periodicity directionality and randomness wold features for image modeling and retrieval one of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems in applications such as database retrieval it is important that image features used in pattern comparison provide good measures of image perceptual similarities we present an image model with a new set of features that address the challenge of perceptual similarity the model is based on the 2d wold decomposition of homogeneous random fields the three resulting mutually orthogonal subfields have perceptual properties which can be described as periodicity directionality and randomness approximating what are indicated to be the three most important dimensions of human texture perception the method presented improves upon earlier wold based models in its tolerance to a variety of local inhomogeneities which arise in natural textures and its invariance under image transformation such as rotation an image retrieval algorithm based on the new texture model is presented different types of image features are aggregated for similarity comparison by using a bayesian probabilistic approach the effectiveness of the wold model at retrieving perceptually similar natural textures is demonstrated in comparison to that of two other well known pattern recognition methods the wold model appears to offer a perceptually more satisfying measure of pattern similarity while exceeding the performance of these other methods by traditional pattern recognition criteria examples of natural scene wold texture modeling are also presented

jensen s inequality for polynomials with concentration at low degrees we give a generalization of jensen s inequality valid for polynomials having some concentration at low degrees we investigate the constants involved both from a theoretical and a numerical point of view

robust rotation invariant texture classification using a model based approach in this paper a model based texture classification procedure is presented the texture is modeled as the output of a linear system driven by a binary image this latter retains the morphological characteristics of the texture and it is specified by its spatial autocorrelation function acf we show that features extracted from the acf of the binary excitation suffice to represent the texture for classification purposes specifically we employ a moment invariants based technique to classify the acf the resulting proposed classification procedure is thus inherently rotation invariant moreover it is robust with respect to additive noise experimental results show that this approach allows obtaining high correct rotation invariant classification rates while containing the size of the feature space

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

a fast nonparametric noncausal mrf based texture synthesis scheme using a novel fkde algorithm in this paper a new algorithm is proposed for fast kernel density estimation fkde based on principal direction divisive partitioning pddp of the data space a new framework is also developed to apply fkde algorithms both proposed and existing within nonparametric noncausal markov random field nnmrf based texture synthesis algorithm the goal of the proposed fkde algorithm is to use the finite support property of kernels for fast estimation of density it has been shown that hyperplane boundaries for partitioning the data space and principal component vectors of the data space are two requirements for efficient fkde the proposed algorithm is compared with the earlier algorithms with a number of high dimensional data sets the error and time complexity analysis proves the efficiency of the proposed fkde algorithm compared to the earlier algorithms due to the local simulated annealing direct incorporation of the fkde algorithms within the nnmrf based texture synthesis algorithm is not possible this work proposes a new methodology to incorporate the effect of local simulated annealing within the fkde framework afterward the developed texture synthesis algorithms have been tested with a number of different natural textures taken from a standard database the comparison in terms of visual similarity and time complexity between the proposed fkde based texture synthesis algorithm with the earlier algorithms show the efficiency

a generalization of jensen s inequality for polynomials having concentration at low degrees in this paper we give some asymptotic estimates for the best lower bound c d k p of the jensen s functional j f email protected 0 2 plog f e i q email protected p for when the polynomial f has a concentration d at low degrees k measured by the l p norm under the l p norm p 2

texture synthesis by analysis with hard limited gaussian processes a twin stage texture synthesis by analysis method is presented it aims to approximate first and second order distributions of the texture accordingly to the julesz conjecture in the first stage the binary textural behavior of a given prototype is represented by means of a hard limited gaussian process in the second stage the texture is synthesized by passing the binary hard limited gaussian process through a linear filter followed by a zero memory histogram equalizer

reduced complexity modeling and reproduction of colored textures an unsupervised color texture synthesis by analysis method is described the texture is reproduced to appear perceptually similar to a given prototype by copying its statistical properties up to the second order the synthesized texture is obtained at the output of a single input three output nonlinear system driven by a realization of a white gaussian random field significant complexity reduction is gained by exploiting the rank deficiency of the cross power spectral density matrix of the color texture samples

multichannel blind image deconvolution using the bussgang algorithm spatial and multiresolution approaches this work extends the bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems we address the restoration of images with poor spatial correlation as well as strongly correlated natural images the spatial nonlinearity employed in the final estimation step of the bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images for spatially correlated images the nonlinearity design is rather conducted using a particular wavelet decomposition that detecting lines edges and higher order structures carries out a task analogous to those of the preattentive stage of the human visual system experimental results pertaining to restoration of motion blurred text images out of focus spiky images and blurred natural images are reported

a perceptually lossless model based texture compression technique in natural scenes still images as well as sequences backgrounds and objects surfaces usually have a textural structure therefore in order to efficiently code images it is crucial to investigate the texture compression problem in this paper a perceptually lossless synthesis by analysis texture coding method is presented the proposed approach is model based the parameters of the model consist of a binary excitation signal and the parsimonious representation of the reconstruction filter the estimated parameters which allow to one synthesize at the decoder site a texture that is perceptually indistinguishable from the original one are then compressed using a lossless strategy which is based on a fast binary wavelet transformation specifically tailored to binary images the proposed method leads to very good perceptual results superior to those of existing techniques

an improved method for 2 d self similar image synthesis we propose a new method called incremental fourier synthesis to generate 2 d self similar images based on a 2d fractional brownian motion fbm model with this method the stationary increments of fbm are created by a fourier synthesis method and the increments are added up to generate the nonstationary 2d fbm process since the new method takes advantage of the fft its computational complexity is only o n sup 2 log sub 2 n and its memory requirement is only o n sup 2 for a self similar image of size n spl times n

texture synthesis textons revisited this paper introduces a technique for synthesizing natural textures with emphasis on quasiperiodic and structural textures textures are assumed to be composed of three components namely illumination structure and stochastic the contribution of this work is that in contrast to previous techniques it proposes a joint approach for handling the texture s global illumination irregular structure and stochastic component which may be correlated to the other two components furthermore the proposed technique does not produce verbatim copies in the synthesized texture more specifically a top down approach is used for extraction of texture elements textons in which in contrast to previous texton based approaches no assumptions regarding perfect periodicity are made the structure itself can be modeled as a stochastic process consequently textons are allowed to have irregular and nonidentical shapes in the synthesis stage a new nonregular textural structure is designed from the original one that defines the place holders for textons we call such place holders empty textons e textons the e textons are filled in by a representative texton since e textons do not have identical shapes a texton shape matching procedure is required after adding the illumination to the structural component a strictly localized version of a block sampling technique is applied to add the stochastic component the block sampling technique combined with the addition of the illumination component provides a significant improvement in the appearance of synthesized textures results show that the proposed method is successful in synthesizing structural textures visually indistinguishable to the original moreover the method is successful in synthesizing a variety of stochastic textures

multiresolution circular harmonic decomposition a dictionary of complex waveforms suited for multiresolution analysis and individually steerable by multiplication by a complex factor is presented it is based on circular harmonic wavelets chw and is useful for pattern analysis under rotations the main theoretical aspects of chws are illustrated and an example of application to motion estimation is provided

phaseless inverse scattering problems in three dimensions three dimensional inverse scattering problems in the frequency domain are considered in the case when only the modulus of the scattered field is given while the phase is unknown uniqueness theorems are proved

texture roughness analysis and synthesis via extended self similar ess model the 2d fractional brownian motion fbm model provides a useful tool to model textured surfaces whose roughness is scale invariant to represent textures whose roughness is scale dependent we generalize the fbm model to the extended self similar ess model in this research we present an estimation algorithm to extract the model parameters from real texture data furthermore a new incremental fourier synthesis algorithm is proposed to generate the 2d realizations of the ess model finally the estimation and rendering methods are combined to synthesize real textured surfaces

two single shot methods for locating multiple electromagnetic scatterers we develop two inverse scattering schemes for locating multiple electromagnetic em scatterers by the electric far field measurement corresponding to a single incident detecting plane wave the first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave the multiple scatterers could be extremely general with an unknown number of components and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content the second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting em wavelength the number of the obstacle components is not required to be known in advance but the shape of each component must be from a certain known admissible class the admissible class may consist of multiple different reference obstacles the second scheme could also be extended to include the medium components if a certain generic condition is s

a multiresolution approach for texture synthesis using the circular harmonic functions in this paper an unsupervised model based texture reproduction technique is described in accordance with the julesz s 1962 conjecture the statistical properties of the prototype up to the second order are copied in order to generate a synthetic texture perceptually indistinguishable from the given sample however this task is accomplished using a hybrid approach which operates partially in the spatial domain and partially in a multiresolution domain the latter employed is the circular harmonic function chf domain since it has been proven to be well suited for mimicking the behavior of the human visual system hvs this approach allows for a wide range of textures typologies obtaining synthetic textures that better match the prototype with respect to the ones obtained using techniques based on the julesz s conjecture operating only in the spatial domain and to dramatically reduce the computational complexity of similar methods operating only in the multiresolution domain

gibbs random fields cooccurrences and texture modeling gibbs random field grf models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination the authors show an explicit relationship between cooccurrences and a large class of grf s this result comes from a new framework based on a set theoretic concept called the aura set and on measures of this set aura measures this framework is also shown to be useful for relating different texture analysis tools the authors show how the aura set can be constructed with morphological dilation how its measure yields cooccurrences and how it can be applied to characterizing the behavior of the gibbs model for texture in particular they show how the aura measure generalizes to any number of gray levels and neighborhood order some properties previously known for just the binary nearest neighbor grf finally the authors illustrate how these properties can guide one s intuition about the types of grf patterns which are most likely to form

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

detection of architectural distortion in prior mammograms we present methods for the detection of sites of architectural distortion in prior mammograms of interval cancer cases we hypothesize that screening mammograms obtained prior to the detection of cancer could contain subtle signs of early stages of breast cancer in particular architectural distortion the methods are based upon gabor filters phase portrait analysis a novel method for the analysis of the angular spread of power fractal analysis laws texture energy measures derived from geometrically transformed regions of interest rois and haralick s texture features with gabor filters and phase portrait analysis 4224 rois were automatically obtained from 106 prior mammograms of 56 interval cancer cases including 301 true positive rois related to architectural distortion and from 52 mammograms of 13 normal cases for each roi the fractal dimension the entropy of the angular spread of power 10 laws measures and haralick s 14 features were computed the areas under the receiver operating characteristic curves obtained using the features selected by stepwise logistic regression and the leave one roi out method are 0 76 with the bayesian classifier 0 75 with fisher linear discriminant analysis and 0 78 with a single layer feed forward neural network free response receiver operating characteristics indicated sensitivities of 0 80 and 0 90 at 5 8 and 8 1 false positives per image respectively with the bayesian classifier and the leave one image out method

estimation of linear parametric models of nongaussian discrete random fields with application to texture synthesis a general possibly asymmetric noncausal and or nonminimum phase 2d autoregressive moving average random field model driven by an independent and identically distributed 2d nongaussian sequence is considered the model is restricted to be invertible i e system zeros are not allowed to lie on the unit bicircle three performance criteria are investigated for parameter estimation of the system parameters given only the output measurements image pixels the proposed criteria are functions of the higher order cumulant statistics of an inverse filter output one of these criteria is novel and the others have been considered in past only for moving average inverses and without any analysis of their consistency in the paper strong consistency of the proposed methods under the assumption that the system order is known is proved the convergence of the proposed parameter estimators under overparametrization is also analyzed experimental results involving synthesized as well as real life textures are presented to illustrate the performance of two of the considered approaches experimental results of synthesis of 128 spl times 128 textures visually resembling several real life textures in the brodatz album and other sources are presented

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

theory of surround system and associated inequalities in this paper we define the surround system s m c l and the surround system with a center s 2 p c l under the proper hypotheses we establish several geometric inequalities for s 2 p c l as applications we give the background of the surround system with a center s 2 p c l in space science

near peak scattering and the corrected kirchhoff approximation for a convex obstacle abstract the uniform asympotic behavior of the scattering amplitude near the forward peak in the case of classical scattering of waves by a convex obstacle is derived a microlocal model is obtained for the scattering operator this is achieved by use of a parametrix for diffractive boundary problems and by a new study of a class of fourier integral operators those with folding canonical relations a crucial ingredient consists of putting a fourier integral operator with folding canonical relation into a normal form the analysis also gives the asymptotic behavior of the normal derivative of the scattered wave on a neighbourhood of the shadow boundary thus providing a corrected version of the kirchhoff approximation

recovering scattering obstacles by multi frequency phaseless far field data abstract it is well known that the modulus of the far field pattern or phaseless far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field so the shape but not the location of the obstacle can be recovered from the phaseless far field data this paper aims to devise an approach to break the translation invariance property of the phaseless far field pattern to this end we make use of the superposition of two plane waves rather than one plane wave as the incident field in this paper it is mathematically proved that the translation invariance property of the phaseless far field pattern can indeed be broken if superpositions of two plane waves are used as the incident fields for all wave numbers in a finite interval furthermore a recursive newton type iteration algorithm in frequencies is also developed to numerically recover both the location and the shape of the obstacle simultaneously from multi frequency phaseless far field data numerical examples are also carried out to illustrate the validity of the approach and the effectiveness of the inversion algorithm

bussgang zero crossing equalization an integrated hos sos approach an integrated higher order statistics hos and second order statistics sos based equalization technique is presented as an extension of the bussgang equalization algorithm this extension allows one to simultaneously take account of the statistical knowledge about the data source as done in the conventional hos approaches and in particular by bussgang like equalization algorithms such as super exponential constant modulus etc and the spectral redundancy usually present in pulse amplitude modulation pam and quadrature amplitude modulation qam modulated signals exploited by sos based approaches the technique presented employs a new form of sos equalization that naturally integrates into the bussgang scheme it is based on a zero crossing zc property of the received signal when it is passed through a suitable filter the novel equalization scheme is presented in a bayesian estimation framework after illustration of the general bussgang paradigm and of the principles of the zc approach from simulated experiments results show that the extended bussgang zc equalizer not only outperforms conventional bussgang equalizers but is also robust to situations where hos and sos approaches individually fail

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

optimal tradeoff circular harmonic function correlation filter methods providing controlled in plane rotation response correlation methods are becoming increasingly attractive tools for image recognition and location this renewed interest in correlation methods is spurred by the availability of high speed image processors and the emergence of correlation filter designs that can optimize relevant figures of merit in this paper a new correlation filter design method is presented that allows one to optimally tradeoff among potentially conflicting correlation output performance criteria while achieving desired correlation peak value behavior in response to in plane rotation of input images such controlled in plane rotation response is useful in image analysis and pattern recognition applications where the sensor follows a pre arranged trajectory while imaging an object since this new correlation filter design is based on circular harmonic function chf theory we refer to the resulting filters as optimal tradeoff circular harmonic function otchf filters underlying theory otchf filter design method and illustrative numerical results are presented

analytic extension and reconstruction of obstacles from few measurements for elliptic second order operators we deal with an inverse obstacle problem for general second order scalar elliptic operators with real principal part and analytic coefficients near the obstacle we assume that the boundary of the obstacle is a non analytic hypersurface we show that when we put dirichlet boundary conditions one measurement is enough to reconstruct the obstacle in the neumann case we have results only for n 2 3 in general more precisely we show that one measurement is enough for n 2 and we need 3 linearly independent inputs for n 3 however in the case for the helmholtz equation we only need n 1 linearly independent inputs for any n 2 here n is the dimension of the space containing the obstacle these are justified by investigating the analyticity properties of the zero set of a real analytic function in addition we give a reconstruction procedure for each case to recover the shape of obstacle although we state the results for the scattering problems similar results are true for the associated boundary value problems

blind equalization for correlated input symbols a bussgang approach this paper addresses the problem of blind equalization in the case of correlated input symbols and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a bussgang blind equalization scheme numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

recovering a polyhedral obstacle by a few backscattering measurements abstract we propose an inverse scattering scheme of recovering a polyhedral obstacle in r n n 2 3 by only a few high frequency acoustic backscattering measurements the obstacle could be sound soft or sound hard it is shown that the modulus of the far field pattern in the backscattering aperture possesses a certain local maximum behavior from which one can determine the exterior normal directions of the front sides faces then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions one can determine the exterior unit normal vector of each side face of the obstacle after the determination of the exterior unit normals the recovery is reduced to a finite dimensional problem of determining a location point of the obstacle and the distance of each side face away from the location point for the latter reconstruction we need to make use of the far field data with phases numerical experiments are also presented to illustrate the effectiveness of the proposed scheme

jensen s functional and polynomials in several variables in this paper we obtain some lower bounds of the integral 0 2 p 0 2 plog p e i q 1 e i q n d q 12 p d q n2 p if the polynomial p z 1 z n in several variables has a concentration at low degrees measured by 1 l p norm under l p norm 1 p 2 2 l p norm under l p norm p 2 3 l p quasi norm under l p quasi norm 0

a high frequency hp boundary element method for scattering by convex polygons in this paper we propose and analyze a hybrid hp boundary element method for the solution of problems of high frequency acoustic scattering by sound soft convex polygons in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution we demonstrate both theoretically and via numerical examples exponential convergence with respect to the order of the polynomials moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern in which the dependence on the frequency of all constants is explicit importantly these estimates prove that to achieve any desired accuracy in the computation of these quantities it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases in contrast to the at least linear growth required by conventional methods

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