some notes on the paper cone metric spaces and fixed point theorems of contractive mappings abstract huang and zhang reviewed cone metric spaces in 2007 huang long guang zhang xian cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 we shall prove that there are no normal cones with normal constant m 1 and for each k 1 there are cones with normal constant m k also by providing non normal cones and omitting the assumption of normality in some results of huang long guang zhang xian cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 we obtain generalizations of the results

common fixed points for maps on cone metric space the purpose of this paper is to generalize and to unify fixed point theorems of das and naik ciric jungck huang and zhang on complete cone metric space

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

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

common fixed points for g f type maps in cone metric spaces abstract in this paper we study common fixed points for the self and non self g f type maps in cone metric spaces our main results are related to the cases when g is f quasi contraction in a sense of das and naik and the cone need not be normal these results generalize several well known comparable results in the literature

texture analysis through a markovian modelling and fuzzyclassification application to urban area extraction fromsatellite images herein we propose a complete procedure to analyze and classify the texture of an image we apply this scheme to solve a specific image processing problem urban areas detection in satellite images first we propose to analyze the texture through the modelling of the luminance field with eight different chain based models we then derived a texture parameter from these models the effect of the lattice anisotropy is corrected by a renormalization group technique coming from statistical physics this parameter which takes into account local conditional variances of the image is compared to classical methods of texture analysis afterwards we develop a modified fuzzy cmeans algorithm that includes an entropy term the advantage of such an algorithm is that the number of classes does not need to be known a priori besides this algorithm provides us with further information i e the probability that a given pixel belongs to a given cluster finally we introduce this information in a markovian model of segmentation some results on spot5 simulated images spot3 images and ers1 radar images are presented these images are provided by the french national space agency cnes and the european space agency esa

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

multiresolution gauss markov random field models for texture segmentation this paper presents multiresolution models for gauss markov random fields gmrfs with applications to texture segmentation coarser resolution sample fields are obtained by subsampling the sample field at fine resolution although the markov property is lost under such resolution transformation coarse resolution non markov random fields can be effectively approximated by markov fields we present two techniques to estimate the gmrf parameters at coarser resolutions from the fine resolution parameters one by minimizing the kullback leibler distance and another based on local conditional distribution invariance we also allude to the fact that different gmrf parameters at the fine resolution can result in the same probability measure after subsampling and present the results for first and second order cases we apply this multiresolution model to texture segmentation different texture regions in an image are modeled by gmrfs and the associated parameters are assumed to be known parameters at lower resolutions are estimated from the fine resolution parameters the coarsest resolution data is first segmented and the segmentation results are propagated upward to the finer resolution we use the iterated conditional mode icm minimization at all resolutions our experiments with synthetic brodatz texture and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm

rhoades type fixed point theorems for a pair of nonself mappings abstract using suitable conditions of weak commutativity we prove theorems for a pair of nonself mappings which generalize earlier results due to rhoades and assad et al some illustrative examples and applications are also discussed

stochastic relaxation on partitions with connected components and its application to image segmentation we present a new method of segmentation in which images are segmented in partitions with connected components we give computationally inexpensive algorithms for probability simulation and simulated annealing on the space of partitions with connected components of a general graph in particular hastings algorithms 1970 and generalized metropolis algorithms are defined to avoid heavy computation to achieve segmentation we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph the algorithm is applied to segment gray level color and textured images

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

fuzzy model based clustering and its application in image segmentation a fuzzy generalized gaussian density ggd segmentation model is proposed a ggd based agglomerative fuzzy algorithm is developed a two stage fuzzy ggd segmentation algorithm is proposed this paper proposes a novel fuzzy model based unsupervised learning algorithm with boundary correction for image segmentation we propose a fuzzy generalized gaussian density ggd segmentation model and the ggd based agglomerative fuzzy algorithm for grouping image pixels the merits of algorithm are that it is not sensitive to initial parameters and that the number of groups can be estimated via the validation technique to minimize the objective function of the model we define a dissimilarity measure based on the kullbackleibler divergence of the ggds that computes the discrepancy between ggds in the space of generalized probability distributions to effectively segment images with various textures we propose a two stage fuzzy ggd segmentation algorithm the first stage adopts the proposed fuzzy algorithm to obtain initial segmentation and the second stage improves initial segmentation by image boundary correction experimental results show that our proposed method has a promising performance compared with existing approaches

scale space classification using area morphology we explore the application of area morphology to image classification from the input image a scale space is created by successive application of an area morphology operator the pixels within the scale space corresponding to the same image location form a scale space vector a scale space vector therefore contains the intensity of a particular pixel for a given set of scales determined in this approach by image granulometry using the standard k means algorithm or the fuzzy c means algorithm the image pixels can be classified by clustering the associated scale space vectors the scale space classifier presented here is rooted in the novel area open close and area close open scale spaces unlike other scale generating filters the area operators affect the image by removing connected components within the image level sets that do not satisfy the minimum area criterion to show that the area open close and area close open scale spaces provide an effective multiscale structure for image classification we demonstrate the fidelity causality and edge localization properties for the scale spaces the analysis also reveals that the area open close and area close open scale spaces improve classification by clustering members of similar objects more effectively than the fixed scale classifier experimental results are provided that demonstrate the reduction in intra region classification error and in overall classification error given by the scale space classifier for classification applications where object scale is important in both visual and objective comparisons the scale space approach outperforms the traditional fixed scale clustering algorithms and the parametric bayesian classifier for classification tasks that depend on object scale

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

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

a sequence based extension of mean field annealing using the forward backward algorithm application to image segmentation optimization based on mean field theory including mean field annealing mfa is widely used for discrete optimization label assignment problems defined on the pixel sites of an image one formulation of mfa is via maximum entropy where one seeks the joint distribution over the random assignments subject to an average level of cost mfa is obtained by assuming the assignments at each pixel are statistically independent given the observed image alternatively we make the less restrictive assumption of independent row labelings the independence assumption means that at each step mfa optimizes over only one pixel whereas our method jointly optimizes over an entire row i e our method is less greedy in principle an mfa extension could be developed that explicitly re estimates the row labeling distributions but such an approach is in practice infeasible even so we can indirectly implement this re estimation by re estimating quantities that determine the row labeling distributions these quantities are the a posteriori site probabilities re estimable via the well known forward backward f b algorithm thus our algorithm which descends in the me lagrangian free energy consists of iterative application of f b to the image rows columns at convergence maximum a posteriori site labeling is performed our method was applied to segmentation of both real and synthetic noise corrupted images it achieved lower markov random field model potentials and better segmentations compared with other methods and in high noise standard mfa

passive error concealment for wavelet coded i frames with an inhomogeneous gauss markov random field model in video communication over lossy packet networks e g the internet packet loss errors can severely damage the transmitted video the damaged video can largely be repaired with passive error concealment where neighboring information is used to estimate missing information we address the problem of passive error concealment for wavelet coded data with dispersive packetization the reported techniques of this kind have many problems and usually fail in the reconstruction of high frequency content this paper presents a novel locally adaptive error concealment method for subband coded i frames based on an inhomogeneous gaussian markov random field model we estimate the parameters of this model from a local context of each lost coefficient and we interpolate the lost coefficients accordingly the results demonstrate a significant improvement over the reported related methods both in terms of objective performance measures and visually the biggest improvement of the proposed method compared to the state of the art in the field is the correct reconstruction of high frequency information such as textures and edges

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

on ciric maps with a generalized contractive iterate at a point and fisher s quasi contractions in cone metric spaces in this paper we generalize and unify some results of sehgal and guseman and ciric s theorem for mappings with a generalized contractive iterate at a point to cone metric spaces in which the cone does not need to be normal as corollaries we obtain recent results of huang and zhang and raja and vaezpour furthermore we introduce the definition of fisher quasi contractions on cone metric spaces and study their properties among other things using new method of proof we solve the open problem for the interval of contractive constant l of ciric quasi contraction in non normal cone metric spaces and as sn immediate corollary we recover the recent result of rezapour and hamlbarani

restriction of a markov random field on a graph and multiresolution statistical image modeling the association of statistical models and multiresolution data analysis in a consistent and tractable mathematical framework remains an intricate theoretical and practical issue several consistent approaches have been proposed previously to combine markov random field mrf models and multiresolution algorithms in image analysis renormalization group subsampling of stochastic processes mrfs defined on trees or pyramids etc for the simulation or a practical use of these models in statistical estimation an important issue is the preservation of the local markovian property of the representation at the different resolution levels it is shown that this key problem may be studied by considering the restriction of a markov random field defined on some simple finite nondirected graph to a part of its original site set several general properties of the restricted field are derived the general form of the distribution of the restriction is given locality of the field is studied by exhibiting a neighborhood structure with respect to which the restricted field is an mrf sufficient conditions for the new neighborhood structure to be minimal are derived several consequences of these general results related to various multiresolution mrf based modeling approaches in image analysis are presented

common fixed point results for noncommuting mappings without continuity in cone metric spaces the existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions without appealing to continuity in a cone metric space is established these results generalize several well known comparable results in the literature

pair of non self mappings and common fixed points we study quasi contraction type non self mappings on takahashi convex metric spaces and common fixed point theorems for a pair of maps results generalizing and unifying fixed point theorems of imdad and kumar das and naik jungck ciric ume khan and pathak and ciric are established

fixed point theorem for two non self mappings in cone metric spaces in this paper we extend a fixed point theorem of imdad and kumar for a pair of non self maps to non normal cone spaces

precise segmentation of multimodal images we propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region of interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels we follow the most conventional approaches in that initial images and desired maps of regions are described by a joint markov gibbs random field mgrf model of independent image signals and interdependent region labels however our focus is on more accurate model identification to better specify region borders each empirical distribution of image signals is precisely approximated by a linear combination of gaussians lcg with positive and negative components we modify an expectation maximization em algorithm to deal with the lcgs and also propose a novel em based sequential technique to get a close initial lcg approximation with which the modified em algorithm should start the proposed technique identifies individual lcg models in a mixed empirical distribution including the number of positive and negative gaussians initial segmentation based on the lcg models is then iteratively refined by using the mgrf with analytically estimated potentials the convergence of the overall segmentation algorithm at each stage is discussed experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms

robust procedures for testing equality of covariance matrices normal theory tests for common variance are very sensitive to departures from normality in both univariate and multivariate applications for mild departures from normality and moderate sample size nominal a 01 produced type i error rates in excess of 20 in simulation studies since a modification of levene s test has been shown to perform well for the univariate problem two multivariate generalizations of this test are proposed both procedures are robust to departures from normality and are simple computationally comparisons of the power of these two procedures and a procedure proposed previously by tiku and balakrishnan 1985 communications in statisticstheory and methods 14 3033 3051 indicate that the three methods should be viewed as complementary

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

text segmentation for mrc document compression the mixed raster content mrc standard itu t t 44 specifies a framework for document compression which can dramatically improve the compression quality tradeoff as compared to traditional lossy image compression algorithms the key to mrc compression is the separation of the document into foreground and background layers represented as a binary mask therefore the resulting quality and compression ratio of a mrc document encoder is highly dependent upon the segmentation algorithm used to compute the binary mask in this paper we propose a novel multiscale segmentation scheme for mrc document encoding based upon the sequential application of two algorithms the first algorithm cost optimized segmentation cos is a blockwise segmentation algorithm formulated in a global cost optimization framework the second algorithm connected component classification ccc refines the initial segmentation by classifying feature vectors of connected components using an markov random field mrf model the combined cos ccc segmentation algorithms are then incorporated into a multiscale framework in order to improve the segmentation accuracy of text with varying size in comparisons to state of the art commercial mrc products and selected segmentation algorithms in the literature we show that the new algorithm achieves greater accuracy of text detection but with a lower false detection rate of nontext features we also demonstrate that the proposed segmentation algorithm can improve the quality of decoded documents while simultaneously lowering the bit rate