texture synthesis and nonparametric resampling of random fields this paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields the motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields we give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field the joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human thus we provide theoretical justification for an algorithm that has already been very successful in practice and suggest an explanation for its perceptually good results

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

hamiltonian formulation of a theory with constraints the hamiltonian formulation of a constrained dynamical system with four degrees of freedom the quantization of which has recently been discussed by hojman and shepley j math phys 32 142 1991 is considered the theory possesses four primary constraints which are all second class the system is quantized using the dirac s procedure next the theory is reduced to the three dimensional one by setting q4 k const it is found that the theory now possesses only three primary constraints which are all first class and consequently the theory now becomes a gauge theory this three dimensional theory is then quantized using the dirac s procedure again under different gauge fixing conditions

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

image estimation using doubly stochastic gaussian random field models the two dimensional 2 d doubly stochastic gaussian dsg model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal here we present the optimal estimator and 2 d fixed lag smoother for this dsg model extending earlier work of ackerson and fu as the optimal estimator has an exponentially growing state space we investigate suboptimal estimators using both a tree and a decision directed method experimental results are presented

a three dimensional edge operator modern scanning techniques such as computed tomography have begun to produce true three dimensional imagery of internal structures the first stage in finding structure in these images like that for standard two dimensional images is to evaluate a local edge operator over the image if an edge segment in two dimensions is modeled as an oriented unit line segment that separates unit squares i e pixels of different intensities then a three dimensional edge segment is an oriented unit plane that separates unit volumes i e voxels of different intensities in this correspondence we derive an operator that finds the best oriented plane at each point in the image this operator which is based directly on the 3 d problem complements other approaches that are either interactive or heuristic extensions of 2 d techniques

a test to control a region growing process within a hierarchical graph hierarchical graphs using a decimation process can be applied to an image to obtain segmentation however this method encounters limitations first the decimation proceeds at each step in a general way on the entire image second a criterion is needed to stop the iterative process when the best segmentation is obtained we propose a statistical test to control the region growing process this test based on moran s spatial autocorrelation coefficient controls the decimation process both globally and locally at the same time results on a composite image indicate that the local and global tests are a powerful tool for optimizing the image segmentation process

texture segmentation using voronoi polygons textures are defined in terms of primitives called tokens a texture segmentation algorithm based on the voronoi tessellation is discussed the algorithm first builds the voronoi tessellation of the tokens that make up the textured image it then computes a feature vector for each voronoi polygon these feature vectors are used in a probabilistic relaxation labeling on the tokens to identify the interior and the border regions of the textures some experimental results are shown

color texture description with novel local binary patterns for effective image retrieval abstract we propose a novel local color texture descriptor called local binary pattern for color images lbpc the proposed descriptor uses a plane to threshold color pixels in the neighborhood of a local window into two categories to boost the discriminative power of the proposed lbpc operator local binary patterns of the hue component in the hsi color space called the local binary pattern of the hue lbph is derived further lbpc lbph are fused to derive lbpc lbph which when combined with the color histogram ch of the hue component results in an effective image retrieval method lbpc lbph ch the uniform patterns of the two proposed descriptors ulbpc and ulbph are combined to yield another low dimension local color descriptor ulbpc ulbph ch which provides a good tradeoff between retrieval accuracy and speed detailed experiments conducted on wang holidays corel 5k and corel 10k datasets demonstrate that the proposed low dimension descriptors lbpc lbph ch and ulbpc ulbph ch outperform the state of the art color texture descriptors in terms of retrieval accuracy and speed

reduced complexity rotation invariant texture classification using a blind deconvolution approach in this paper we present a texture classification procedure that makes use of a blind deconvolution approach specifically the texture is modeled as the output of a linear system driven by a binary excitation we show that features computed from one dimensional slices extracted from the two dimensional autocorrelation function acf of the binary excitation allows representing the texture for rotation invariant classification purposes the two dimensional classification problem is thus reconduced to a more simple one dimensional one which leads to a significant reduction of the classification procedure computational complexity

parameter estimation for optimal object recognition theory andapplication object recognition systems involve parameters such as thresholds bounds and weights these parameters have to be tuned before the system can perform successfully a common practice is to choose such parameters manually on an it add hoc basis which is a disadvantage this paper presents a novel theory of parameter estimation for optimization based object recognition where the optimal solution is defined as the global minimum of an energy function the theory is based on supervised learning from examples it correctness and it instability are established as criteria for evaluating the estimated parameters a correct estimate enables the labeling implied in each exemplary configuration to be encoded in a unique global energy minimum the instability is the ease with which the minimum is replaced by a non exemplary configuration after a perturbation the optimal estimate minimizes the instability algorithms are presented for computing correct and minimal instability estimates the theory is applied to the parameter estimation for mrf based recognition and promising results are obtained

involution and constrained dynamics ii the faddeev jackiw approach for pt i see seiler et al ibid vol 28 p 4431 1995 we study the symplectic approach to first order systems with constraints from the point of view of the formal theory of differential equations we concentrate especially on systems without first class constraints and give a geometric interpretation of an approach recently proposed by barcelos neto and wotzasek 1992 we further study the numerical properties of this approach we also comment on some problems concerning the application to field theories

rotation invariant texture classification using a complete space frequency model a method of rotation invariant texture classification based on a complete space frequency model is introduced a polar analytic form of a two dimensional 2 d gabor wavelet is developed and a multiresolution family of these wavelets is used to compute information conserving microfeatures from these microfeatures a micromodel which characterizes spatially localized amplitude frequency and directional behavior of the texture is formed the essential characteristics of a texture sample its macrofeatures are derived from the estimated selected parameters of the micromodel classification of texture samples is based on the macromodel derived from a rotation invariant subset of macrofeatures in experiments comparatively high correct classification rates were obtained using large sample sets

constraint satisfaction neural networks for image segmentation abstract constraint satisfaction neural networks csnns are proposed for image recognition which is the process to identify objects of interest in an image the image recognition problem is formulated as a constraint satisfaction problem csp the regions resulting from a signal based image segmentation algorithm can be considered as objects and their entities as labels in the csp the proposed neural network is multi layered and the function of each layer is to identify one physical entity label from the input regions objects through cascading these layers each label can be assigned to the corresponding region s attention is focused on recognizing x ray ct computed tomography images of human heads e g anatomic structure in a medical image the proposed csnn is capable of identifying the components of a brain in a preliminarily segmented image the major components in a human head include bone ventricle and gyrus therefore three layers are needed for this task each layer is constructed based on the principles proposed in kohonen s self organizing feature maps and the optimal linear associative memories and their weights are trained by the features of each entity in the prestored model the experimental results show that the proposed approach is very promising

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

pixon based image segmentation with markov random fields image segmentation is an essential processing step for many image analysis applications we propose a novel pixon based adaptive scale method for image segmentation the key idea of our approach is that a pixon based image model is combined with a markov random field mrf model under a bayesian framework we introduce a new pixon scheme that is more suitable for image segmentation than the fuzzy pixon scheme the anisotropic diffusion equation is successfully used to form the pixons in our new pixon scheme experimental results demonstrate that our algorithm performs fairly well and computational costs decrease dramatically compared with the pixel based mrf algorithm

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

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

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

on the estimation of markov random field parameters we examine the histogram method for estimating the parameters associated with a markov random field this method relies on the estimation of the local interaction sums from histogram data we derive an estimator for these quantities that is optimal in a well defined sense furthermore we show that the final step of the histogram method the solution of a least squares problem can be done substantially faster than one might expect if no equation culling is used we also examine the use of weighted least squares and see that this seems to lead to better estimates even with small amounts of data

a fast parallel method for synthesis of random patterns abstract a new method for generation of nonhomogeneous anisotropic random patterns defined on a square lattice is presented first a hierarchy of seed structures is derived by recursively deleting the sites of the square lattice this decimation process is parallel and employs local ordering of i i d random numbers at every level of the hierarchy the surviving seeds expand and incorporate the decimated sites into cells the ensemble of cells down projected onto the square lattice defines a random tessellation whose coarseness increases with the level in the hierarchy nonhomogeneous random patterns are obtained by concatenating cells taken from different levels anisotropic patterns by employing unequal weights in the generation process the underlying hierarchical structure assures that the random patterns are synthesised in o log image size time

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

the linear spatial temporal interaction process and its relation to 1 ω noise if we are to gain an understanding of the evolutionary processes which generate pattern then time cannot be ignored since a purely spatial viewpoint disregards the fundamental generating mechanism of the underlying process we therefore develop a spectral approach based on a general growth interaction model individuals grow at intrinsic rate while two individuals a distance r apart interact at rate a times their size difference special cases considered involve nearest neighbour geometric logarithmic and cauchy type dependence a separate study is made of long term persistence an autoregressive binomial weight structure is used to generate processes with power law spectra d

estimating gaussian markov random field parameters in a nonstationary framework application to remote sensing imaging in this paper we tackle the problem of estimating textural parameters we do not consider the problem of texture synthesis but the problem of extracting textural features for tasks such as image segmentation we take into account nonstationarities occurring in the local mean we focus on gaussian markov random fields for which two estimation methods are proposed and applied in a nonstationary framework the first one consists of extracting conditional probabilities and performing a least square approximation this method is applied to a nonstationary framework dealing with the piecewise constant local mean this framework is adapted to practical tasks when discriminating several textures on a single image the blurring effect affecting edges between two different textures is thus reduced the second proposed method is based on renormalization theory statistics involved only concern variances of gaussian laws leading to cramer rao estimators this method is thus especially robust with respect to the size of sampling moreover nonstationarities of the local mean do not affect results we then demonstrate that the estimated parameters allow texture discrimination for remote sensing data the first proposed estimation method is applied to extract urban areas from spot images since discontinuities of the local mean are taken into account we obtain an accurate urban areas delineation finally we apply the renormalization based on method to segment ice in polar regions from avhrr data

topological properties of the spaces of regular fuzzy sets abstract by identifying the space f 0 x of regular fuzzy sets with a subspace t 0 x of some compact set valued function space we define a uniform topology on f 0 x and discuss several topological properties such as first countability separability connectedness etc when x is a reflexive banach space f 0 x is imbedded into a locally convex topological vector space and a definition of integration and differentiation for f 0 x valued functions is given

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

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

on a parameter estimation method for gibbs markov random fields this correspondence is about a gibbs markov random field gmrf parameter estimation technique proposed by derin and elliott 1987 we will refer to this technique as the histogramming h method first the relation of the h method to the conditional maximum likelihood method is considered second a bias reduction based modification of the h method is proposed to improve its performance especially in the case of small amounts of image data

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

equivalent conditions for laws of large numbers for t related l r fuzzy numbers in this paper we give some necessary and sufficient conditions for laws of large numbers for sequence of mutually t related l r fuzzy numbers when t is an continuous archimedean t norm and diameter of support of the fuzzy numbers is not uniformly bounded we also consider some necessary and sufficient conditions for laws of large numbers for l r fuzzy random numbers and generalize earlier results of fuller fuzzy sets and systems 45 1992 299 303 triesch fuzzy sets and systems 58 1993 339 342 and hong and lee fuzzy sets and systems 121 2001 537 543

an iterative gibbsian technique for reconstruction of m ary images abstract the reconstruction of m ary images corrupted by independent noise is treated the original image is modeled by a markov random field mrf whose parameters are unknown likewise the probabilistic structure of the noise is unknown this paper presents an iterative procedure which performs the parameter estimation and image reconstruction tasks at the same time the procedure that we call gibbsian em algorithm is a generalization to the mrf context of a general algorithm known as the em algorithm used to approximate maximum likelihood estimates for incomplete data problems a number of experiments are presented in the case of gaussian noise and binary noise showing that the gibbsian em algorithm is useful and effective for image reconstruction and segmentation

multispectral random field models for synthesis and analysis of color images multispectral extensions to the traditional gray level simultaneous autoregressive sar and markov random field mrf models are considered furthermore a new image model is proposed the pseudo markov model which retains the characteristics of the multispectral markov model yet admits to a simplified parameter estimation method these models are well suited to analysis and modeling of color images for each model considered procedures are developed for parameter estimation and image synthesis experimental results based on known image models and natural texture samples substantiate the validity of thee results

classification of rotated and scaled textured images using gaussian markov random field models consideration is given to the problem of classifying a test textured image that is obtained from one of c possible parent texture classes after possibly applying unknown rotation and scale changes to the parent texture the training texture images parent classes are modeled by gaussian markov random fields gmrfs to classify a rotated and scaled test texture the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the gmrf for the rotated and scaled image a bona fide likelihood function that shows the explicit dependence of the likelihood function on the gmrf parameters as well as on the rotation and scale parameters is derived although in general the scaled and or rotated texture does not correspond to a finite order gmrf it is possible nonetheless to write down a likelihood function for the image data the likelihood function of the discrete fourier transform of the image data corresponds to that of a white nonstationary gaussian random field with the variance at each pixel i j being a known function of the rotation the scale the gmrf model parameters and i j the variance is an explicit function of the appropriately sampled power spectral density of the gmrf the estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete fourier transform of the image data cramer rao error bounds on the scale and rotation estimates are easily computed a modified bayes decision rule is used to classify a given test image into one of c possible texture classes the classification power of the method is demonstrated through experimental results on natural textures from the brodatz album

the construction of a poisson structure out of a symmetry and a conservation law of a dynamical system a method to construct hamiltonian theories for systems of both ordinary and partial differential equations is presented the knowledge of a lagrangian is not at all necessary to achieve the result the only ingredients required for the construction are one solution of the symmetry perturbation equation and one constant of motion of the original system it turns out that the poisson bracket structure for the dynamical variables is far from becoming uniquely determined by the differential equations of motion examples in classical mechanics as well as in field theory are presented

no lagrangian no quantization this work starts with classical equations of motion and sets very general quantization conditions commutation relations it is proved that these conditions imply that the equations of motion are equivalent to the euler lagrange equations of a lagrangian l the result is a generalization of work by feynman recently reported by dyson am j phys 58 209 211 1990 the lagrangian l need not be unique examples are given including classical equations that do not come from a lagrangian and therefore cannot be quantized consistently

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

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

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

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

hierarchical image analysis using irregular tessellations a novel multiresolution image analysis technique based on hierarchies of irregular tessellations generated in parallel by independent stochastic processes is presented like traditional image pyramids these hierarchies are constructed in a number of steps on the order of log image size steps however the structure of a hierarchy is adapted to the image content and artifacts of rigid resolution reduction are avoided two applications of these techniques are presented connected component analysis of labeled images and segmentation of gray level images in labeled images every connected component is reduced to a separate root with the adjacency relations among the components also extracted in gray level images the output is a segmentation of the image into a small number of classes as well as the adjacency graph of the classes

exploring space frequency co occurrences via local quantized patterns for texture representation local binary pattern lbp has shown its power in texture classification and face recognition however the lbp operator is performed in the original image space and it lacks deeper pixel interactions to capture a richer description in this paper we propose to explore space frequency co occurrences via local quantized patterns for texture representation the proposed method proceeds in two channels in each channel the multi resolution spatial maps are first obtained by specific spatial filtering and local frequency features spectral maps are subsequently extracted by applying the local fourier transform to the spatial map two types of quantization via global thresholding are employed to quantize the spatial and spectral maps into three and two levels respectively the quantized patterns are then jointly encoded to construct a space frequency co occurrence histogram finally the two channel histograms are combined to characterize the texture without resort to the texton based representation our method directly encodes the joint information in the space and frequency domains while preserving the robustness to image rotation illumination scale and viewpoint changes extensive experiments have been conducted on three well known texture databases and our method achieves the best classification results compared with state of the art approaches investigated highlightstwo channel space frequency feature spaces are designed to obtain invariant features two types of quantization via global thresholding are developed the joint space frequency coding is explored to capture a richer description our method outperforms the state of the art on three well known texture datasets

on fuzzy random sets and their mathematical expectations abstract in this article we construct an embedding of the space of fuzzy sets into a normed linear space we then discuss several classes of random sets which take values either in the space of classical subsets or in the space of fuzzy subsets the mathematical expectations of random sets are discussed the embedding provided here can also be applied to study the calculus of set valued functions and fuzzy functions

modeling of ultrasound speckle with application in flaw detection in metals rf ultrasound backscatter speckle is modeled by a parametric noncausal gaussian markov field that appears to capture the speckle structure well is consistent with the first order marginal statistics of the complex amplitude speckle and explains the homogeneous coarseness appearance of the speckle in terms of a homogeneous colored random field with a definite correlation structure the markov property results in the compact parametrization of the backscatter echo field by a few parameters and constitutes a huge reduction in the representation and analysis complexity of the backscatter image use is made of the intensity as well as phase information associated with the acoustic image by analyzing and modeling the acoustic rf data rather than the intensity data the additional phase information associated with the rf data allows for the statistics of the complex backscatter echo field or equivalently that of the rf field to be completely specified the approach provides a coherent theoretical basis for the design of statistical tests for detecting targets embedded in the speckle image for the case where the speckle model parameters are either a priori known or unknown

comment on hamiltonian formulation of a theory with constraints u kulshreshta j math phys 33 633 1992 the hamiltonian formulation of a constrained dynamical system analyzed by kulshreshta j math phys 33 633 1992 is discussed the theory possesses four coordinates and four primary second class constraints and thus two physical degrees of freedom the correct equations of motion for the system are given the reduced theory q4 k is shown to have three primary and one secondary second class constraints instead of three primary first class ones as claimed by kulshreshta the equations of motion are derived using the dirac bracket

high dimensional ising model selection using l1 regularized logistic regression we consider the problem of estimating the graph associated with a binary ising markov random field we describe a method based on l1 regularized logistic regression in which the neighborhood of any given node is estimated by performing logistic regression subject to an l1 constraint the method is analyzed under high dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n our main results provide sufficient conditions on the triple n p d and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously with coherence conditions imposed on the population fisher information matrix we prove that consistent neighborhood selection can be obtained for sample sizes n d3log p with exponentially decaying error when these same conditions are imposed directly on the sample matrices we show that a reduced sample size of n d2log p suffices for the method to estimate neighborhoods consistently although this paper focuses on the binary graphical models we indicate how a generalization of the method of the paper would apply to general discrete markov random fields

bispectral analysis and model validation of texture images statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian and or asymmetric in this paper higher than second order statistics are used to derive and implement 2 d gaussianity linearity and spatial reversibility tests that validate the respective modeling assumptions the nonredundant region of the 2 d bispectrum is correctly defined and proven a consistent parameter estimator for nonminimum phase asymmetric noncausal 2 d arma models is derived by minimizing a quadratic error polyspectrum matching criterion simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported

sasi a generic texture descriptor for image retrieval in this paper a generic texture descriptor namely statistical analysis of structural information sasi is introduced as a representation of texture sasi is based on statistics of clique autocorrelation coefficients calculated over structuring windows sasi defines a set of clique windows to extract and measure various structural properties of texture by using a spatial multi resolution method experimental results performed on various image databases indicate that sasi is more successful then the gabor filter descriptors in capturing small granularities and discontinuities such as sharp corners and abrupt changes due to the flexibility in designing the clique windows sasi reaches higher average retrieval rates compared to gabor filter descriptors however the price of this performance is increased computational complexity

symmetries of lagrangians and of their equations of motion a new kind of lagrangian symmetry is defined in such a way that the resulting set of lagrangian symmetries coincides with the set of symmetries of its equations of motion several constants of motion may be associated to each of the new symmetry transformations one example is presented

texture synthesis using 2 d noncausal autoregressive models the purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive ncar models for the synthesis of textures these models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable we first show that the class of ncar models is capable of generating a wide variety of image patterns posessing the local replication attribute an essential ingredient of many natural textures it is also shown that the theoretical variograms of many ncar models possess an oscillatory behavior a characteristic of the variograms of many natural textures next we give experimental results of synthesis of 64 64 textures resembling several real textures in the brodatz album the synthetic textures generated by 16 parameter ncar models retain most the visual characteristics of the original textures the variograms of the original and synthetic textures are also similar

bayesian segmentation via asymptotic partition functions asymptotic approximations to the partition function of gaussian random fields are derived textures are characterized via gaussian random fields induced by stochastic difference equations determined by finitely supported stationary linear difference operators adjusted to be nonstationary at the boundaries it is shown that as the scale of the underlying shape increases the log normalizer converges to the integral of the log spectrum of the operator inducing the random field fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator induced random field model matrix analysis techniques are proposed for handling textures with variable orientation examples of texture parameters estimated from training data via asymptotic maximum likelihood are shown isotropic models involving powers of the laplacian and directional models involving partial derivative mixtures are explored parameters are estimated for mitochondria and actin myocin complexes in electron micrographs and clutter in forward looking infrared images deformable template models are used to infer the shape of mitochondria in electron micrographs with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds

image representation using block pattern models and its image processing applications an image representation scheme using a set of block pattern models bpms consisting of three categories constant oriented and irregular is introduced algorithms for model classification model parameter estimation and image reconstruction from model parameters are presented and these provide the necessary vehicles for applying the proposed representation scheme to various image processing tasks the applications of the proposed models in image coding image zooming and image smoothing are described satisfactory coded images have been obtained at bit rates between 0 5 approximately 0 6 b p p bits per pixel with a high rate realization and between 0 3 approximately 0 5 b p p with a low rate realization the high rate realization has a simple structure suitable for real time implementation the methods for image zooming and smoothing are similar where both adapt the processing for each pixel according to the model of its neighborhood by using directional filters in oriented regions edges and lines are rendered sharper in a smoother manner than with conventional linear filtering approaches which leads to significant improvement in perceived image quality

a markov random field model based approach to image interpretation an image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph and image interpretation is achieved through assigning object labels or interpretations to the segmented regions or nodes using domain knowledge extracted feature measurements and spatial relationships between the various regions the interpretation labels are modeled as a markov random field mrf on the corresponding adjacency graph and the image interpretation problem is then formulated as a maximum a posteriori map estimation rule given domain knowledge and region based measurements simulated annealing is used to find this best realization or optimal map interpretation this approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the gibbs distribution representing the pdf of the underlying mrf a general methodology is provided for the design of the clique functions results of image interpretation experiments on synthetic and real world images are described

quantization of non standard hamiltonian systems the quantization of classical theories that admit more than one hamiltonian description is considered this is done from a geometrical viewpoint both at the quantization level geometric quantization and at the level of the dynamics of the quantum theory a spin system is taken as an example in which all the steps can be completed it is shown that the geometry of the quantum theory imposes restrictions on the physically allowed non standard quantum theories

support functions for fuzzy sets the main purpose of this paper is to introduce and develop the notion of support functions for fuzzy sets this approach gives the opportunity to investigate a lot of properties of fuzzy valued functions functions with values in space of fuzzy sets defined on banach space using rich apparatus of functionals in this paper we examine some aspects of measurability integrability and measure theory

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

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

gmm estimation of 2d rca models with applications to texture image classification the 2d indexed random coefficients autoregressive 2d rca models are obtained by introducing appropriate random field coefficients to an ar model on mathrm z 2 the study of such models is motivated by their capability to capture the space varying behavior of the volatility a generalized method of moment approach is considered to estimate the 2d rca models consistency and asymptotic normality of the estimates are derived estimated parameters are used at a later stage as pixel features in texture image classification

nonlinear operator for oriented texture texture is an important part of the visual world of animals and humans and their visual systems successfully detect discriminate and segment texture relatively recently progress was made concerning structures in the brain that are presumably responsible for texture processing neurophysiologists reported on the discovery of a new type of orientation selective neuron in areas v1 and v2 of the visual cortex of monkeys which they called grating cells such cells respond vigorously to a grating of bars of appropriate orientation position and periodicity in contrast to other orientation selective cells grating cells respond very weakly or not at all to single bars which do not make part of a grating elsewhere we proposed a nonlinear model of this type of cell and demonstrated the advantages of grating cells with respect to the separation of texture and form information in this paper we use grating cell operators to obtain features and compare these operators in texture analysis tasks with commonly used feature extracting operators such as gabor energy and co occurrence matrix operators for a quantitative comparison of the discrimination properties of the concerned operators a new method is proposed which is based on the fisher 1923 linear discriminant and the fisher criterion the operators are also qualitatively compared with respect to their ability to separate texture from form information and their suitability for texture segmentation

visually improved image compression by combining a conventional wavelet codec with texture modeling human observers are very sensitive to a loss of image texture in photo realistic images for example a portrait image without the fine skin texture appears unnatural once the image is decomposed by a wavelet transformation this texture is represented by many wavelet coefficients of low and medium amplitude the conventional encoding of all these coefficients is very bitrate expensive instead such an unstructured or stochastic texture can be modeled by a noise process and be characterized with very few parameters thus a hybrid scheme can be designed that encodes the structural image information by a conventional wavelet codec and the stochastic texture in a model based manner such a scheme called witch wavelet based image texture coding hybrid is proposed it implements such an hybrid coding approach while nevertheless preserving the features of progressive and lossless coding its low computational complexity and the parameter coding costs of only 0 01 bpp make it a valuable extension of conventional codecs a comparison with the jpeg2000 image compression standard showed that the witch scheme achieves the same subjective quality while increasing the compression ratio by more than a factor of two

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

entropy based texture analysis in the spatial frequency domain an approach which uses regional entropy measures in the spatial frequency domain for texture discrimination is presented the measures provide texture discriminating information independent of that contained in the usual summed energy within based frequency domain features performance of the entropy features as measured by a between to within class scatter criterion is comparable to that of traditional frequency domain features and gray level co occurrence contrast features a method of frequency scaling is introduced to enable the comparison of texture samples of different subimage size the resulting regional entropy measures are subimage size invariant subject to certain constraints which arise from properties of the discrete fourier transform

representation of fuzzy valued mappings by the sequence of single valued mappings abstract in this paper the analysis focusses on the important classes of fuzzy valued mappings measurable fuzzy valued mappings integrable fuzzy valued mappings our aim is to discuss the problem of representation of such mappings by countable family of single valued mappings this is a most useful result since it provides us with a remarkable list of alternative definitions criteria and proofs of theorems related to this type of fuzzy mappings

the helmholtz conditions in terms of constants of motion in classical mechanics the helmholtz conditions are the necessary and sufficient conditions for a set of second order differential equations to be equivalent to a variational principle in this work an alternative approach to the inverse problem in classical mechanics is described it is proven that the helmholtz conditions can be transformed into a set of conditions for a nonsingular antisymmetric matrix whose entries are constants of motion of the problem in question

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

new fusion operations for digitized binary images and their applications this paper proposes a new class of fusion operations which are useful for binary image processing to begin with an algorithm for the classical fusion operations is presented they are sequentially composed of two basic operations that is expansion and contraction the strategy of the proposed algorithm is as follows the first operation is performed with the distance transformation and the second operation utilizes the distance information obtained in the first operation next a topological contraction and a topological expansion are defined the topological contraction preserves the euler number of an input image except that some simply connected components of 1 pixels are erased the topological expansion preserves the euler number of an input image except that some simply connected holes are filled then several new fusion operations are obtained by combining the classical contraction and the topological expansion or the classical expansion and the topological contraction sequentially the algorithms for them use the same strategy as the proposed algorithm for the classical fusion operations finally experimental results show that the new fusion operations and their combinations are effectively used in the binary image processing such as shape smoothing merging and separating connected components and structure analysis

on the inverse problem of the calculus of variations we consider the inverse problem of the calculus of variations for any system by writing its differential equations of motion in first order form we provide a way of constructing infinitely many lagrangians for such a system in terms of its constants of motion using a covariant geometrical approach we present examples of first order lagrangians for systems for which no second order lagrangians exist the hamiltonian theory for first order degenerate lagrangians is constructed using dirac s method for singular lagrangians

two dimensional linear prediction model based decorrelation method a unified feature extraction scheme the two dimensional 2 d linear prediction model based decorrelation method is presented by applying 2 d causal linear prediction model to decorrelate a textured image the very heavy computation load required when using a whitening operator to decorrelate the image or the significant information loss when using the gradient operator to approximately whiten the image is avoided the texture model based decorrelation provides three sets of features to perform texture classification the coefficients of the 2 d linear prediction the moments of error residuals and the autocorrelation values an optimum feature selection scheme using modified branch and bound method was introduced to reduce information redundancy after feature selection 100 classification accuracy was achieved for a 20 class texture problem experiments show that this feature extraction scheme is truly information lossless effective and fast

a study of gaussian mixture models of color and texture features for image classification and segmentation the aims of this paper are two fold to define gaussian mixture models gmms of colored texture on several feature spaces and to compare the performance of these models in various classification tasks both with each other and with other models popular in the literature we construct gmms over a variety of different color and texture feature spaces with a view to the retrieval of textured color images from databases we compare supervised classification results for different choices of color and texture features using the vistex database and explore the best set of features and the best gmm configuration for this task in addition we introduce several methods for combining the color and structure information in order to improve the classification performances we then apply the resulting models to the classification of texture databases and to the classification of man made and natural areas in aerial images we compare the gmm model with other models in the literature and show an overall improvement in performance

correction to rotation and gray scale transform invariant texture classification using spiral resampling subband decomposition and hidden markov model this paper proposes a new texture classification algorithm that is invariant to rotation and gray scale transformation first we convert two dimensional 2 d texture images to one dimensional 1 d signals by spiral resampling then we use a quadrature mirror filter qmf bank to decompose sampled signals into subbands in each band we take high order autocorrelation functions as features features in different bands which form a vector sequence are then modeled as a hidden markov model bmm during classification the unknown texture is matched against all the models and the best match is taken as the classification result simulations showed that the highest correct classification rate for 16 kinds of texture was 95 14

a new texture generation method based on pseudo dct coefficients in this paper a new method for generating different texture images is presented this method involves a simple transform from a certain one dimensional 1 d signal to an expected two dimensional 2 d image unlike traditional methods the input signal is generated by a simple 1 d function in our work instead of a sample texture we first transform the 1 d input signal into frequency domain using fast fourier transform based on the sufficient analysis in 2 d discrete cosine transform dct domain where each of the coefficients expresses a texture feature in a certain direction the 2 d pseudo dct coefficients are then constructed by appropriately rearranging the fourier coefficients in terms of their frequency components finally the corresponding texture image can be produced by 2 d inverse dct algorithm we applied the proposed method to generate several stochastic textures i e cloud illumination and sand and several structural texture images experimental results indicate the good performance of the proposed method

texture classification using dense micro block difference this paper is devoted to the problem of texture classification motivated by recent advancements in the field of compressive sensing and keypoints descriptors a set of novel features called dense micro block difference dmd is proposed these features provide highly descriptive representation of image patches by densely capturing the granularities at multiple scales and orientations unlike most of the earlier work on local features the dmd does not involve any quantization thus retaining the complete information we demonstrate that the dmd have dimensionality much lower than scale invariant feature transform sift and can be computed using integral image much faster than sift the proposed features are encoded using the fisher vector method to obtain an image descriptor which considers high order statistics the proposed image representation is combined with the linear support vector machine classifier extensive experiments are conducted on five texture data sets kth tips umd kth tips 2a brodatz and curet using standard protocols the results demonstrate that our approach outperforms the state of the art in texture classification

image modeling using inverse filtering criteria with application to textures statistical approaches to image modeling have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian this constrains the parameters of noncausal image models to be symmetric and therefore the underlying random field to be spatially reversible research indicates that this assumption may not be always valid for texture images in this paper higher than second order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving average arma image models with known orders contrary to existing approaches fir inverse filters are employed and image models with zeros on the unit bicircle can be handled one of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date consistency of these estimators is established and their performance is evaluated with monte carlo simulations as well as texture classification and synthesis experiments

granolds a novel texture representation in this paper we describe a new image texture representation using two different parameterised monotonic mappings this new technique transforms the input image into a function on two dimensions that may be regarded as a surface that we have named the granold the nature of this surface is such that corners appear at positions where there are simultaneously large changes in the response of the monotonic mappings to the input image the shape and position of these corners is then analysed to provide information about the texture of the input image the use of grey level thresholds and morphological granulometries in the formation of the granold is presented then these mappings are generalised and a mathematical analysis of the new technique including constraints for the parameterised monotonic mappings is presented a number of experiments are described that use grey level thresholds and morphological granulometries to fundamentally test and demonstrate the new technique are presented the results from these experiments are presented and discussed including a qualitative discussion of the behaviour of the new technique in response to changes in the input image the conclusion is that the new technique performs in an expected repeatable and predictable manner in accordance with its mathematical analysis c 2000 pattern recognition society published by elsevier science ltd all rights reserved

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

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

three dimensional structural texture modeling and segmentation the structural approach one of the various modeling techniques in texture analysis perceives texture as a region composed of detectable primitive elements tokens in this paper we extend this concept to three dimensional 3d image and develop a segmentation scheme based on clustering of 3d texture tokens 3d structural texture is composed of texture tokens which are modeled as tiny objects embedded inside image sequence texture tokens located spatially close to one another and having similar shape are grouped into homogenous texture volume some of the texture tokens may be in contact with one another to form clump like structures our approach first disconnects these clumps by a 3d clump decomposition process a 3d irregular pyramid construction process is then carried out on these isolated 3d tokens the process inputs a delaunay graph with each vertex representing the shape feature vector of a texture token and each edge representing the neighborhood relationship of two texture tokens through stepwise grouping of similar shape tokens a segmentation of the texture volume is obtained