is used to solve this set of equations using the diagonalization properties of the discrete fourier transform dft for circulant matrices the rctls estimate is computed in the dft domain this significantly reduces the computational cost of this approach and makes its implementation possible even for large images an error analysis of the rctls estimate based on the mean squared error mse criterion is performed to verify its superiority over the constrained total least squares ctls estimate numerical experiments for different errors in the psf are performed to test the rctls estimator objective and visual comparisons are presented with the linear minimum mean squared error lmmse and the regularized least squares rls estimator our experiments show that the rctls estimator reduces significantly ringing artifacts around edges as compared to the two other approaches

bayesian pixel classification using spatially variant finite mixtures and the generalized em algorithm a spatially variant finite mixture model is proposed for pixel labeling and image segmentation for the case of spatially varying mixtures of gaussian density functions with unknown means and variances an expectation maximization em algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities an a priori density function is formulated for the spatially variant mixture weights a generalized em algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived this algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent gaussian densities have been used for simplicity but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities the accuracy of the algorithm is quantitatively evaluated through monte carlo simulation and its performance is qualitatively assessed via experimental images from computerized tomography ct and magnetic resonance imaging mri

factorizations of upper triangular matrices if d is an integral domain in which every element can be factored as a product of irreducible elements then every element a tn d the semigroup of upper triangular matrices with nonzero determinant can be factored as a product of irreducible elements we classify both the irreducible elements and units of this cancellative semigroup having achieved this we provide a means of measuring the uniqueness or non uniqueness of these factorizations in terms of the uniqueness or non uniqueness of factorizations in d in addition to using well studied invariants from factorization theory of commutative semigroups we introduce a new tool weak transfer homomorphisms which are more appropriate for noncommutative settings

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

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

puiseux monoids and transfer homomorphisms abstract there are several families of atomic monoids whose arithmetical invariants have received a great deal of attention during the last two decades the factorization theory of finitely generated monoids strongly primary monoids krull monoids and c monoids are among the most systematically studied puiseux monoids which are additive submonoids of q 0 consisting of nonnegative rational numbers have only been studied recently in this paper we provide evidence that this family comprises plenty of monoids with a basically unexplored atomic structure we do this by showing that the arithmetical invariants of the well studied atomic monoids mentioned earlier cannot be transferred to most puiseux monoids via homomorphisms that preserve atomic configurations i e transfer homomorphisms specifically we show that transfer homomorphisms from a non finitely generated atomic puiseux monoid to a finitely generated monoid do not exist we also find a large family of puiseux monoids that fail to be strongly primary in addition we prove that the only nontrivial puiseux monoid that accepts a transfer homomorphism to a krull monoid is n 0 finally we classify the puiseux monoids that happen to be c monoids

algorithmic enumeration of ideal classes for quaternion orders we provide algorithms to count and enumerate representatives of the right ideal classes of an eichler order in a quaternion algebra defined over a number field we analyze the run time of these algorithms and consider several related problems including the computation of two sided ideal classes isomorphism classes of orders connecting ideals for orders and ideal principalization we conclude by giving the complete list of definite eichler orders with class number at most 2

upper triangular matrices over information algebras abstract factorization in matrix rings has been investigated in a wide variety of contexts recently this study has provided a wealth of information about how factorization works in noncommutative settings it is often the case that when s is a ring of matrices over a base ring r multiplicative factorization in r drives the multiplicative factorization in s that is the additive structure of r is largely irrelevant to how elements of s factor multiplicatively recently chen et al studied factorization of the semiring of upper triangular matrices with entries in n 0 the semiring of nonnegative integers in this work we show that their results fit within the larger context of factorization in upper triangular matrices over reduced information algebras we illustrate that factorization in t n h 0 depends on both the multiplicative and additive structure of h 0 if h 0 is such an information algebra we classify the irreducible elements of t n h 0 and describe the degree to which factorization in t n h 0 is nonunique by considering elasticities delta sets and unions of sets in addition we show that unlike many important classes of semigroups whose arithmetic has been studied t n h 0 is not transfer krull for h 0 n 0 we extend previously known results and give explicit descriptions of nonunique factorization in t n n 0

increasing positive monoids of ordered fields are ff monoids abstract given an ambient ordered field k a positive monoid is a countably generated additive submonoid of the nonnegative cone of k in this paper we first generalize several atomic features exhibited by puiseux monoids of the field of rational numbers to the more general setting of positive monoids of archimedean fields accordingly arguing that such generalizations might fail if the ambient field is not archimedean in particular we show that a positive monoid p of an archimedean field is a bf monoid provided that p 0 does not have 0 as a limit point then we prove our main result every increasing positive monoid of an ordered field is an ff monoid finally we deduce that every increasing positive monoid is hereditarily atomic

factorizations of block triangular matrices abstract transfer homomorphisms have long been used as tools in factorization theory the idea is to transfer information about factorizations in a semigroup of interest from simpler easier to understand semigroups unfortunately there exist noncommutative semigroups which admit no transfer homomorphism to any commutative semigroup the weak transfer homomorphism was introduced to study such semigroups in particular these weak transfer homomorphisms were used to study factorizations of semigroups of upper triangular matrices with entries coming from a commutative integral domain in this work we extend this study finding weak transfer homomorphisms to both commutative and noncommutative semigroups from upper triangular matrices with entries coming from noncommutative rings in particular we study factorizations of block triangular matrices

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

parameter estimation and tissue segmentation from multispectral mr images a statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time t sub 1 t sub 2 and proton density p sub d weighted magnetic resonance images the method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values t sub 1 t sub 2 p sub d at each location within that tissue regions the method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a markov random field prior in classifying the tissue types the method models the likelihood of realizing the images as a finite multivariate mixture function the class parameters associated with the tissue types i e the weighted intensity means variances and correlation coefficients of the multivariate function as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood the estimation fits the class parameters to the image data via the expectation maximization algorithm the number of classes associated with the tissue types is determined by the information criterion of minimum description length the method segments the tissue regions given the estimated class parameters by maximum a posteriori probability the prior is constructed by the tissue region membership of the first and second order neighborhood the method is tested by a few sets of t sub 1 t sub 2 and p sub d weighted images of the brain acquired with a 1 5 tesla whole body scanner the number of classes and the associated class parameters are automatically estimated the regions of different brain tissues are satisfactorily segmented

permanence and stability of equilibrium for a two prey one predator discrete model in this letter a predator prey system of two prey one predator discrete model is investigated it is proved that the system is permanence under some appropriate conditions by jacobian matrix method a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system meanwhile we give a suitable example for supporting our theoretical result

corrigendum algorithmic enumeration of ideal classes for quaternion orders this note corrects a mathematical error in the article algorithmic enumeration of ideal classes for quaternion orders siam j comput 39 2010 pp 1714 1747

a bayesian framework for image segmentation with spatially varying mixtures a new bayesian model is proposed for image segmentation based upon gaussian mixture models gmm with spatial smoothness constraints this model exploits the dirichlet compound multinomial dcm probability density to model the mixing proportions i e the probabilities of class labels and a gauss markov random field mrf on the dirichlet parameters to impose smoothness the main advantages of this model are two first it explicitly models the mixing proportions as probability vectors and simultaneously imposes spatial smoothness second it results in closed form parameter updates using a maximum a posteriori map expectation maximization em algorithm previous efforts on this problem used models that did not model the mixing proportions explicitly as probability vectors or could not be solved exactly requiring either time consuming markov chain monte carlo mcmc or inexact variational approximation methods numerical experiments are presented that demonstrate the superiority of the proposed model for image segmentation compared to other gmm based approaches the model is also successfully compared to state of the art image segmentation methods in clustering both natural images and images degraded by noise

persistence and global stability in a delayed gause type predator prey system without dominating instantaneous negative feedbacks abstract a delayed gause type predator prey system without dominating instantaneous negative feedbacks is investigated it is proved that the system is uniformly persistent under some appropriate conditions by means of constructing a suitable lyapunov functional sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system

texture segmentation using gaussian markov random fields and neural oscillator networks we propose an image segmentation method based on texture analysis our method is composed of two parts the first part determines a novel set of texture features derived from a gaussian markov random fields gmrf model unlike a gmrf based approach our method does not employ model parameters as features or require the extraction of features for a fixed set of texture types a priori the second part is a 2d array of locally excitatory globally inhibitory oscillator networks legion after being filtered for noise suppression features are used to determine the local couplings in the network when legion runs the oscillators corresponding to the same texture tend to synchronize whereas different texture regions tend to correspond to distinct phases in simulations a large system of differential equations is solved for the first time using a recently proposed method for integrating relaxation oscillator networks we provide results on real texture images to demonstrate the performance of our method

sets of lengths in maximal orders in central simple algebras abstract let o be a holomorphy ring in a global field k and r a classical maximal o order in a central simple algebra over k we study sets of lengths of factorizations of cancellative elements of r into atoms irreducibles in a large majority of cases there exists a transfer homomorphism to a monoid of zero sum sequences over a ray class group of o which implies that all the structural finiteness results for sets of lengths valid for commutative krull monoids with finite class group hold also true for r if o is the ring of algebraic integers of a number field k we prove that in the remaining cases no such transfer homomorphism can exist and that several invariants dealing with sets of lengths are infinite

statistic based map image reconstruction from poisson data using gibbs priors a statistical method for selecting the gibbs parameter in map image restoration from poisson data using gibbs priors is presented the gibbs parameter determines the degree to which the prior influences the restoration the presented method yields a map restored image minimally influenced by the prior for which a statistic falls within an appropriate confidence interval the method assumes that a close approximation to the blurring function is known a simple iterative feedback algorithm is presented to statistically select the parameter as the map image restoration is being performed this algorithm is heuristically based on a model reference control formulation but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value the performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2 d and 3 d images

robust student s t mixture model with spatial constraints and its application in medical image segmentation finite mixture model based on the student s t distribution which is heavily tailed and more robust than gaussian has recently received great attention for image segmentation a new finite student s t mixture model smm is proposed in this paper existing models do not explicitly incorporate the spatial relationships between pixels first our model exploits dirichlet distribution and dirichlet law to incorporate the local spatial constrains in an image secondly we directly deal with the student s t distribution in order to estimate the model parameters whereas the student s t distributions in previous models are represented as an infinite mixture of scaled gaussians that lead to an increase in complexity finally instead of using expectation maximization em algorithm the proposed method adopts the gradient method to minimize the higher bound on the data negative log likelihood and to optimize the parameters the proposed model is successfully compared to the state of the art finite mixture models numerical experiments are presented where the proposed model is tested on various simulated and real medical images

an em approach to map solution of segmenting tissue mixtures a numerical analysis this work presents an iterative expectation maximization em approach to the maximum a posteriori map solution of segmenting tissue mixtures inside each image voxel each tissue type is assumed to follow a normal distribution across the field of view fov furthermore all tissue types are assumed to be independent from each other under these assumptions the summation of all tissue mixtures inside each voxel leads to the image density mean value at that voxel the summation of all the tissue mixtures unobservable random processes leads to the observed image density at that voxel and the observed image density value also follows a normal distribution image data are observed to follow a normal distribution in many applications by modeling the underlying tissue distributions as a markov random field across the fov the conditional expectation of the posteriori distribution of the tissue mixtures inside each voxel is determined given the observed image data and the current iteration estimation of the tissue mixtures estimation of the tissue mixtures at next iteration is computed by maximizing the conditional expectation the iterative em approach to a map solution is achieved by a finite number of iterations and reasonable initial estimate this map em framework provides a theoretical solution to the partial volume effect which has been a major cause of quantitative imprecision in medical image processing numerical analysis demonstrated its potential to estimate tissue mixtures accurately and efficiently

quantification of mr brain images by mixture density and partial volume modeling the problem of automatic quantification of brain tissue by utilizing single valued single echo magnetic resonance imaging mri brain scans is addressed it is shown that this problem can be solved without classification or segmentation a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap the general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues the quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture this problem is solved by tree annealing with and without partial volume utilized the results compared and the sensitivity of the tree annealing algorithm to various parameters is exhibited the actual quantification is performed by two methods a classification based method called bayes quantification and parameter estimation results from each method are presented for synthetic and actual data

arithmetic of mori domains and monoids in this paper we introduce weakly c monoids as a new class of v noetherian monoids weakly c monoids generalize c monoids and make it possible to study multiplicative properties of a wide class of mori domains e g rings of generalized power series with coefficients in a field and exponents in a finitely generated monoid the main goal of the paper is to study the question when a weakly c monoid is locally tame after having proved a classification theorem for local tameness we use it to show that every locally tame weakly c monoid whose complete integral closure has finite class group has finite catenary degree and finite set of distances

component analysis approach to estimation of tissue intensity distributions of 3d images many segmentation algorithms in medical imaging rely on accurate modeling and estimation of tissue intensity probability density functions gaussian mixture modeling currently the most common approach has several drawbacks such as reliance on a gaussian model and iterative local optimization used to estimate the model parameters it also does not take advantage of substantially larger amount of data provided by 3d acquisitions which are becoming standard in clinical environment we propose a novel and completely non parametric algorithm to estimate the tissue intensity probabilities in 3d images instead of relying on traditional framework of iterating between classification and estimation we pose the problem as an instance of a blind source separation problem where the unknown distributions are treated as sources and histograms of image subvolumes as mixtures the new approach performed well on synthetic data and real magnetic resonance imaging mri scans of the brain robustly capturing intensity distributions of even small image structures and partial volume voxels

stability and delays in a predator prey system abstract sufficient conditions for both local and global stability of the positive equilibrium in a predator prey system with time delays are obtained by constructing suitable lyapunov functionals a remark on the mistake by k n murty and m a s srinivas j math anal appl 158 1991 333 341 is also included

geometric and combinatorial aspects of submonoids of a finite rank free commutative monoid abstract if f is an ordered field and m is a finite rank torsion free monoid then one can embed m into a finite dimensional vector space over f via the inclusion m gp m f z gp m where gp m is the grothendieck group of m let c be the class consisting of all monoids up to isomorphism that can be embedded into a finite rank free commutative monoid here we investigate how the atomic structure and arithmetic properties of a monoid m in c are connected to the combinatorics and geometry of its conic hull cone m f z gp m first we show that the submonoids of m determined by the faces of cone m account for all divisor closed submonoids of m then we appeal to the geometry of cone m to characterize whether m is a factorial half factorial and other half factorial monoid finally we investigate the cones of finitary primary finitely primary and strongly primary monoids in c along the way we determine the cones that can be realized by monoids in c and by finitary monoids in c

sets of lengths of factorizations of integer valued polynomials on dedekind domains with finite residue fields abstract let d be a dedekind domain with infinitely many maximal ideals all of finite index and k its quotient field let int d f k x f d d be the ring of integer valued polynomials on d given any finite multiset k 1 k n of integers greater than 1 we construct a polynomial in int d which has exactly n essentially different factorizations into irreducibles in int d the lengths of these factorizations being k 1 k n we also show that there is no transfer homomorphism from the multiplicative monoid of int d to a block monoid

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

statistical approach to segmentation of single channel cerebral mr images a statistical model is presented that represents the distributions of major tissue classes in single channel magnetic resonance mr cerebral images using the model cerebral images are segmented into gray matter white matter and cerebrospinal fluid csf the model accounts for random noise magnetic field inhomogeneities and biological variations of the tissues intensity measurements are modeled by a finite gaussian mixture smoothness and piecewise contiguous nature of the tissue regions are modeled by a three dimensional 3 d markov random field mrf a segmentation algorithm based on the statistical model approximately finds the maximum a posteriori map estimation of the segmentation and estimates the model parameters from the image data the proposed scheme for segmentation is based on the iterative conditional modes icm algorithm in which measurement model parameters are estimated using local information at each site and the prior model parameters are estimated using the segmentation after each cycle of iterations application of the algorithm to a sample of clinical mr brain scans comparisons of the algorithm with other statistical methods and a validation study with a phantom are presented the algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of mr images in the presence of the random noise and intensity inhomogeneities

global stability in delay differential systems without dominating instantaneous negative feedbacks abstract most of the global stability or convergence results appearing so far for delayed lotka volterra type systems or other delay differential systems require that the instantaneous negative feedbacks dominate both delayed feedback and interspecific interactions such a requirement is rarely met in real systems since feedbacks are generally delayed this leads to the long standing question under what conditions will the global stability of a nonnegative steady state of a differential delay system persist when time delays involved in some part of the negative feedbacks are small enough this paper presents a partial answer to this open question roughly our results show that if the delay differential system remains dissipative when delays are introduced then the above open question has an affirmative answer our results also improve some recent findings

a spatially constrained generative model and an em algorithm for image segmentation in this paper we present a novel spatially constrained generative model and an expectation maximization em algorithm for model based image segmentation the generative model assumes that the unobserved class labels of neighboring pixels in the image are generated by prior distributions with similar parameters where similarity is defined by entropic quantities relating to the neighboring priors in order to estimate model parameters from observations we derive a spatially constrained em algorithm that iteratively maximizes a lower bound on the data log likelihood where the penalty term is data dependent our algorithm is very easy to implement and is similar to the standard em algorithm for gaussian mixtures with the main difference that the labels posteriors are smoothed over pixels between each e and m step by a standard image filter experiments on synthetic and real images show that our algorithm achieves competitive segmentation results compared to other markov based methods and is in general faster

unsupervised image segmentation using an unlabeled region process abstract the segmentation of a gray scale image of regions of uniform or slowly varying intensity is discussed a gibbsian representation is given for a partition of a lattice with no labels the homogeneity of each segment is measured by the sample variance of observations in a region merging algorithm the posterior probability of the segmentation is gradually increased it is shown how to simulate partitions with the gibbs sampler and how to combine information in simulated segmentations when the segments cannot be grouped into genuine classes the segmentation methods are preferable to classification by iterated conditional modes icm or by the maximizer of posterior marginals mpm

on the arithmetic of krull monoids with finite davenport constant abstract let h be a krull monoid with class group g g p g the set of classes containing prime divisors and d g p the davenport constant of g p we show that the finiteness of the davenport constant implies the structure theorem for sets of lengths more precisely if d g p then there exists a constant m for which we derive an explicit upper bound in terms of d g p such that the set of lengths of every element a h is an almost arithmetical multiprogression with bound m

unsupervised texture segmentation using markov random field models the problem of unsupervised segmentation of textured images is considered the only explicit assumption made is that the intensity data can be modeled by a gauss markov random field gmrf the image is divided into a number of nonoverlapping regions and the gmrf parameters are computed from each of these regions a simple clustering method is used to merge these regions the parameters of the model estimated from the clustered segments are then used in two different schemes one being all approximation to the maximum a posterior estimate of the labels and the other minimizing the percentage misclassification error the proposed approach is contrasted with the algorithm of s lakshamanan and h derin 1989 which uses a simultaneous parameter estimation and segmentation scheme the results of the adaptive segmentation algorithm of lakshamanan and derin are compared with a simple nearest neighbor classification scheme to show that if enough information is available simple techniques could be used as alternatives to computationally expensive schemes

a markov random field model based approach to unsupervised texture segmentation using local and global spatial statistics many studies have proven that statistical model based texture segmentation algorithms yield good results provided that the model parameters and the number of regions be known a priori in this correspondence we present an unsupervised texture segmentation method that does not require knowledge about the different texture regions their parameters or the number of available texture classes the proposed algorithm relies on the analysis of local and global second and higher order spatial statistics of the original images the segmentation map is modeled using an augmented state markov random field including an outlier class that enables dynamic creation of new regions during the optimization process a bayesian estimate of this map is computed using a deterministic relaxation algorithm results on real world textured images are presented