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

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

a function transformation method and exact solutions to a generalized sinh gordon equation based on a transformed painleve property and the variable separated ode method a function transformation method is proposed to search exact solutions to some partial differential equations pdes with hyperbolic or exponential functions the new approach provides a more systematical and convenient handling of the solution process for the nonlinear equations its key point is to eradicate the hyperbolic or exponential terms by a transformed painleve property and reduce the given pdes to a variable coefficient ordinary differential equations then we look for solutions to the resulting equations by some methods as an application exact solutions for a generalized sinh gordon equation are formally derived

travelling wave solutions for combined and double combined sine cosine gordon equations by the variable separated ode method abstract a combined sine cosine gordon and a double combined sine cosine gordon equations that combine the effects of sine and cosine are investigated the analysis rests mainly on the newly developed variable separated ode method sirendaoreji sun jiong a direct method for solving sinh gordon type equation phys lett a 298 2002 133 139 exact travelling wave solutions for the combined equations are formally derived by using this method the work emphasizes the power of the method that can be used in problems of identical nonlinearities

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

the sharp quantitative sobolev inequality for functions of bounded variation abstract the classical sobolev embedding theorem of the space of functions of bounded variation bv r n into l n r n is proved in a sharp quantitative form

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

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

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

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

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

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

the variable separated ode and the tanh methods for solving the combined and the double combined sinh cosh gordon equations abstract exact travelling wave solutions for the combined sinh cosh gordon and the double combined sinh cosh gordon equation are formally derived the painleve property v eu will be used to back up the tanh method to derive a first set of solutions the newly developed variable separated ode method is also used to derive a second set of solutions each method provides travelling wave solutions of distinct physical structures

the tanh method exact solutions of the sine gordon and the sinh gordon equations in this work we use the tanh method for traveling wave solutions of the sine gordon and the sinh gordon equations several exact solutions of distinct physical structures are obtained the method is powerful with minimal algebra work and is demonstrated for four models

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

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

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

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 travelling wave solutions to some nonlinear equations via a combined method abstract based on the sine gordon and the sinh gordon equations transformations are introduced in a variable separated ode method to construct entirely new doubly periodic jacobian elliptic function solutions of some nonlinear differential equations which are powerful and simple distinct sets of exact doubly periodic solutions that possess distinct physical structures are obtained for the mkdv sine gordon the mkdv sinh gordon equations and born infeld equation when the module m 1 or 0 the corresponding solitary wave solutions are also found this approach can be also applied to solve other nonlinear differential equations

travelling wave solutions for the mkdv sine gordon and the mkdv sinh gordon equations by using a variable separated ode method in this work we formally derive exact travelling wave solutions for the modified kdv sine gordon mkdv sine gordon equation and the modified kdv sinh gordon equation mkdv sinh gordon the proposed analysis depends mainly on a variable separated ode method two distinct sets of exact solitary wave solutions that possess distinct physical structures are formally derived for each equation the derived solutions include others results and introduce entirely new solutions

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

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

the tanh method for traveling wave solutions of nonlinear equations in this work we employ the tanh method for traveling wave solutions of nonlinear equations the study is extended to equations that do not have tanh polynomial solutions the efficiency of the method is demonstrated by applying it for a variety of selected equations