shape preserving local histogram modification a novel approach for shape preserving contrast enhancement is presented in this paper contrast enhancement is achieved by means of a local histogram equalization algorithm which preserves the level sets of the image this basic property is violated by common local schemes thereby introducing spurious objects and modifying the image information the scheme is based on equalizing the histogram in all the connected components of the image which are defined based both on the grey values and spatial relations between pixels in the image and following mathematical morphology constitute the basic objects in the scene we give examples for both grey value and color images

finitely many delta interactions with supports on concentric spheres using the theory of self adjoint extensions of symmetric operators the precise mathematical definition of the quantum hamiltonian describing a finite number of interactions with supports on concentric spheres is given its resolvent is also derived its spectral properties are described and it is shown how this hamiltonian can be obtained as a norm resolvent limit of a family of local scaled short range hamiltonians

rotation and gray scale transform invariant texture identification using wavelet decomposition and hidden markov model in this correspondence we have presented a rotation and gray scale transform invariant texture recognition scheme using the combination of quadrature mirror filter qmf bank and hidden markov model hmm in the first stage the qmf bank is used as the wavelet transform to decompose the texture image into subbands the gray scale transform invariant features derived from the statistics based on first order distribution of gray levels are then extracted from each subband image in the second stage the sequence of subbands is modeled as a hidden markov model hmm and one hmm is designed for each class of textures the hmm is used to exploit the dependence among these subbands and is able to capture the trend of changes caused by rotation during recognition the unknown texture is matched against all the models the best matched model identifies the texture class up to 93 33 classification accuracy is reported

potential approximations to δ an inverse klauder phenomenon with norm resolvent convergence we show that there is a family schrodinger operators with scaled potentials which approximates the interaction hamiltonian in the norm resolvent sense this approximation based on a formal scheme proposed by cheon and shigehara has nontrivial convergence properties which are in several respects opposite to those of the klauder phenomenon

spectral asymptotics for schrodinger operators with periodic point interactions abstract spectrum of the second order differential operator with periodic point interactions in l 2 r is investigated classes of unitary equivalent operators of this type are described spectral asymptotics for the whole family of periodic operators are calculated it is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely it is proven that the spectrum of the operators with anomalous spectral asymptotics when the ratio between the lengths of the bands and gaps tends to zero at infinity can be approximated by standard periodic weighted operators with step wise density functions it is shown that this sequence of periodic weighted operators converges in the norm resolvent sense to the formal generalized resolvent of the periodic schrodinger operator with certain energy dependent boundary conditions the operator acting in an extended hilbert space such that its resolvent restricted to l 2 r coincides with the formal resolvent is constructed explicitly

a new class of solvable models in quantum mechanics describing point interactions on the line the authors provide a detailed analysis of properties of the schrodinger operator in l2 r which formally can be written as d2 dx2 sigma y in gamma nu y delta y where delta is the derivative of dirac s delta function and y contained in implied by r is discrete this model allows for an explicit calculation of spectral properties special emphasis is given to the periodic case y z nu nu j j in z where the spectrum and the density of states are explicitly computed also the spectrum for a half crystal is given the authors study in detail spectral consequences when various defects and impurities are added to the periodic case

energy dependent point interactions in one dimension we consider a new type of point interaction in one dimensional quantum mechanics it is characterized by a boundary condition at the origin that involves the second and or higher order derivatives of the wavefunction the interaction is effectively energy dependent it leads to a unitary s matrix for the transmission reflection problem the energy dependence of the interaction can be chosen such that any given unitary s matrix or the transmission and reflection coefficients can be reproduced at all energies generalization of the results to coupled channel cases is discussed

one dimensional schrodinger operators with interactions singular on a discrete set on etudie le caractere auto adjoint des operateurs de schrodinger sur y u j i x j y j ou on suppose y j x j 1

distribution theory for discontinuous test functions and differential operators with generalized coefficients investigation of the differential operators with the generalized coefficients having singular support on a disjoint set of points requires the consideration of the distribution theory with the set of discontinuous test functions such a distribution theory for test functions having discontinuity at one point is developed a four parameter family of schrodinger operators formed by the operators with singular potential singular metrics and singular gauge field is considered it is proved that this family of singular interactions describes all possible selfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point approximation by operators with smooth coefficients is discussed c 1996 academic press inc

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

texture characterization using shape co occurrence patterns texture characterization is a key problem in image understanding and pattern recognition in this paper we present a flexible shape based texture representation using shape co occurrence patterns more precisely texture images are first represented by a tree of shapes each of which is associated with several geometrical and radiometric attributes then four typical kinds of shape co occurrence patterns based on the hierarchical relationships among the shapes in the tree are learned as codewords three different coding methods are investigated for learning the codewords which can be used to encode any given texture image into a descriptive vector in contrast with existing works the proposed approach not only inherits the shape based method s strong ability to capture geometrical aspects of textures and high robustness to variations in imaging conditions but also provides a flexible way to consider shape relationships and to compute high order statistics on the tree to the best of our knowledge this is the first time that co occurrence patterns of explicit shapes have been used as a tool for texture analysis experiments on various texture and scene data sets demonstrate the efficiency of the proposed approach

flat zones filtering connected operators and filters by reconstruction this correspondence deals with the notion of connected operators starting from the definition for operator acting on sets it is shown how to extend it to operators acting on function typically a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions it is shown that from any connected operator acting on sets one can construct a connected operator for functions however it is not the unique way of generating connected operators for functions moreover the concept of pyramid is introduced in a formal way it is shown that if a pyramid is based on connected operators the flat zones of the functions increase with the level of the pyramid in other words the flat zones are nested filters by reconstruction are defined and their main properties are presented finally some examples of application of connected operators and use of flat zones are described

the finite spectrum of sturm liouville problems with transmission conditions for any positive integer n and a set of positive integers m i i 1 2 ldots n 1 we construct a class of regular sturm liouville problems with n transmission conditions which have exactly sum n 1 i 1 m i n 1 eigenvalues and further we show that these sum n 1 i 1 m i n 1 eigenvalues can be distributed arbitrarily throughout the complex plane in the non self adjoint case and anywhere along the real line in the self adjoint case

projective injective modules serre functors and symmetric algebras we describe serre functors for generalisations of the category o associated with a semisimple complex lie algebra in our approach projective injective modules that is modules which are both

log polar wavelet energy signatures for rotation and scale invariant texture classification classification of texture images is important in image analysis and classification this paper proposes an effective scheme for rotation and scale invariant texture classification using log polar wavelet signatures the rotation and scale invariant feature extraction for a given image involves applying a log polar transform to eliminate the rotation and scale effects but at same time produce a row shifted log polar image which is then passed to an adaptive row shift invariant wavelet packet transform to eliminate the row shift effects so the output wavelet coefficients are rotation and scale invariant the adaptive row shift invariant wavelet packet transform is quite efficient with only o n spl middot log n complexity a feature vector of the most dominant log polar wavelet energy signatures extracted from each subband of wavelet coefficients is constructed for rotation and scale invariant texture classification in the experiments we employed a mahalanobis classifier to classify a set of 25 distinct natural textures selected from the brodatz album the experimental results based on different testing data sets for images with different orientations and scales show that the proposed classification scheme using log polar wavelet signatures outperforms two other texture classification methods its overall accuracy rate for joint rotation and scale invariance being 90 8 percent demonstrating that the extracted energy signatures are effective rotation and scale invariant features concerning its robustness to noise the classification scheme also performs better than the other methods

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

characterization of one dimensional point interactions for the schrodinger operator by means of boundary conditions we find a new representation of all boundary conditions corresponding to the so called point interactions we show that there is one to one correspondence between one dimensional point interactions and boundary conditions of the form with satisfying 2 2 1

new generalized coherent states we construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation de q x dx e q qx with 0 q 1 and e q 0 1 we use this function in place of the usual exponential to generate new coherent states q z from the vacuum which are normalized and continuous in their label z these states allow the resolution of unity and a corresponding weight function is furnished by the exact solution of the associated stieltjes moment problem they also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally ordered function of boson operators we exemplify this by showing that the photon number statistics for these states is sub poissonian for any q 1 the states q z are squeezed we obtain and discuss their signal to quantum noise ratio the function e q x allows a natural generation of multiboson coherent states of arbitrary multiplicity which is impossible for the usual coherent states for q 1 all the above resul

an exactly solvable periodic schrodinger operator the authors explicitly determine the band spectrum of a periodically strongly singular schrodinger operator in l2 r associated with the differential expression d2 dx2 s2 1 4 cos2 x s 2 1 4 sin2 x x epsilon r x epsilon pi z 2 0 s s 1 the corresponding density of states is calculated analytically

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

twisted filtrations of soergel bimodules and linear rouquier complexes abstract we consider twisted standard filtrations of soergel bimodules associated to arbitrary coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the hecke algebra this corresponds to the positivity of the polynomials occurring when expressing an element of the canonical basis in a generalized standard basis twisted by a biclosed set of roots in the sense of dyer and comes as a corollary of soergel s conjecture we then show the positivity of the corresponding inverse polynomials in the case where the biclosed set is an inversion set of an element or its complement by generalizing a result of elias and williamson on the linearity of the rouquier complexes associated to lifts of these basis elements in the artin tits group these lifts turn out to be generalizations of mikado braids as introduced in a joint work with digne this second positivity property generalizes a result of dyer and lehrer from finite to arbitrary coxeter groups

pt invariant point interactions in one dimension by using wu and yu s pseudo potential we construct point interactions in one dimension that are complex but conform to space time reflection invariance the resulting point interactions are equivalent to those obtained by albeverio fei and kurasov as self adjoint extensions of the kinetic energy operator

connected shape size pattern spectra for rotation and scale invariant classification of gray scale images in this paper we describe a multiscale and multishape morphological method for pattern based analysis and classification of gray scale images using connected operators compared with existing methods which use structuring elements our method has three advantages first in our method the time needed for computing pattern spectra does not depend on the number of scales or shapes used i e the computation time is independent of the dimensions of the pattern spectrum second size and strict shape attributes can be computed which we use for the construction of joint 2d shape size pattern spectra third our method is significantly less sensitive to noise and is rotation invariant although rotation invariance can also be approximated by methods using structuring elements at different angles this tends to be computationally intensive the classification performance of these methods is discussed using four image sets brodatz coil 20 coil 100 and diatoms the new method obtains better or equal classification performance to the best competitor with a 5 to 9 fold speed gain

a lie algebraic approach to non hermitian hamiltonians with real spectra an algebraic technique useful in studying non hermitian hamiltonians with real spectra is presented the method is illustrated by explicit application to a family of one dimensional potentials

hierarchical segmentation using tree based shape spaces current trends in image segmentation are to compute a hierarchy of image segmentations from fine to coarse a classical approach to obtain a single meaningful image partition from a given hierarchy is to cut it in an optimal way following the seminal approach of the scale set theory while interesting in many cases the resulting segmentation being a non horizontal cut is limited by the structure of the hierarchy in this paper we propose a novel approach that acts by transforming an input hierarchy into a new saliency map it relies on the notion of shape space a graph representation of a set of regions extracted from the image each region is characterized with an attribute describing it we weigh the boundaries of a subset of meaningful regions local minima in the shape space by extinction values based on the attribute this extinction based saliency map represents a new hierarchy of segmentations highlighting regions having some specific characteristics each threshold of this map represents a segmentation which is generally different from any cut of the original hierarchy this new approach thus enlarges the set of possible partition results that can be extracted from a given hierarchy qualitative and quantitative illustrations demonstrate the usefulness of the proposed method

group theoretical properties and band structure of the lame hamiltonian we study the group theoretical properties of the lame equation and its relation to su 1 1 and su 2 we compute the band structure dispersion relation and transfer matrix and discuss the dynamical symmetry limits

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

a topdown algorithm for computation of level line trees we introduce an optimal topdown algorithm for computing and representing level line trees of 2 d intensity images the running time of the algorithm is where is the size of the input image and is the total length of all level lines the properties of level line trees are also investigated the efficiency of the algorithm is illustrated by experiments on images of different sizes and scenes

quivers floer cohomology and braid group actions we consider the derived categories of modules over a certain family a m of graded rings and floer cohomology of lagrangian intersections in the symplectic manifolds which are the milnor fibres of simple singularities of type a m we show that each of these two rather different objects encodes the topology of curves on an m 1 punctured disc we prove that the braid group b m 1 acts faithfully on the derived category of a m modules and that it injects into the symplectic mapping class group of milnor fibers the philosophy behind our results is as follows using floer cohomology one should be able to associate to the milnor fibre a triangulated category its construction has not been carried out in detail this triangulated category should contain a full subcategory which is equivalent up to a slight difference in the grading to the derived category of a m modules the full embedding would connect the two occurrences of the braid group thus explaining the similarity between them

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

locally rotation contrast and scale invariant descriptors for texture analysis textures within real images vary in brightness contrast scale and skew as imaging conditions change to enable recognition of textures in real images it is necessary to employ a similarity measure that is invariant to these properties furthermore since textures often appear on undulating surfaces such invariances must necessarily be local rather than global despite these requirements it is only relatively recently that texture recognition algorithms with local scale and affine invariance properties have begun to be reported typically they comprise detecting feature points followed by geometric normalization prior to description we describe a method based on invariant combinations of linear filters unlike previous methods we introduce a novel family of filters which provides scale invariance resulting in a texture description invariant to local changes in orientation contrast and scale and robust to local skew significantly the family of filters enables local scale invariants to be defined without using a scale selection principle or a large number of filters a texture discrimination method based on the chi2 similarity measure applied to histograms derived from our filter responses outperforms existing methods for retrieval and classification results for both the brodatz textures and the university of illinois urbana champaign uiuc database which has been designed to require local invariance

on the completeness of coherent states generated by binomial distribution we demonstrate the completeness of boson and spin coherent states generated by binomial distribution by furnishing the exact analytical form of their respective positive weight functions in resolution of unity these weight functions are solutions of the associated truncated stieltjes power moment problem we elaborate on the non unique character of these solutions

rotation invariant texture classification using feature distributions abstract a distribution based classification approach and a set of recently developed texture measures are applied to rotation invariant texture classification the performance is compared to that obtained with the well known circular symmetric autoregressive random field csar model approach a difficult classification problem of 15 different brodatz textures and seven rotation angles is used in experiments the results show much better performance for our approach than for the csar features a detailed analysis of the confusion matrices and the rotation angles of misclassified samples produces several interesting observations about the classification problem and the features used in this study

mtos a tree of shapes for multivariate images the topographic map of a gray level image also called tree of shapes provides a high level hierarchical representation of the image contents this representation invariant to contrast changes and to contrast inversion has been proved very useful to achieve many image processing and pattern recognition tasks its definition relies on the total ordering of pixel values so this representation does not exist for color images or more generally multivariate images common workarounds such as marginal processing or imposing a total order on data are not satisfactory and yield many problems this paper presents a method to build a tree based representation of multivariate images which features marginally the same properties of the gray level tree of shapes briefly put we do not impose an arbitrary ordering on values but we only rely on the inclusion relationship between shapes in the image definition domain the interest of having a contrast invariant and self dual representation of multivariate image is illustrated through several applications filtering segmentation and object recognition on different types of data color natural images document images satellite hyperspectral imaging multimodal medical imaging and videos

on energy gaps in a new type of analytically solvable model in quantum mechanics abstract a new type of analytically solvable one dimensional model in quantum mechanics formally given by d2 dx2 j z j x yj j yj r is analyzed besides calculating the density of states of various periodic arrangements of such and models we also prove a generalization of the saxon hutner conjecture concerning the existence of gaps in the energy spectrum of certain substitutional alloys of or interactions in addition the spectrum of the corresponding random hamiltonians i e j j z ergodic stochastic processes is investigated and explicitly determined in certain cases

lie algebras for systems with mixed spectra i the scattering poschl teller potential starting from an n body quantum space we consider the lie algebraic framework where the poschl teller hamiltonian 1 2 2 c sech2 s csch2 is the single sp 2 r casimir operator the spectrum of this system is mixed it contains a finite number of negative energy bound states and a positive energy continuum of free states it is identified with the clebsch gordan series of the d d representation coupling the wave functions are the sp 2 r clebsch gordan coefficients of that coupling in the parabolic basis using only lie algebraic techniques we find the asymptotic behavior of these wave functions for the special pure trough potential s 0 we derive thus the transmission and reflection amplitudes of the scattering matrix

the fermi pseudo potential in one dimension wu and yu recently examined point interactions in one dimension in the form of the fermi pseudo potential on the other hand there are point interactions in the form of self adjoint extensions saes of the kinetic energy operator we examine the relationship between the point interactions in these two forms in the one channel and two channel cases in the one channel case the pseudo potential leads to the standard three parameter family of saes in the two channel case the pseudo potential furnishes a ten parameter family of saes

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

fast computation of a contrast invariant image representation this paper sets out a new representation of an image which is contrast independent the image is decomposed into a tree of shapes based on connected components of level sets which provides a full and nonredundant representation of the image a fast algorithm to compute the tree the fast level lines transform fllt is explained in detail some simple and direct applications of this representation are shown

coexistence problem for the one dimensional schrodinger operators with the double or triple periodic δ 1 interactions abstract we discuss the coexistence problem for the one dimensional schrodinger operator with the double or triple periodic 1 interactions for each j n we determine whether or not the jth spectral gap is degenerate

viewpoint invariant texture description using fractal analysis image texture provides a rich visual description of the surfaces in the scene many texture signatures based on various statistical descriptions and various local measurements have been developed existing signatures in general are not invariant to 3d geometric transformations which is a serious limitation for many applications in this paper we introduce a new texture signature called the multifractal spectrum mfs the mfs is invariant under the bi lipschitz map which includes view point changes and non rigid deformations of the texture surface as well as local affine illumination changes it provides an efficient framework combining global spatial invariance and local robust measurements intuitively the mfs could be viewed as a better histogram with greater robustness to various environmental changes and the advantage of capturing some geometrical distribution information encoded in the texture experiments demonstrate that the mfs codes the essential structure of textures with very low dimension and thus represents an useful tool for texture classification

mittag leffler coherent states we create a family of boson coherent states using the functions of mittag leffler ml e z 0 and their generalizations e z 0 instead of exponentials these states are shown to satisfy the usual requirements of normalizability continuity in the label and the resolution of unity with a positive weight function this last quantity is found for arbitrary 0 as a solution of an associated stieltjes moment problem in addition for m 1 2 3 and 1 corresponding to em z we propose and analyse special q deformations 0 q1 of the functions em z which serve as a tool to define q deformed coherent states of ml type we provide the expressions for expectation values of physical quantities for all the above states we discuss physical properties of these states noting that they are squeezed the ml coherent states are sub poissonian in nature whereas the q deformed ml states can be sub and super poissonian depending on q all these states are shown to be eigenstates of deformed boson operators whose commutation relations are given

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

the hodge theory of soergel bimodules we prove soergel s conjecture on the characters of indecomposable soergel bimodules we deduce that kazhdan lusztig polynomials have positive coecients for arbitrary coxeter systems using results of soergel one may deduce an algebraic proof of the kazhdan lusztig conjecture

optimizing gabor filter design for texture edge detection and classification an effective and efficient texture analysis method based on a new criterion for designing gabor filter sets is proposed the commonly used filter sets are usually designed for optimal signal representation we propose here an alternative criterion for designing the filter set we consider a set of filters and its response to pairs of harmonic signals two signals are considered separable if the corresponding two sets of vector responses are disjoint in at least one of the components we propose an algorithm for deriving the set of gabor filters that maximizes the fraction of separable harmonic signal pairs in a given frequency range the resulting filters differ significantly from the traditional ones we test these maximal harmonic discrimination mhd filters in several texture analysis tasks clustering recognition and edge detection it turns out that the proposed filters perform much better than the traditional ones in these tasks they can achieve performance similar to that of state of the art distribution based texton methods while being simpler and more computationally efficient

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

equivariant sheaves on flag varieties we show that the borel equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of differential graded modules over the extension algebra of the direct sum of the simple equivariant perverse sheaves this proves a conjecture of soergel and lunts in the case of flag varieties

shape based invariant texture indexing this paper introduces a new texture analysis scheme which is invariant to local geometric and radiometric changes the proposed methodology relies on the topographic map of images obtained from the connected components of level sets this morphological tool providing a multi scale and contrast invariant representation of images is shown to be well suited to texture analysis we first make use of invariant moments to extract geometrical information from the topographic map this yields features that are invariant to local similarities or local affine transformations these features are invariant to any local contrast change we then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases the obtained experimental results outperform the current state of the art in locally invariant texture analysis

brief review of invariant texture analysis methods this paper considers invariant texture analysis texture analysis approaches whose performances are not affected by translation rotation affine and perspective transform are addressed existing invariant texture analysis algorithms are carefully studied and classified into three categories statistical methods model based methods and structural methods the importance of invariant texture analysis is presented first each approach is reviewed according to its classification and its merits and drawbacks are outlined the focus of possible future work is also suggested

dynamical symmetry approach to periodic hamiltonians we show that dynamical symmetry methods can be applied to hamiltonians with periodic potentials we construct dynamical symmetry hamiltonians for the scarf potential and its extensions using representations of su 1 1 and so 2 2 energy bands and gaps are readily understood in terms of representation theory we compute the transfer matrices and dispersion relations for these systems and find that the complementary series plays a central role as well as nonunitary representations

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

1 d schrodinger operators with local point interactions on a discrete set abstract spectral properties of 1 d schrodinger operators h x d 2 d x 2 x n x n x x n with local point interactions on a discrete set x x n n 1 are well studied when d inf n k n x n x k 0 our paper is devoted to the case d 0 we consider h x in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding weyl functions we show that the spectral properties of h x like self adjointness discreteness and lower semiboundedness correlate with the corresponding spectral properties of certain classes of jacobi matrices based on this connection we obtain necessary and sufficient conditions for the operators h x to be self adjoint lower semibounded and discrete in the case d 0 the operators with type interactions are investigated too the obtained results demonstrate that in the case d 0 as distinguished from the case d 0 the spectral properties of the operators with and type interactions are substantially different

generalized kronig penney hamiltonians abstract in this article we extend the study of generalized point interactions to the periodic case and we investigate analogues of the kronig penney model for the class of point interactions introduced in joint work with p chernoff in addition to periodic and potentials which follow as special cases several examples are studied in detail in general the models under consideration are shown to have purely absolutely continuous spectrum and in some cases all gaps in the spectrum close

spatial size distributions applications to shape and texture analysis this paper proposes new descriptors for binary and gray scale images based on newly defined spatial size distributions ssd the main idea consists of combining a granulometric analysis of the image with a comparison between the geometric covariograms for binary images or the auto correlation function for gray scale images of the original image and its granulometric transformation the usual granulometric size distribution then arises as a particular case of this formulation examples are given to show that in those cases in which a finer description of the image is required the more complex descriptors generated from the ssd could be advantageously used it is also shown that the new descriptors are probability distributions so their intuitive interpretation and properties can be appropriately studied from the probabilistic point of view the usefulness of these descriptors in shape analysis is illustrated by some synthetic examples and their use in texture analysis is studied various cases of ssd and several former methods for texture classification are compared

wavelet modeling using finite mixtures of generalized gaussian distributions application to texture discrimination and retrieval this paper addresses statistical based texture modeling using wavelets we propose a new approach to represent the marginal distribution of the wavelet coefficients using finite mixtures of generalized gaussian mogg distributions the mogg captures a wide range of histogram shapes which provides better description and discrimination of texture than using single probability density functions pdf s as proposed by recent state of the art approaches moreover we propose a model similarity measure based on kullback leibler divergence kld approximation using monte carlo sampling methods through experiments on two popular texture data sets we show that our approach yields significant performance improvements for texture discrimination and retrieval as compared with recent methods of statistical based wavelet modeling