color texture classification using shortest paths in graphs color textures are among the most important visual attributes in image analysis this paper presents a novel method to analyze color textures by modeling a color image as a graph in two different and complementary manners each color channel separately and the three color channels altogether and by obtaining statistical moments from the shortest paths between specific vertices of this graph such an approach allows to create a set of feature vectors which were extracted from vistex usptex and tc00013 color texture databases the best classification results were 99 07 96 85 and 91 54 lda with leave one out 87 62 66 71 and 88 06 1nn with holdout and 98 62 96 16 and 91 34 lda with holdout of success rate percentage of samples correctly classified for these three databases respectively these results prove that the proposed approach is a powerful tool for color texture analysis to be explored

weight adjustment rule of neural networks for computing discrete 2 d gabor transforms image processing it is demonstrated that the weight adjustment rule used in the neural network for computing the 2 d gabor transform proposed by j daugman 1988 can be shown to be equivalent to the jacobi iteration scheme for solving simultaneous linear equations it is shown that faster convergence of the algorithm can be achieved by using gauss seidel iteration successive overrelaxation conjugate gradient algorithms and multigrid methods

complex multipole beam approach to acoustic scattering problems a novel approach to reducing the matrix size associated with the boundary element moment method solution of the problem of acoustic scattering from arbitrarily shaped closed bodies is presented in this paper the key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space on the scatterer boundary the fields generated by these multipole sources resemble the gabor basis functions by utilizing the properties of the gabor series guidelines for selecting the orders as well as locations of the multipole sources are developed the present approach not only reduces the number of unknowns but also generates a generalized impedance matrix with a banded structure the accuracy of the proposed method is verified by using internal accuracy checks and by comparing the numerical results with the analytic solutions for spherical scatterers

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

color spectral analysis for spatial structure characterization of textures in ihls color space in this article a linear prediction model based approach for color texture characterization and classification in the improved hue luminance and saturation color space is presented pure chrominance structure information is used in addition to the normally used luminance structure information for color texture classification hue and saturation channels of a color image in ihls color space are combined using a complex exponential to give a single channel which holds all the chrominance information of the image two dimensional complex multichannel versions of the non symmetric half plane autoregressive model the quarter plane autoregressive model and the gauss markov random field model are used to perform parametric power spectrum estimation of both luminance and the combined chrominance channels of the image the accuracy and precision of these spectral estimates are proven quantitatively by performing tests on a large number of images spectral distance measures are calculated for the spectral information of luminance and chrominance channels individually as well as combined through a combination coefficient using these distance measures color texture classification is done with k nearest neighbor algorithm experimental results verify that the ihls color space exhibits better performance than the rgb color space indicating the significance of using ihls for such analysis they also show that color texture characterization and percentage classification obtained by combined luminance and chrominance structure information is better than the color texture classification done using only the luminance structure information

color texture classification by integrative co occurrence matrices abstract integrative co occurrence matrices are introduced as novel features for color texture classification the extended co occurrence notation allows the comparison between integrative and parallel color texture concepts the information profit of the new matrices is shown quantitatively using the kolmogorov distance and by extensive classification experiments on two datasets applying them to the rgb and the luv color space the combined color and intensity textures are studied and the existence of intensity independent pure color patterns is demonstrated the results are compared with two baselines gray scale texture analysis and color histogram analysis the novel features improve the classification results up to 20 and 32 for the first and second baseline respectively

efficient computation of gabor filter based multiresolution responses abstract multiresolution representation in machine vision systems provides a means to detect analyze and interpret the information content of an image at multiple resolutions the pyramidal representation of images suggested by burt and crowley and the hierarchical construction of orientation and velocity tuned filters developed by fleet and jepson are some of the examples for multiresolution representation of image details in recent years gabor filter based methods have been suggested by several researchers for machine vision applications such as edge detection texture classification and optical flow estimation these applications require generating a family of gabor filters tuned to several resolutions and orientations and computing their responses the computation of gabor filter responses at multiple resolutions and orientations is a very computationally intensive task two efficient schemes for computing gabor filter based multiresolution responses are proposed the first scheme namely recursive filtering method generates a family of gabor filters and their responses starting from a high resolution and proceeding towards the lowest resolution in steps of an octave the second approach namely successive sampling method generates the same responses in the reverse order in both these methods the symmetric asymmetric and wavelet nature of gabor filters are exploited in order to speed up the computation the applicability and usefulness of the schemes are established through experimental results special purpose architectures are proposed to implement the proposed techniques in hardware in order to further speed up the computation

semiclassical asymptotics of eigenvalues for schrodinger operators with magnetic fields abstract we consider schrodinger operators with magnetic fields on a two dimensional compact manifold or on r 2 the purpose is to study the semiclassical asymptotics of the eigenvalues by two different methods we obtain some facts on the harmonic oscillators under uniform magnetic fields and we also discuss them

oscillatory integrals with quadratic phase function on a real abstract wiener space abstract stochastic oscillatory integrals with quadratic phase function are studied in the case where amplitude functions are multiple wiener integrals we show that a principle of stationary phase holds when kernels of multiple wiener integrals are of trace class on the way we establish a new criterion for a wiener functional to be analytic

the canonical coordinates method for pattern deformation theoretical and computational considerations a method for the analysis of deformed patterns is presented and analyzed the image is transformed into a new set of coordinates in which the deformation has a particular simple form a number of deformations are considered the practical implementation of the method is discussed similar aspects of biological vision are also considered

design of steerable wavelets to detect multifold junctions we propose a framework for the detection of junctions in images although the detection of edges and key points is a well examined and described area the multiscale detection of junction centers especially for odd orders poses a challenge in pattern analysis the goal of this paper is to build optimal junction detectors based on 2d steerable wavelets that are polar separable in the fourier domain the approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions the backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix we are able to detect m fold junctions in different scales and orientations we provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm

analysis of wiener functionals malliavin calculus and its applications to heat kernels on donne un expose facilement accessible du calcul de malliavin du calcul differentiel de dimension infinie sur l espace de wiener

perceptually uniform color spaces for color texture analysis an empirical evaluation rgb a nonuniform color space is almost universally accepted by the image processing community as the means for representing color on the other hand perceptually uniform spaces such as l a b as well as approximately uniform color spaces such as hsv exist in which measured color differences are proportional to the human perception of such differences this paper compares rgb with l a b and hsv in terms of their effectiveness in color texture analysis there has been a limited but increasing amount of work on the color aspects of textured images the results have shown that incorporating color into a texture analysis and recognition scheme can be very important and beneficial the presented methodology uses a family of gabor filters specially tuned to measure specific orientations and sizes within each color texture effectiveness is measured by the classification performance of each color space as well as by classifier independent measures experimental results are obtained with a variety of color texture images perceptually uniform spaces are shown to outperform rgb in many cases

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

what is the goal of sensory coding a number of recent attempts have been made to describe early sensory coding in terms of a general information processing strategy in this paper two strategies are contrasted both strategies take advantage of the redundancy in the environment to produce more effective representations the first is described as a compact coding scheme a compact code performs a transform that allows the input to be represented with a reduced number of vectors cells with minimal rms error this approach has recently become popular in the neural network literature and is related to a process called principal components analysis pca a number of recent papers have suggested that the optimal compact code for representing natural scenes will have units with receptive field profiles much like those found in the retina and primary visual cortex however in this paper it is proposed that compact coding schemes are insufficient to account for the receptive field properties of cells in the mammalian visual pathway in contrast it is proposed that the visual system is near to optimal in representing natural scenes only if optimality is defined in terms of sparse distributed coding in a sparse distributed code all cells in the code have an equal response probability across the class of images but have a low response probability for any single image in such a code the dimensionality is not reduced rather the redundancy of the input is transformed into the redundancy of the firing pattern of cells it is proposed that the signature for a sparse code is found in the fourth moment of the response distribution i e the kurtosis in measurements with 55 calibrated natural scenes the kurtosis was found to peak when the bandwidths of the visual code matched those of cells in the mammalian visual cortex codes resembling wavelet transforms are proposed to be effective because the response histograms of such codes are sparse i e show high kurtosis when presented with natural scenes it is proposed that the structure of the image that allows sparse coding is found in the phase spectrum of the image it is suggested that natural scenes to a first approximation can be considered as a sum of self similar local functions the inverse of a wavelet possible reasons for why sensory systems would evolve toward sparse coding are presented

segmentation of color textures this paper describes an approach to perceptual segmentation of color image textures a multiscale representation of the texture image generated by a multiband smoothing algorithm based on human psychophysical measurements of color appearance is used as the input initial segmentation is achieved by applying a clustering algorithm to the image at the coarsest level of smoothing the segmented clusters are then restructured in order to isolate core clusters i e patches in which the pixels are definitely associated with the same region the image pixels representing the core clusters are used to form 3d color histograms which are then used for probabilistic assignment of all other pixels to the core clusters to form larger clusters and categorise the rest of the image the process of setting up color histograms and probabilistic reassignment of the pixels to the clusters is then propagated through finer levels of smoothing until a full segmentation is achieved at the highest level of resolution

on the shiftability of dual tree complex wavelet transforms the dual tree complex wavelet transform dt bbcwt is known to exhibit better shift invariance than the conventional discrete wavelet transform we propose an amplitude phase representation of the dt ibbc wt which among other things offers a direct explanation for the improvement in the shift invariance the representation is based on the shifting action of the group of fractional hilbert transform fht operators which extends the notion of arbitrary phase shifts from sinusoids to finite energy signals wavelets in particular in particular we characterize the shift ability of the dt bbcwt in terms of the shifting property of the fhts at the heart of the representation are certain fundamental invariances of the fht group namely that of translation dilation and norm which play a decisive role in establishing the key properties of the transform it turns out that these fundamental invariances are exclusive to this group next by introducing a generalization of the bedrosian theorem for the fht operator we derive an explicitly understanding of the shifting action of the fht for the particular family of wavelets obtained through the modulation of lowpass functions e g the shannon and gabor wavelet this in effect links the corresponding dual tree transform with the framework of windowed fourier analysis finally we extend these ideas to the multidimensional setting by introducing a directional extension of the fht the fractional directional hilbert transform in particular we derive a signal representation involving the superposition of direction selective wavelets with appropriate phase shifts which helps explain the improved shift invariance of the transform along certain preferential directions

a new feature extractor invariant to intensity rotation and scaling of color images this paper proposes a new method for extracting the invariant features of an image based on the concept of principal component analysis and a competitive learning algorithm the proposed algorithm can be applied to binary gray level or colored texture images with a size greater than 256x256 pixels in addition to translation scaling and rotation invariant extraction the extraction of a feature invariant to color intensity can be implemented by using this method in our experiment the proposed method shows the capability to differentiate images having the same shape but different colored textures the experimental results report the effectiveness of this technique and its performance as measured by recognition accuracy rate and computational time these results are also compared with those obtained by classical techniques

ranging through gabor logons a consistent hierarchical approach in this work the correspondence problem in stereo vision is handled by matching two sets of dense feature vectors inspired by biological evidence these feature vectors are generated by a correlation between a bank of gabor sensors and the intensity image the sensors consist of two dimensional gabor filters at various scales spatial frequencies and orientations which bear close resemblance to the receptive field profiles of simple v1 cells in visual cortex a hierarchical stochastic relaxation method is then used to obtain the dense stereo disparities unlike traditional hierarchical methods for stereo feature based hierarchical processing yields consistent disparities to avoid false matchings due to static occlusion a dual matching based on the imaging geometry is used

shape quantization and recognition with randomized trees we explore a new approach to shape recognition based on a virtually infinite family of binary features queries of the image data designed to accommodate prior information about shape invariance and regularity each query corresponds to a spatial arrangement of several local topographic codes or tags which are in themselves too primitive and common to be informative about shape all the discriminating power derives from relative angles and distances among the tags the important attributes of the queries are a natural partial ordering corresponding to increasing structure and complexity semi invariance meaning that most shapes of a given class will answer the same way to two queries that are successive in the ordering and stability since the queries are not based on distinguished points and substructures no classifier based on the full feature set can be evaluated and it is impossible to determine a priori which arrangements are informative our approach is to select informative features and build tree classifiers at the same time by inductive learning in effect each tree provides an approximation to the full posterior where the features chosen depend on the branch that is traversed due to the number and nature of the queries standard decision tree construction based on a fixed length feature vector is not feasible instead we entertain only a small random sample of queries at each node constrain their complexity to increase with tree depth and grow multiple trees the terminal nodes are labeled by estimates of the corresponding posterior distribution over shape classes an image is classified by sending it down every tree and aggregating the resulting distributions the method is applied to classifying handwritten digits and synthetic linear and nonlinear deformations of three hundred l at e x symbols stateof the art error rates are achieved on the national institute of standards and technology database of digits the principal goal of the experiments on l at e x symbols is to analyze invariance generalization error and related issues and a comparison with artificial neural networks methods is presented in this context

choice of a pertinent color space for color texture characterization using parametric spectral analysis this article presents a comparison of different color spaces including rgb ihls and email protected a b for color texture characterization this comparison is based on the fusion of the independent spatial structure and color feature cues in ihls and l a b two channel complex color images are created from the luminance and the chrominance values for such images two dimensional complex multichannel linear prediction models are used to perform parametric power spectrum estimation and the structure feature cues are computed from this estimated power spectrum quantitative comparison of auto spectra of luminance and combined chrominance channels for different color spaces is done this comparison is based on the degree of decorrelation between luminance and chrominance information provided by different color space transformations three dimensional histograms are used as color feature cues then to classify color textures kullback leibler divergence based symmetric distance measures are calculated for pure color luminance structure and chrominance structure feature cues individual as well as combined effect of information from all feature cues on classification results is then compared for different color spaces and different color texture data sets the proposed color texture classification method performs better than the state of the art methods in certain cases the l a b color space gives us a better characterization of the chrominance spatial structure as well as the overall spatial structure for all of the chosen data sets experimental results on pixel classification of color textures are also presented and discussed

the space requirements of indexing under perspective projections object recognition systems can be made more efficient through the use of table lookup to match features the cost of this indexing process depends on the space required to represent groups of model features in such a lookup table we determine the space required to perform indexing of arbitrary sets of 3d model points for lookup from a single 2d image formed under perspective projection we show that in this case one must use a 3d surface to represent model groups and we provide an analytic description of such a surface this is in contrast to the cases of scaled orthographic or affine projection in which only a 2d surface is required to represent a group of model features this demonstrates a fundamental way in which the recognition of objects under perspective projection is more complex than is recognition under other projection models

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

return to thermal equilibrium by the solution of a quantum langevin equation a quantum mechanical treatment of the evolution of an anharmonic oscillator coupled to a heat bath is given it is shown that for a certain class of anharmonic potentials the heat bath drives the oscillator to an equilibrium state close to the quantum gibbs state associated to the potential thus a partial proof is provided for a conjecture of r benguria and m kac

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

a multi expert approach for robust face detection both detection accuracy and speed are of major concerns in developing a robust face detection system for real world applications to this end we propose a robust face detection approach by combining multiple experts in both cascade and parallel manner we design three detection experts which employ different feature representation schemes of local images 2d haar wavelet gradient direction and gabor filter the three features are classified using the same classification model namely a polynomial neural network pnn on reduced feature subspace the detection experts are used in multiple stages with simple ones in proceeding stages and complex ones in succeeding stages for improving detection speed meanwhile the output of each expert is combined with the outputs of its preceding experts to improve detection accuracy the effectiveness of the multi expert approach has been demonstrated in experiments on a large number of images the obtained detection results are superior to the best individual expert and state of the art approaches while the detection speed is fast

fuzzy aura matrices for texture classification the aura concept has been developed from the set theory and is an efficient tool to characterize texture images it is based on the notion of aura set and on the associated aura measure that involve the neighborhood of each image pixel in this paper we propose to extend this concept to the framework of fuzzy sets in order to take the imprecise nature of images into account we define the notions of fuzzy aura sets and of aura measures to compute fuzzy aura matrices as texture descriptors fuzzy aura measures assume no restrictions about the neighborhood shape size and spatial invariance extensive tests of texture classification on outex benchmark datasets show that fuzzy aura matrices computed with spatially variant neighborhoods often outperform other powerful texture descriptors on both gray level and color images highlightsto characterize texture images we extend the aura concepts to the fuzzy framework we define fuzzy aura sets and measures to describe textures by fuzzy aura matrices fuzzy aura measures can use spatially variant neighborhoods such adaptivity is interesting to classify both gray level and color texture images

levy s stochastic area and the principle of stationary phase abstract let w 0 h 0 0 be the 2 dimensional classical pinned wiener space over 0 1 a localization phenomenon will be shown for stochastic oscillatory integrals with levy s stochastic area as phase function

color texture classification based on gravitational collapse texture and color are essential attributes to be analyzed for any robust computer vision system this paper presents a novel method to analyze color texture images based on representing states of a simplified gravitational collapse from each image color channel and extracting information from each state using the bouligand minkowski fractal dimension and the lacunarity method in this approach we obtained the best classification results when the images of each channel evolved in times t 1 5 10 15 each time representing a state using radius r 3 4 5 6 for the bouligand minkowski method and box size l 2 3 4 5 6 for the lacunarity method the best classification results were 99 37 and 96 57 of success rate percentage of samples correctly classified for vistex and usptex databases respectively these results prove that the proposed approach opens a promising source of research in color texture analysis still to be explored

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

facial expression recognition in perceptual color space this paper introduces a tensor perceptual color framework tpcf for facial expression recognition fer which is based on information contained in color facial images the tpcf enables multilinear image analysis in different color spaces and demonstrates that color components provide additional information for robust fer using this framework the components in either rgb ycbcr cielab or cieluv space of color images are unfolded to 2 d tensors based on multilinear algebra and tensor concepts from which the features are extracted by log gabor filters the mutual information quotient method is employed for feature selection these features are classified using a multiclass linear discriminant analysis classifier the effectiveness of color information on fer using low resolution and facial expression images with illumination variations is assessed for performance evaluation experimental results demonstrate that color information has significant potential to improve emotion recognition performance due to the complementary characteristics of image textures furthermore the perceptual color spaces cielab and cieluv are better overall for fer than other color spaces by providing more efficient and robust performance for fer using facial images with illumination variation

influence of normalization and color space to color texture classification abstract color texture classification has recently attracted significant attention due to its multiple applications the color texture images depend on the texture surface and its albedo the illumination the camera and its viewing position a key problem to get an acceptable performance is the ambient illumination which can vary the perceived structures in the surface given a color texture classification problem it would be desirable to know which is the best approach to solve the problem making the minimal assumptions about the illumination conditions the present work does an exhaustive evaluation of the state of the art color texture classification methods considering 5 different color spaces 12 normalization methods to achieve illumination invariances 19 texture feature vectors and 23 pure color feature vectors our experiments allow to conclude that parallel approaches are better than integrative approaches for color texture classification achieving the first positions in the friedman ranking multiresolution local binary patterns mlbp are the best intensity texture features followed by wavelet and gabor filters combined with luminance chrominance color spaces lab and lab2000hl and for pure color classification the best are first order statistics fos calculated in rgb color space for intensity texture features the learning methods work better on the four smallest datasets although they could not be tested in other four bigger datasets due to its huge computational cost nor with color texture classification normalization and color spaces slightly increase the average accuracy of color texture classification although the differences achieved using normalization are not statistically significant in a paired t test lab2000hl and rgb are the best color spaces but the former is the slowest one regarding elapsed time the best vector features mlbp for intensity texture daub4 daubechies filters using mean and variance statistics for color texture and fos for pure color are nearly the fastest or are in the middle interval of all the tested methods

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

on wiener functionals of order 2 associated with soliton solutions of the kdv equation abstract the eigenvalues and eigenvectors of the hilbert schmidt operators corresponding to the wiener functionals of order 2 which give a rise of soliton solutions of the kdv equation are determined two explicit expressions of the stochastic oscillatory integral with such wiener functional as phase function are given one is of infinite product type and the other is of levy s formula type as an application the asymptotic behavior of the stochastic oscillatory integral will be discussed

content based image retrieval using color difference histogram this paper presents a novel image feature representation method namely color difference histograms cdh for image retrieval this method is entirely different from the existing histograms most of the existing histogram techniques merely count the number or frequency of pixels however the unique characteristic of cdhs is that they count the perceptually uniform color difference between two points under different backgrounds with regard to colors and edge orientations in l a b color space this method pays more attention to color edge orientation and perceptually uniform color differences and encodes color orientation and perceptually uniform color difference via feature representation in a similar manner to the human visual system the method can be considered as a novel visual attribute descriptor combining edge orientation color and perceptually uniform color difference as well as taking the spatial layout into account without any image segmentation learning processes or clustering implementation experimental results demonstrate that it is much more efficient than the existing image feature descriptors that were originally developed for content based image retrieval such as mpeg 7 edge histogram descriptors color autocorrelograms and multi texton histograms it has a strong discriminative power using the color texture and shape features while accounting for spatial layout

adaptive smoothing respecting feature directions accurate extraction of the image feature directions is essential to image smoothing and other image processing tasks we show that the gradient based feature direction extraction method can be very erroneous the gradient is too local and it cannot detect oscillations we have developed two new methods the hessian method an approach using higher order differentiations and the gabor 1946 method an approach using space frequency analysis

gabor filter based edge detection abstract it is common practice to utilize evidence from biological and psychological vision experiments to develop computational models for low level feature extraction the receptive profiles of simple cells in mammalian visual systems have been found to closely resemble gabor filters daugman proved that gabor filters achieve joint minimal joint uncertainty these results led researchers to develop computational models based on gabor filters for several low level vision applications such as edge detection texture classification optical flow estimation and data compression in this paper the performance of a gabor odd filter based edge detector is investigated using the measures proposed by canny based on this performance analysis a design criterion for one dimensional 1d gabor filter based edge detector is derived it is shown that this design criterion also holds good for a two dimensional 2d gabor filter based edge detector experimental results are presented to demonstrate the performance of the gabor filter based edge detector

handprinted character recognition based on spatial topology distance measurement in this work we present a self organization matching approach to accomplish the recognition of handprinted characters drawn with thick strokes this approach is used to flex the unknown handprinted character toward matching its object characters gradually the extracted character features used in the self organization matching are center loci orientation and major axes of ellipses which fit the inked area of the patterns simulations provide encouraging results using the proposed method

ergodic properties for a quantum nonlinear dynamics we present a quantum system composed of infinitely many particles subject to a nonquadratic hamiltonian for which it is possible to investigate the long time behavior of the dynamics and its ergodic properties we do so both for the kms states and for a large class of locally normal invariant states whose very existence is already of some interest

on the invertibility of moller morphisms local perturbations of the dynamics of infinite quantum systems are considered it is known that if the mo ller morphisms associated to the dynamics and its perturbation are invertible the perturbed evolution is isomorphic to the unperturbed one and thereby shares its ergodic properties it was claimed by v ya golodets theor math phys 23 525 1975 that the above condition holds whenever the observable algebra is asymptotically abelian for the unperturbed evolution and the perturbed evolution has a kms state the present paper contains a counterexample to this statement and a construction of a spatial representation of the mo ller morphisms

non markovian quantal brownian motion model a non markovian version of the quantal brownian motion model is given the integrodifferential equations of motion are solved establishing the analytic form of the resolvent poles and analyzing their properties an explicit investigation of the poles at zero temperature is performed in this frame a rule can be found that relates the relevant poles of the non markovian resolvent to the eigenvalues of the associated markovian generator of the motion

wave propagation and sampling theory part ii sampling theory and complex waves morlet et al 1982 this issue showed the advantages of using complex values for both waves and characteristics of the media we simulated the theoretical tools we present here using the goupillaud kunetz algorithm now we present sampling methods for complex signals or traces corresponding to received waves and sampling methods for complex characterization of multilayered or heterogeneous media regarding the complex signals we present a twodimecsional 2 d method of sampling in the time frequency domain using a special or extended gabor expansion on a set of basic wavelets adapted to phase preservation such a 2 d expansion permits us to handle in a proper manner instantaneous frequency spectra we show the differences between wavelet resolution and sampling grid resolution we also show the importance of phase preservation in high resolution seismic regarding the media we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution analytical studies of wave propagation in periodic structures are well known in solid state physics and lead to the so called bloch waves the introduction of complex waves leads to replacing the classical wave equation by a schriidinger equation finally we show that complex wave equations gabor expansion and bloch waves are three different ways of introducing the tools of quantum mechanics in highresolution seismic gabor 1946 kittel 1976 morlet 1975 and conversely the goupillaud kunetz algorithm and an extended gabor expansion may be of some use in solid state physics

wave propagation and sampling theory part i complex signal and scattering in multilayered media from experimental studies in digital processing of seismic reflection data geophysicists know that a seismic signal does vary in amplitude shape frequency and phase versus propagation time to enhance the resolution of the seismic reflection method we must investigate these variations in more detail we present quantitative results of theoretical studies on propagation of plane waves for normal incidence through perfectly elastic multilayered media as wavelet shapes we use zero phase cosine wavelets modulated by a gaussian envelope and the corresponding complex wavelets a finite set of such wavelets for an appropriate sampling of the frequency domain may be taken as the basic wavelets for a gabor expansion of any signal or trace in a two dimensional 2 d domain time and frequency we can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals these results appear as complex 2 d functions of time and frequency i e as instantaneous frequency spectra choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces for this purpose we developed a gabor expansion involving basic wavelets with a constant time duration mean period ratio for layered media as found in sedimentary basins

a joint frequency position domain structure identification of nonlinear discrete time systems by neural networks a new technique is proposed to identify the structure and the parameters of nonlinear discrete time system models the structure is represented in a frequency position domain of gabor basis functions gbfs a simplification to the gbf is also presented where the spatial gaussian envelope of gbf is replaced with a triangular one a modification to the gbf has also been introduced in order to suppress the effects of noise on the procedure a three layered neural network augmented with nonuniform sampling is described for solving the system identification problem

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

acceleration of the frame algorithm shows how polynomial acceleration techniques which have been developed for the solution of large linear systems can be employed to improve and accelerate the frame algorithm these methods permit a reduction in the number of necessary iterations by an order of magnitude when the frame algorithm is slow the author gives several examples from the theory of irregular sampling from wavelet theory and from gabor theory where these methods are probably mandatory for efficient reconstruction

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

visual recognition and categorization on the basis of similarities to multiple class prototypes one of the difficulties of object recognition stems from the need to overcome the variability in object appearance caused by pose and other factors such as illumination the influence of these factors can be countered by learning to interpolate between stored views of the target object taken under representative combinations of viewing conditions difficulties of another kind arise in daily life situations that require categorization rather than recognition of objects although categorization cannot rely on interpolation between stored examples we show that knowledge of several representative members or prototypes of each of the categories of interest can provide the necessary computational substrate for the categorization of new instances we describe a system that represents input shapes by their similarities to several prototypical objects and show that it can recognize new views of the familiar objects discriminate among views of previously unseen shapes and attribute the latter to familiar categories

two different approaches for iris recognition using gabor filters and multiscale zero crossing representation abstract importance of biometric user identification is increasing everyday one of the most promising techniques is the one based on the human iris the authors in this work describe different approaches to develop this biometric technique based on the works carried out by daugman the authors have worked using gabor filters and hamming distance but in addition they have also worked in zero crossing representation of the dyadic wavelet transform applied to two different iris signatures one based on a single virtual circle of the iris the other one based on an annular region also other metrics have been applied to be compared with the results obtained with the hamming distance in this work euclidean distance and d z will be shown the last proposed approach is translation rotation and scale invariant results will show a classification success up to 99 6 achieving an equal error rate down to 0 12 and the possibility of having null false acceptance rates with very low false rejection rates

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

temperature states on loop groups theta functions and the luttinger model abstract we consider projective representations of the loop group of u n suggested by statistical mechanics these representations are defined by certain positive definite functions called temperature states on the universal central extension of the loop group we find that the boson fermion correspondence known to exist in a mathematically precise form at zero temperature persists at non zero temperature by expressing the temperature state for u 1 in two different ways we obtain identities between elliptic functions we apply these ideas to a simple model in statistical physics the luttinger model establishing the existence of a projective representation of the loop group of u 1 u 1 in the presence of interaction and at all temperatures a rigorous derivation of the correlation functions for this model is given using the boson fermion correspondence

face recognition the problem of compensating for changes in illumination direction a face recognition system must recognize a face from a novel image despite the variations between images of the same face a common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations examples of such representations are edge maps image intensity derivatives and images convolved with 2d gabor like filters here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination as well as viewpoint and facial expression our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination similar results were obtained for changes due to viewpoint and expression image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination however systems based only on such representations failed to recognize up to 20 percent of the faces in our database humans performed considerably better under the same conditions we discuss possible reasons for this superiority and alternative methods for overcoming illumination effects in recognition

similarity connectionism and the problem of representation in vision a representational scheme under which the ranking between represented similarities is isomorphic to the ranking between the corresponding shape similarities can support perfectly correct shape classification because it preserves the clustering of shapes according to the natural kinds prevailing in the external world this article discusses the computational requirements of representation that preserves similarity ranks and points out the relative straightforwardness of its connectionist implementation

object recognition using gabor co occurrence similarity we present an object recognition approach using co occurrence similarities of gabor magnitude textures in this paper a novel image descriptor multichannel gabor magnitude co occurrence matrices mgmcms is designed to characterize gabor textures for object representation and similarity matching the descriptor is a generalization of multichannel color co occurrence matrices mcms which focus on using robust and discriminative magnitude textures in filtered images our approach starts from gabor wavelet transformation of each object image an exploratory learning algorithm is proposed for learning channel adaptive magnitude truncation parameters and level parameters this allows us to design the magnitude quantization that can reduce overall biased and peaked levels of resulting feature distributions in each channel to avoid over sparse co occurrence distributions on average the direction based grouping is adopted for computational complexity reduction of mgmcms extraction under a specific neighborhood mode on the grouped rescaled magnitude images of per object image when each mgmcm is treated as a probability distribution lying on a multinomial manifold we represent per object image as a point on a product multinomial manifold using multinomial geometry and metric extension technique we construct the p order minkowski co occurrence information distance for similarity matching between the albums of gabor magnitude textures the feasibility and effectiveness of the approach is validated by the experimental results on the yale and feret face databases polyu palmprint database coil 20 object database and zurich buildings database

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features

analytic functions cauchy formula and stationary phase on a real abstract wiener space abstract a new complexification of a real abstract wiener space will be introduced and some analogs of the algebra of analytic functions on finite dimensional euclidean space will be considered analytic functions on the original space their holomorphic prolongation to the complexified space and holomorphic functions and a cauchy formula on the complexified space the cauchy formula is a key tool to study probabilistic quantities via deformation of the contour integration namely it will be applied to establish i an explicit representation of stochastic oscillatory integrals with quadratic phase function and ii a stationary phase estimation of the integrals further the later estimation is applicable to study gevrey type smoothness of density functions an integration by parts formula on a totally real submanifold in the complexified space is also studied

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

reinterpreting the application of gabor filters as a manipulation of the margin in linear support vector machines linear filters are ubiquitously used as a preprocessing step for many classification tasks in computer vision in particular applying gabor filters followed by a classification stage such as a support vector machine svm is now common practice in computer vision applications like face identity and expression recognition a fundamental problem occurs however with respect to the high dimensionality of the concatenated gabor filter responses in terms of memory requirements and computational efficiency during training and testing in this paper we demonstrate how the preprocessing step of applying a bank of linear filters can be reinterpreted as manipulating the type of margin being maximized within the linear svm this new interpretation leads to sizable memory and computational advantages with respect to existing approaches the reinterpreted formulation turns out to be independent of the number of filters thereby allowing the examination of the feature spaces derived from arbitrarily large number of linear filters a hitherto untestable prospect further this new interpretation of filter banks gives new insights other than the often cited biological motivations into why the preprocessing of images with filter banks like gabor filters improves classification performance

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed