fuzzy wavelet networks for function learning inspired by the theory of multiresolution analysis mra of wavelet transforms and fuzzy concepts a fuzzy wavelet network fwn is proposed for approximating arbitrary nonlinear functions the fwn consists of a set of fuzzy rules each rule corresponding to a sub wavelet neural network wnn consists of single scaling wavelets through efficient bases selection the dimension of the approximated function does not cause the bottleneck for constructing fwn especially by learning the translation parameters of the wavelets and adjusting the shape of membership functions the model accuracy and the generalization capability of the fwn can be remarkably improved furthermore an algorithm for constructing and training the fuzzy wavelet networks is proposed simulation examples are also given to illustrate the effectiveness of the method

multiple features data fusion method in color texture analysis a new algorithm is developed to represent colored texture by effectively merging the texture feature color feature together with spatial correlation of color and texture based on incomplete tree structured wavelet decomposition experiments are conducted on a set of 20 natural colored texture images in which multiple features fusion and classification performance are compared on the basis of the pyramid wavelet decomposition pwd incomplete tree structured wavelet decomposition ictswd and wavelet packet decomposition wpd class correct rates of multiple features fusion based on pwd is 85 78 and class correct rates based on wpd is 91 03 with the dimensionality increased exponentially however the dimensionality of feature fusion based on ictswd is descended greatly because of selective decomposition in subband which class correct rates is 90 63 it is demonstrated that multiple features fusion based on ictswd has better classification performance and anti noise ability than fusion based on pwd and wpd

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

optimized wavelet denoising for self similar alpha stable processes we investigate the performance of wavelet shrinkage methods for the denoising of symmetric alpha stable text s alpha text s self similar stochastic processes corrupted by additive white gaussian noise awgn where alpha is tied to the sparsity of the process the wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean square approximation error mmse estimator we derive the corresponding formula for the expected value of the averaged estimation error we show that the predicted mmse is a monotone function of a simple criterion that depends on the wavelet and the statistical parameters of the process using the calculus of variations we then optimize this criterion to find the best performing wavelet within the extended family of meyer wavelets which are bandlimited these are compared with the daubechies wavelets which are compactly supported in time we find that the wavelets that are shorter in time in particular the haar basis are better suited to denoise the sparser processes say alpha while the bandlimited ones including the held and shannon wavelets offer the best performance for alpha 1 6 the limit corresponding to the gaussian case fbm with alpha 2

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

fisher tensors for classifying human epithelial cells analyzing and classifying human epithelial type 2 hep 2 cells using indirect immunofluorescence protocol has been the golden standard for detecting connective tissue diseases such as rheumatoid arthritis however this suffers from numerous shortcomings such as being subjective as well as time and labor intensive recently several studies explore the advantages of artificial systems to automate the process not only to reduce the test turn around time but also to deliver more consistent results in this paper we extend the conventional bag of word models from euclidean space to non euclidean riemannian manifolds and utilize them to classify the hep 2 cells the main motivation comes from the observation that hep 2 cells can be efficiently described by symmetric positive definite matrices which lie on a riemannian manifold with this motivation we first discuss an intrinsic bag of riemannian words model we then propose fisher tensors which can in turn encode additional information about the distribution of the signatures in a bag of word model experiments on two challenging hep 2 images datasets namely icprcontest and snphep 2 show that the proposed methods obtain notable improvements in discrimination accuracy in comparison to baseline and several state of the art methods the proposed framework while hand crafted towards cell classification is a generic framework for object recognition this is supported by assessing the performance of our proposal on a challenging texture classification task

deterministic and stochastic surface growth with generalized nonlinearity the scaling behavior of the interface width for the generalized kardar parisi zhang kpz equation ensuremath partial h ensuremath partial t ensuremath nu mathrm ensuremath nabla 2 h ensuremath lambda ensuremath vert ensuremath nabla h mathrm ensuremath vert mathrm ensuremath mu ensuremath eta x t is studied in two dimensions as a function of ensuremath mu with and without the additive noise term ensuremath eta in the case of additive noise the scaling of the surface width is found for all ensuremath mu to be the same as for the ordinary kpz equation ensuremath mu 2 in contrast to a previous conjecture this appears to be due to the combined action of the nonlinearity ensuremath vert ensuremath nabla h mathrm ensuremath vert mathrm ensuremath mu and the noise under renormalization which together induce a ensuremath vert ensuremath nabla h mathrm ensuremath vert 2 term for the deterministic case corresponding to the smoothing of an initially rough interface with roughness exponent ensuremath alpha good agreement with the scaling relation z min 2 ensuremath alpha 1 ensuremath mu ensuremath mu is obtained for ensuremath mu ensuremath ge 1 however for ensuremath mu 1 an instability is observed which leads to a fluctuating grooved surface for an asymptotically large system the roughness exponent is 1 and the growth exponent is approximately equal to 1 2 the evolution of two slightly different surfaces is studied in order to determine a lyapunov exponent characterizing this instability

isotropic polyharmonic b splines scaling functions and wavelets in this paper we use polyharmonic b splines to build multidimensional wavelet bases these functions are nonseparable multidimensional basis functions that are localized versions of radial basis functions we show that rabut s elementary polyharmonic b splines do not converge to a gaussian as the order parameter increases as opposed to their separable b spline counterparts therefore we introduce a more isotropic localization operator that guarantees this convergence resulting into the isotropic polyharmonic b splines next we focus on the two dimensional quincunx subsampling scheme this configuration is of particular interest for image processing because it yields a finer scale progression than the standard dyadic approach however up until now the design of appropriate filters for the quincunx scheme has mainly been done using the mcclellan transform in our approach we start from the scaling functions which are the polyharmonic b splines and as such explicitly known and we derive a family of polyharmonic spline wavelets corresponding to different flavors of the semi orthogonal wavelet transform e g orthonormal b spline and dual the filters are automatically specified by the scaling relations satisfied by these functions we prove that the isotropic polyharmonic b spline wavelet converges to a combination of four gabor atoms which are well separated in the frequency domain we also show that these wavelets are nearly isotropic and that they behave as an iterated laplacian operator at low frequencies we describe an efficient fast fourier transform based implementation of the discrete wavelet transform based on polyharmonic b splines

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

automatic identification of the pectoral muscle in mammograms the pectoral muscle represents a predominant density region in most medio lateral oblique mlo views of mammograms its inclusion can affect the results of intensity based image processing methods or bias procedures in the detection of breast cancer local analysis of the pectoral muscle may be used to identify the presence of abnormal axillary lymph nodes which may be the only manifestation of occult breast carcinoma we propose a new method for the identification of the pectoral muscle in mlo mammograms based upon a multiresolution technique using gabor wavelets this new method overcomes the limitation of the straight line representation considered in our initial investigation using the hough transform the method starts by convolving a group of gabor filters specially designed for enhancing the pectoral muscle edge with the region of interest containing the pectoral muscle after computing the magnitude and phase images using a vector summation procedure the magnitude value of each pixel is propagated in the direction of the phase the resulting image is then used to detect the relevant edges finally a post processing stage is used to find the true pectoral muscle edge the method was applied to 84 mlo mammograms from the mini mias mammographic image analysis society london u k database evaluation of the pectoral muscle edge detected in the mammograms was performed based upon the percentage of false positive fp and false negative fn pixels determined by comparison between the numbers of pixels enclosed in the regions delimited by the edges identified by a radiologist and by the proposed method the average fp and fn rates were respectively 0 58 and 5 77 furthermore the results of the gabor filter based method indicated low hausdorff distances with respect to the hand drawn pectoral muscle edges with the mean and standard deviation being 3 84 spl plusmn 1 73 mm over 84 images

fuzzy multiresolution signal representation we present a multiresolution signal representation technique which uses fuzzy rules a fuzzy tree is used to connect different levels of resolution we apply our representation to several random processes and demonstrate some useful properties of our representation when applied to fractals

lightweight probabilistic texture retrieval this paper contemplates the framework of probabilistic image retrieval in the wavelet domain from a computational point of view we not only focus on achieving high retrieval rates but also discuss possible performance bottlenecks which might prevent practical application we propose a novel retrieval approach which is motivated by previous research work on modeling the marginal distributions of wavelet transform coefficients the building blocks of our work are the dual tree complex wavelet transform and a number of statistical models for the coefficient magnitudes image similarity measurement is accomplished by using closed form solutions for the kullback leibler divergences between the statistical models we provide an in depth computational analysis regarding the number of arithmetic operations required for similarity measurement and model parameter estimation the experimental retrieval results on a widely used texture image database show that we achieve competitive retrieval results at low computational cost

multiscale autoregressive models and wavelets the multiscale autoregressive mar framework was introduced to support the development of optimal multiscale statistical signal processing its power resides in the fast and flexible algorithms to which it leads while the mar framework was originally motivated by wavelets the link between these two worlds has been previously established only in the simple case of the haar wavelet the first contribution of this paper is to provide a unification of the mar framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem the second contribution of this paper is to develop wavelet based approximate internal mar models for stochastic processes this will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients taking advantage of the statistical machinery provided by the mar framework we will illustrate the application of our models to sample path generation and estimation from noisy irregular and sparse measurements

on k 1 of a self product of a curve we present elements of h 1 c c 62 for certain specific curves c the image of the element under the boundary map arising from the localization sequence of k theory is the graph of frobenius endomorphism of the reduction of the curve modulo 3

zero cycles on hilbert blumenthal surfaces introduction the main object of study in this paper with respect to zero cycles is a special class of hilbert blumenthal surfaces x which are defined over q as smooth compactifications of quasi projective varieties s q more precisely of coarse moduli schemes s that represent the moduli stack of polarized abelian surfaces with real multiplication by the ring of integers in a real quadratic field f q d we assume that d q is a prime 1 4 and that the class number of f is 1 then s c the complex points of s can be described as h h sl2 of where h is the upper halfplane in the early seventies hirzebruch and zagier hz defined for each integer n a curve tn on s called hirzebruch zagier cycles and showed that their intersection numbers occur as fourier coefficients of modular forms of level q with nebentypes eq the quadratic character of f q in this connection with modular forms hirzebruchzagier cycles reveal very similar properties to hecke correspondences on the selfproduct of the modular curve x0 q this crucial observation of hirzebruch and zagier together with tunnell s proof of the tate conjecture for a product of modular curves inspired harder langlands and rapoport hlr to prove the tate conjecture for divisors on hilbert blumenthal surfaces over abelian number fields the proof of the tate conjecture was then accomplished by klingenberg kl and murty and ramakrishnan mr in the general case from the new strategy to study torsion zero cycles on algebraic surfaces as developed in ls and used in l1 l2 compare also lr it is clear that a crucial point is the tate conjecture in characteristic p at good reduction primes as one of our main results we prove the tate conjecture in characteristic p for primes p that split in f for a certain class of hilbert blumenthal surfaces for this we recall that to each modular cusp form f of weight 2 level q and nebentypes eq that is f s2 0 q eq w e associate a hilbert modular cusp form f s2 sl2 of under the doi naganuma

ensemble of local and global information for finger knuckle print recognition biometrics authentication is an effective method for automatically recognizing a person s identity recently it has been found that the finger knuckle print fkp which refers to the inherent skin patterns of the outer surface around the phalangeal joint of one s finger has high capability to discriminate different individuals making it an emerging biometric identifier in this paper based on the results of psychophysics and neurophysiology studies that both local and global information is crucial for the image perception we present an effective fkp recognition scheme by extracting and assembling local and global features of fkp images specifically the orientation information extracted by the gabor filters is coded as the local feature by increasing the scale of gabor filters to infinite actually we can get the fourier transform of the image and hence the fourier transform coefficients of the image can be taken as the global features such kinds of local and global features are naturally linked via the framework of time frequency analysis the proposed scheme exploits both local and global information for the fkp verification where global information is also utilized to refine the alignment of fkp images in matching the final matching distance of two fkps is a weighted average of local and global matching distances the experimental results conducted on our fkp database demonstrate that the proposed local global information combination scheme could significantly improve the recognition accuracy obtained by either local or global information and lead to promising performance of an fkp based personal authentication system

gabor based kernel pca with doubly nonlinear mapping for face recognition with a single face image in this paper a novel gabor based kernel principal component analysis pca with doubly nonlinear mapping is proposed for human face recognition in our approach the gabor wavelets are used to extract facial features then a doubly nonlinear mapping kernel pca dkpca is proposed to perform feature transformation and face recognition the conventional kernel pca nonlinearly maps an input image into a high dimensional feature space in order to make the mapped features linearly separable however this method does not consider the structural characteristics of the face images and it is difficult to determine which nonlinear mapping is more effective for face recognition in this paper a new method of nonlinear mapping which is performed in the original feature space is defined the proposed nonlinear mapping not only considers the statistical property of the input features but also adopts an eigenmask to emphasize those important facial feature points therefore after this mapping the transformed features have a higher discriminating power and the relative importance of the features adapts to the spatial importance of the face images this new nonlinear mapping is combined with the conventional kernel pca to be called doubly nonlinear mapping kernel pca the proposed algorithm is evaluated based on the yale database the ar database the orl database and the yaleb database by using different face recognition methods such as pca gabor wavelets plus pca and gabor wavelets plus kernel pca with fractional power polynomial models experiments show that consistent and promising results are obtained

multiscale recursive estimation data fusion and regularization we describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and or noisy measurements which may also be at several scales in particular multiscale signal representations lead naturally to pyramidal or tree like data structures in which each level in the tree corresponds to a particular scale of representation a class of multiscale dynamic models evolving on dyadic trees is introduced the main focus of this paper is on the description analysis and application of an extremely efficient optimal estimation algorithm for this class of models this algorithm consists of a fine to coarse filtering sweep followed by a coarse to fine smoothing step corresponding to the dyadic tree generalization of kalman filtering and rauch tung striebel smoothing the kalman filtering sweep consists of the recursive application of three steps a measurement update step a fine to coarse prediction step and a fusion step we illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of fractal regularizations of ill posed signal and image processing problems encountered

orientation selection using modified fcm for competitive code based palmprint recognition coding based methods are among the most promising palmprint recognition methods because of their small feature size fast matching speed and high verification accuracy the competitive coding scheme one representative coding based method first convolves the palmprint image with a bank of gabor filters with different orientations and then encodes the dominant orientation into its bitwise representation despite the effectiveness of competitive coding few investigations have been given to study the influence of the number of gabor filters and the orientation of each gabor filter in this paper based on the statistical orientation distribution and the orientation separation characteristics we propose a modified fuzzy c means cluster algorithm to determine the orientation of each gabor filter since the statistical orientation distribution is based on a set of real palmprint images the proposed method is more suitable for palmprint recognition experimental results indicate that the proposed method achieves higher verification accuracy while compared with that of the original competitive coding scheme and several state of the art methods such as ordinal measure and rloc considering both the computational complexity and the verification accuracy competitive code with six orientations would be the optimal choice for palmprint recognition

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

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

fractal estimation using models on multiscale trees we estimate the hurst parameter h of fractional brownian motion or by extension the fractal exponent spl phi of stochastic processes having 1 f sup spl phi like spectra by applying a multiresolution framework this framework admits an efficient likelihood function evaluation allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease in addition to yielding results that compare well with other proposed methods and in contrast with other approaches our method is directly applicable with at most very simple modification in a variety of other contexts including fractal estimation given irregularly sampled data or nonstationary measurement noise and the estimation of fractal parameters for 2 d random fields

image analysis and reconstruction using a wavelet transform constructed from a reducible representation of the euclidean motion group inspired by the early visual system of many mammalians we consider the construction of and reconstruction from an orientation score it u f mathbb r 2 times s 1 to mathbb c as a local orientation representation of an image f mathbb r 2 to mathbb r the mapping f mapsto it u f is a wavelet transform mathcal w psi corresponding to a reducible representation of the euclidean motion group onto mathbb l 2 mathbb r 2 and oriented wavelet psi in mathbb l 2 mathbb r 2 this wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the practical advantage over the usual wavelet approaches in image analysis constructed by irreducible representations of the similitude group that it allows a stable reconstruction from one single scale orientation score since our wavelet transform is a unitary mapping with stable inverse we directly relate operations on orientation scores to operations on images in a robust manner furthermore by geometrical examination of the euclidean motion group g mathbb r 2 mathbb r times mathbb t which is the domain of our orientation scores we deduce that an operator on orientation scores must be left invariant to ensure that the corresponding operator mathcal w psi 1 phi mathcal w psi on images is euclidean invariant as an example we consider all linear second order left invariant evolutions on orientation scores corresponding to stochastic processes on g as an application we detect elongated structures in medical images and automatically close the gaps between them finally we consider robust orientation estimates by means of channel representations where we combine robust orientation estimation and learning of wavelets resulting in an auto associative processing of orientation features here linear averaging of the channel representation is equivalent to robust orientation estimation and an adaptation of the wavelet to the statistics of the considered image class leads to an auto associative behavior of the system

feature based lucas kanade and active appearance models lucas kanade and active appearance models are among the most commonly used methods for image alignment and facial fitting respectively they both utilize nonlinear gradient descent which is usually applied on intensity values in this paper we propose the employment of highly descriptive densely sampled image features for both problems we show that the strategy of warping the multichannel dense feature image at each iteration is more beneficial than extracting features after warping the intensity image at each iteration motivated by this observation we demonstrate robust and accurate alignment and fitting performance using a variety of powerful feature descriptors especially with the employment of histograms of oriented gradient and scale invariant feature transform features our method significantly outperforms the current state of the art results on in the wild databases

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

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

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

hypercomplex signals a novel extension of the analytic signal to the multidimensional case the construction of gabor s 1946 complex signal which is also known as the analytic signal provides direct access to a real one dimensional 1 d signal s local amplitude and phase the complex signal is built from a real signal by adding its hilbert transform which is a phase shifted version of the signal as an imaginary part to the signal since its introduction the complex signal has become an important tool in signal processing with applications for example in narrowband communication different approaches to an n d analytic or complex signal have been proposed in the past we review these approaches and propose the hypercomplex signal as a novel extension of the complex signal to n d this extension leads to a new definition of local phase which reveals information on the intrinsic dimensionality of the signal the different approaches are unified by expressing all of them as combinations of the signal and its partial and total hilbert transforms examples that clarify how the approaches differ in their definitions of local phase and amplitude are shown an example is provided for the two dimensional 2 d hypercomplex signal which shows how the novel phase concept can be used in texture segmentation

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

wavelet based fingerprint image retrieval this paper presents a novel approach for personal identification based on a wavelet based fingerprint retrieval system which encompasses three image retrieval tasks namely feature extraction similarity measurement and feature indexing we propose the use of different types of wavelets for representing and describing the textural information presented in fingerprint images in a compact way for that purpose the feature vectors used to characterize the fingerprints are obtained by computing the mean and the standard deviation of the decomposed images in the wavelet domain these feature vectors are used both to retrieve the most similar fingerprints given a query image and their indexation is used to reduce the search spaces of candidate images the different types of wavelets used in our study include gabor wavelets tree structured wavelet decomposition using both orthogonal and bi orthogonal filter banks as well as the steerable wavelets to evaluate the retrieval accuracy of the proposed approach a total number of eight different data sets were considered we also took into account different combinations of the above wavelets with six similarity measures the results show that the gabor wavelets combined with the square chord similarity measure achieves the best retrieval effectiveness

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

multiscale systems kalman filters and riccati equations an algorithm analogous to the rauch tung striebel algorithm spl minus consisting of a fine to coarse kalman filter like sweep followed by a coarse to fine smoothing step spl minus was developed previously by the authors ibid vol 39 no 3 p 464 78 1994 in this paper they present a detailed system theoretic analysis of this filter and of the new scale recursive riccati equation associated with it while this analysis is similar in spirit to that for standard kalman filters the structure of the dyadic tree leads to several significant differences in particular the structure of the kalman filter error dynamics leads to the formulation of an ml version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the hamiltonian for the smoothing problem in addition the notion of stability for dynamics requires some care as do the concepts of reachability and observability using these system theoretic constructs the stability and steady state behavior of the fine to coarse kalman filter and its riccati equation are analysed

image representation by complex cell responses we present an analysis of the representation of images as the magnitudes of their transform with complex valued gabor wavelets such a representation is a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding because it makes the representation insensitive to small local shifts we show that if the images are band limited and of zero mean then reconstruction from the magnitudes is unique up to the sign for almost all images

robustness of regional matching scheme over global matching scheme analyzing the effect of concentrated noise on a typical decision making process of a simplified two candidate voting model we have demonstrated that a local approach using a regional matching process is more robust and stable than a direct approach using a global matching process by establishing that the former is capable of accommodating a higher level of noise than the latter before the result of the decision overturns to extend the theory to imagery analysis we pose a conjecture that our conclusion on the robustness of the regional matching processes remains valid not only for the simpler vote counting schemes but also for practically more important decision making schemes in image analysis which involve dimension reducing transforms or other features extraction processes such as principal component analysis or gablor transforms two convincing experimental verifications are provided supporting not only the theory by a white black flag recognition problem on a pixel by pixel basis but also the validity of the conjecture by a facial recognition problem in the presence of localized noise typically represented by clutter or occlusion in imagery

band reweighed gabor kernel embedding for face image representation and recognition face recognition with illumination or pose variation is a challenging problem in image processing and pattern recognition a novel algorithm using band reweighed gabor kernel embedding to deal with the problem is proposed in this paper for a given image it is first transformed by a group of gabor filters which output gabor features using different orientation and scale parameters fisher scoring function is used to measure the importance of features in each band and then the features with the largest scores are preserved for saving memory requirements the reduced bands are combined by a vector which is determined by a weighted kernel discriminant criterion and solved by a constrained quadratic programming method and then the weighted sum of these nonlinear bands is defined as the similarity between two images compared with existing concatenation based gabor feature representation and the uniformly weighted similarity calculation approaches our method provides a new way to use gabor features for face recognition and presents a reasonable interpretation for highlighting discriminant orientations and scales the minimum mahalanobis distance considering the spatial correlations within the data is exploited for feature matching and the graphical lasso is used therein for directly estimating the sparse inverse covariance matrix experiments using benchmark databases show that our new algorithm improves the recognition results and obtains competitive performance

image representation using 2d gabor wavelets this paper extends to two dimensions the frame criterion developed by daubechies for one dimensional wavelets and it computes the frame bounds for the particular case of 2d gabor wavelets completeness criteria for 2d gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision since recent neurophysiological evidence from the visual cortex of mammalian brains suggests that the filter response profiles of the main class of linearly responding cortical neurons called simple cells are best modeled as a family of self similar 2d gabor wavelets we therefore derive the conditions under which a set of continuous 2d gabor wavelets will provide a complete representation of any image and we also find self similar wavelet parametrization which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis approximating a tight frame generates redundancy which allows low resolution neural responses to represent high resolution images