image filtering edge detection and edge tracing using fuzzy reasoning we characterize the problem of detecting edges in images as a fuzzy reasoning problem the edge detection problem is divided into three stages filtering detection and tracing images are filtered by applying fuzzy reasoning based on local pixel characteristics to control the degree of gaussian smoothing filtered images are then subjected to a simple edge detection algorithm which evaluates the edge fuzzy membership value for each pixel based on local image characteristics finally pixels having high edge membership are traced and assembled into structures again using fuzzy reasoning to guide the tracing process the filtering detection and tracing algorithms are tested on several test images comparison is made with a standard edge detection technique

karhunen loeve expansion of a set of rotated templates we propose a novel method for efficiently calculating the eigenvectors of uniformly rotated images of a set of templates as we show the images can be optimally approximated by a linear series of eigenvectors which can be calculated without actually decomposing the sample covariance matrix

spectral hp least squares finite element formulation for the navier stokes equations we consider the application of least squares finite element models combined with spectral hp methods for the numerical solution of viscous flow problems the paper presents the formulation validation and application of a spectral hp algorithm to the numerical solution of the navier stokes equations governing two and three dimensional stationary incompressible and low speed compressible flows the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity or velocity gradients as additional independent variables and the least squares method is used to develop the finite element model high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method spectral convergence of the l2 least squares functional and l2 error norms is verified using smooth solutions to the two dimensional stationary poisson and incompressible navier stokes equations numerical results for flow over a backward facing step steady flow past a circular cylinder three dimensional lid driven cavity flow and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

the hermite transform applications it is demonstrated how the hermite transform can be used for image coding and analysis hierarchical coding structures based on increasingly specified basic patterns i e general 2 d patterns general 1 d patterns and specific 1 d patterns such as edges and corners are presented in the image coding application the relation with existing pyramid coders is described a new coding scheme based on local one dimensional image approximations is introduced in the image analysis application the relation between the hermite transform and existing line edge detection schemes is described it is shown that by concentrating on more specific patterns the coding efficiency can be increased since fewer coefficients have to be coded meanwhile sufficient descriptive power can be maintained for approximating the most interesting features in natural images

shifted fourier transform based tensor algorithms for the 2 d dct in this paper tensor algorithms for calculating the two dimensional 2 d discrete cosine transform dct are presented the tensor approach is based on the concept of the covering revealing the transforms which yields in particular the splitting of the shifted 2 sup r spl times 2 sup r point fourier and cosine transforms into 2 sup r 1 3 one dimensional 1 d incomplete 2 sup r point transforms the multiplicative complexity of the 2 d 2 sup r spl times 2 sup r point discrete cosine transforms in terms of the tensor representation is 4 sup r 3 2 sup r 2 r sup 2 7r 14 which is reduced to 4 sup r 8 3 2 sup r r sup 2 7r 10 20 3 when using the improved tensor algorithm the multiplicative complexity in the general l sup r spl times l sup r case with a prime l 2 as well as in the l sub 1 l sub 2 spl times l sub 1 l sub 2 case with arbitrary co prime l sub 1 l sub 2 1 is provided the examples of the tensor algorithms for calculating the 8 spl times 8 point dct through 104 88 and 84 multiplications are given in detail based on the proposed concept the fast algorithm for calculating the 1 d dct i is also developed the multiplicative complexity of the 2 sup r point dct i is 2 sup r 1 r 2 r 5 2 8 the comparative estimates with the known algorithms are given

high order non reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements abstract high order non reflecting boundary conditions are introduced to create a finite computational space and for the solution of dispersive waves using a spectral element formulation with high order time integration numerical examples are used to demonstrate the synergy of using high order spatial time and boundary discretization we show that by balancing all numerical errors involved high order accuracy can be achieved for unbounded domain problems in polar coordinate systems

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

parallel direct poisson solver for discretisations with one fourier diagonalisable direction in the context of time accurate numerical simulation of incompressible flows a poisson equation needs to be solved at least once per time step to project the velocity field onto a divergence free space due to the non local nature of its solution this elliptic system is one of the most time consuming and difficult to parallelise parts of the code in this paper a parallel direct poisson solver restricted to problems with one uniform periodic direction is presented it is a combination of a direct schur complement based decomposition dsd and a fourier diagonalisation the latter decomposes the original system into a set of mutually independent 2d systems which are solved by means of the dsd algorithm since no restrictions are imposed in the non periodic directions the overall algorithm is well suited for solving problems discretised on extruded 2d unstructured meshes the load balancing between parallel processes and the parallelisation strategy are also presented and discussed the scalability of the solver is successfully tested using up to 8192 cpu cores for meshes with up to 10 9 grid points finally the performance of the dsd algorithm as 2d solver is analysed by direct comparison with two preconditioned conjugate gradient methods for this purpose the turbulent flow around a circular cylinder at reynolds numbers 3900 and 10 000 are used as problem models

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

extrapolative spatial models for detecting perceptual boundaries in colour images we present a novel approach for automatically building image specific extrapolative spatial models of non boundary local energy that can be used to perform local statistical tests to detect perceptual boundaries the non boundary model consists of statistics of local energy that are spatially extrapolated by a non boundary confidence map and a scale adaptive normalised filtering algorithm we exploit the flexibility of steerable filters to both extract oriented local energy and to provide local statistics of the energy distribution in the orientation domain to compute the non boundary confidence map finally we apply our local thresholding technique separately to the three channels of colour images and adopt a max operator to combine the results we provide a qualitative and quantitative comparison on real images from a hand segmented natural image database against the best combination of the most widely cited colour edge detectors and automatic global thresholding methods

design of multiparameter steerable functions using cascade basis reduction an efficient method of computing the least squares optimal basis functions to steer any function locally is presented the method combines the lie group theoretic and the singular value decomposition approaches its efficiency is demonstrated with the design of basis functions to steer a gabor function under the four parameter linear transformation group

a converse lyapunov theorem for nonlinear switched systems abstract in this paper we present a converse lyapunov theorem for uniform asymptotic stability of switched nonlinear systems its proof is a simple consequence of some results on converse lyapunov theorems for systems with bounded disturbances obtained by lin et al siam j control optim 34 1996 124 160 once an association of the switched system with a nonlinear system with disturbances is established

a vector quantizer for image restoration this paper presents a novel technique for image restoration based on nonlinear interpolative vector quantization nlivq the algorithm performs nonlinear restoration of diffraction limited images concurrently with quantization it is trained on image pairs consisting of an original image and its diffraction limited counterpart the discrete cosine transform is used in the codebook design process to control complexity simulation results are presented that demonstrate improvements in visual quality and peak signal to noise ratio of the restored images

a condition for the stability of switched nonlinear systems in this paper we present a sufficient condition for the global asymptotic stability of a switched nonlinear system composed of a finite family of subsystems we show that the global asymptotic stability of each subsystem and the pairwise commutation of the vector fields that define the subsystems i e the lie bracket of any pair of them is zero are sufficient for the global asymptotic stability of the switched system we also show that these conditions are sufficient for the existence of a common lyapunov function

a parallel time space least squares spectral element solver for incompressible flow problems abstract the least squares spectral element method lsq sem is a very promising numerical method which combines the least squares formulation with the spectral element method in this article a parallel space time implementation of a least squares spectral element method for incompressible flows is presented in the space time formulation time is included as an extra dimension providing an efficient framework for handling time dependent independent multidimensional problems the algebraic solver is based on the shur complement method numerical experiments are performed for showing the capability and computational efficiency of the solver besides the scalability of the code is tested

nonlocal hierarchical dictionary learning using wavelets for image denoising exploiting the sparsity within representation models for images is critical for image denoising the best currently available denoising methods take advantage of the sparsity from image self similarity pre learned and fixed representations most of these methods however still have difficulties in tackling high noise levels or noise models other than gaussian in this paper the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets experimental results show that our proposed method outperforms two state of the art image denoising algorithms on higher noise levels furthermore our approach is more adaptive to the less extensively researched uniform noise

flexible spatial configuration of local image features local image features have been designed to be informative and repeatable under rigid transformations and illumination deformations even though current state of the art local image features present a high degree of repeatability their local appearance alone usually does not bring enough discriminative power to support a reliable matching resulting in a relatively high number of mismatches in the correspondence set formed during the data association procedure as a result geometric filters commonly based on global spatial configuration have been used to reduce this number of mismatches however this approach presents a trade off between the effectiveness to reject mismatches and the robustness to nonrigid deformations in this paper we propose two geometric filters based on a semilocal spatial configuration of local features that are designed to be robust to nonrigid deformations and to rigid transformations without compromising its efficacy to reject mismatches we compare our methods to the hough transform which is an efficient and effective mismatch rejection step based on the global spatial configuration of features in these comparisons our methods are shown to be more effective in the task of rejecting mismatches for rigid transformations and nonrigid deformations at comparable time complexity figures finally we demonstrate how we can integrate these methods in a probabilistic recognition system such that the final verification step uses not only the similarity between features but also their semilocal configuration

sorted random projections for robust rotation invariant texture classification this paper presents a simple novel yet very powerful approach for robust rotation invariant texture classification based on random projection the proposed sorted random projection maintains the strengths of random projection in being computationally efficient and low dimensional with the addition of a straightforward sorting step to introduce rotation invariance at the feature extraction stage a small set of random measurements is extracted from sorted pixels or sorted pixel differences in local image patches the rotation invariant random features are embedded into a bag of words model to perform texture classification allowing us to achieve global rotation invariance the proposed unconventional and novel random features are very robust yet by leveraging the sparse nature of texture images our approach outperforms traditional feature extraction methods which involve careful design and complex steps we report extensive experiments comparing the proposed method to six state of the art methods rp patch lbp wmfs and the methods of lazebnik et al and zhang et al in texture classification on five databases curet brodatz uiuc umd and kth tips our approach leads to significant improvements in classification accuracy producing consistently good results on each database including what we believe to be the best reported results for brodatz umd and kth tips

an efficient solver for space time isogeometric galerkin methods for parabolic problems abstract in this work we focus on the preconditioning of a galerkin space time isogeometric discretization of the heat equation exploiting the tensor product structure of the basis functions in the parametric domain we propose a preconditioner that is the sum of kronecker products of matrices and that can be efficiently applied thanks to an extension of the classical fast diagonalization method the preconditioner is robust w r t the polynomial degree of the spline space and the time required for the application is almost proportional to the number of degrees of freedom for a serial execution by incorporating some information on the geometry parametrization and on the equation coefficients we keep high efficiency with non trivial domains and variable thermal conductivity and heat capacity coefficients

a modified k means algorithm for circular invariant clustering several important pattern recognition applications are based on feature vector extraction and vector clustering directional patterns are commonly represented by rotation variant vectors f sub d formed from features uniformly extracted in m directions it is often desirable that pattern recognition algorithms are invariant under pattern rotation this paper introduces a distance measure and a k means based algorithm namely circular k means ck means to cluster vectors containing directional information such as f sub d in a circular shift invariant manner a circular shift of f sub d corresponds to pattern rotation thus the algorithm is rotation invariant an efficient fourier domain representation of the proposed measure is presented to reduce computational complexity a split and merge approach smck means suited to the proposed ck means technique is proposed to reduce the possibility of converging at local minima and to estimate the correct number of clusters experiments performed for textural images illustrate the superior performance of the proposed algorithm for clustering directional vectors f sub d compared to the alternative approach that uses the original k means and rotation invariant feature vectors transformed from f sub d

a morphological affine and galilean invariant scale space for movies we study a model of multiscale analysis or scale space applied to movies this model comes from a thorough formalization that has been done in the theory of scale space of static image this formulation has led one to associate with each multiscale analysis a partial differential equation pde we examine the case of movies and insist on the motion aspects more precisely it has been proved by alvarez guichard lions and morel 1993 that there exists a unique affine and morphological and galilean invariant scale space for movies the amg model this model is described by a partial differential equation we focus on terms appearing in that equation we show that this model provides a reliable definition of an optical multiscale acceleration at the practical level scale is interpreted as a way of characterizing reliable trajectories as we prove by experiments the amg model is a riddle for decimating spurious trajectories due to any kinds of nonadditive impurities and noise simple discrete formulae are given to implement the model

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

curvilinear structure analysis by ranking the orientation responses of path operators the analysis of thin curvilinear objects in 3d images is a complex and challenging task in this article we introduce a new non linear operator called rorpo ranking the orientation responses of path operators inspired by the multidirectional paradigm currently used in linear filtering for thin structure analysis rorpo is built upon the notion of path operator from mathematical morphology this operator unlike most operators commonly used for 3d curvilinear structure analysis is discrete non linear and non local from this new operator two main curvilinear structure characteristics can be estimated an intensity feature that can be assimilated to a quantitative measure of curvilinearity and a directional feature providing a quantitative measure of the structure s orientation we provide a full description of the structural and algorithmic details for computing these two features from rorpo and we discuss computational issues we experimentally assess rorpo by comparison with three of the most popular curvilinear structure analysis filters namely frangi vesselness optimally oriented flux and hybrid diffusion with continuous switch in particular we show that our method provides up to 8 percent more true positive and 50 percent less false positives than the next best method on synthetic and real 3d images

fast eigenspace decomposition of correlated images we present a computationally efficient algorithm for the eigenspace decomposition of correlated images our approach is motivated by the fact that for a planar rotation of a two dimensional 2 d image analytical expressions can be given for the eigendecomposition based on the theory of circulant matrices these analytical expressions turn out to be good first approximations of the eigendecomposition even for three dimensional 3 d objects rotated about a single axis in addition the theory of circulant matrices yields good approximations to the eigendecomposition for images that result when objects are translated and scaled we use these observations to automatically determine the dimension of the subspace required to represent an image with a guaranteed user specified accuracy as well as to quickly compute a basis for the subspace examples show that the algorithm performs very well on a number of test cases ranging from images of 3 d objects rotated about a single axis to arbitrary video sequences

recognition by symmetry derivatives and the generalized structure tensor we suggest a set of complex differential operators that can be used to produce and filter dense orientation tensor fields for feature extraction matching and pattern recognition we present results on the invariance properties of these operators that we call symmetry derivatives these show that in contrast to ordinary derivatives all orders of symmetry derivatives of gaussians yield a remarkable invariance they are obtained by replacing the original differential polynomial with the same polynomial but using ordinary coordinates x and y corresponding to partial derivatives moreover the symmetry derivatives of gaussians are closed under the convolution operator and they are invariant to the fourier transform the equivalent of the structure tensor representing and extracting orientations of curve patterns had previously been shown to hold in harmonic coordinates in a nearly identical manner as a result positions orientations and certainties of intricate patterns e g spirals crosses parabolic shapes can be modeled by use of symmetry derivatives of gaussians with greater analytical precision as well as computational efficiency since gaussians and their derivatives are utilized extensively in image processing the revealed properties have practical consequences for local orientation based feature extraction the usefulness of these results is demonstrated by two applications 1 tracking cross markers in long image sequences from vehicle crash tests and 2 alignment of noisy fingerprints

the sure let approach to image denoising we propose a new approach to image denoising based on the image domain minimization of an estimate of the mean squared error stein s unbiased risk estimate sure unlike most existing denoising algorithms using the sure makes it needless to hypothesize a statistical model for the noiseless image a key point of our approach is that although the nonlinear processing is performed in a transformed domain typically an undecimated discrete wavelet transform but we also address nonorthonormal transforms this minimization is performed in the image domain indeed we demonstrate that when the transform is a ldquotightrdquo frame an undecimated wavelet transform using orthonormal filters separate subband minimization yields substantially worse results in order for our approach to be viable we add another principle that the denoising process can be expressed as a linear combination of elementary denoising processes linear expansion of thresholds let armed with the sure and let principles we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient quite remarkably the very competitive results obtained by performing a simple threshold image domain sure optimized on the undecimated haar wavelet coefficients show that the sure let principle has a huge potential

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

stability analysis of second order switched homogeneous systems we study the stability of second order switched homogeneous systems using the concept of generalized first integrals we explicitly characterize the most destabilizing switching law and construct a lyapunov function that yields an easily verifiable necessary and sufficient condition for asymptotic stability using the duality between stability analysis and control synthesis this also leads to a novel algorithm for designing a stabilizing switching controller

feature vector field and feature matching in this paper we propose a feature vector field for images which is built by the inner products and exterior products of image gradients the feature vector field effectively represents image edges and feature points including corners and edge points with big curvature using the feature vector field some novel descriptors are constructed for point matching and curve matching the descriptors are all invariant to image euclidean transformations and linear intensity changes the experiments show that the descriptors also have a good adaptability to small image affine transformation jpeg compression and nonlinear changes of intensity

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

maximum likelihood orientation estimation of 1 d patterns in laguerre gauss subspaces a method for measuring the orientation of linear 1 d patterns based on a local expansion with laguerre gauss circular harmonic lg ch functions is presented it lies on the property that the polar separable lg ch functions span the same space as the 2 d cartesian separable hermite gauss 2 d hg functions exploiting the simple steerability of the lg ch functions and the peculiar block linear relationship among the two expansion coefficients sets maximum likelihood ml estimates of orientation and cross section parameters of 1 d patterns are obtained projecting them in a proper subspace of the 2 d hg family it is shown in this paper that the conditional ml solution derived by elimination of the cross section parameters surprisingly yields the same asymptotic accuracy as the ml solution for known cross section parameters the accuracy of the conditional ml estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials a thorough proof of the key relationship between the lg ch and the 2 d hg expansions is also provided

on quadratic lyapunov functions a topological structure as a subset of 0 2 spl pi sup l spl times spl ropf sub sup n 1 is proposed for the set of quadratic lyapunov functions qlfs of a given stable linear system a necessary and sufficient condition for the existence of a common qlf of a finite set of stable matrices is obtained as the positivity of a certain integral the structure and the conditions are considerably simplified for planar systems it is also proved that a set of block upper triangular matrices share a common qlf if each set of diagonal blocks share a common qlf

computing steerable principal components of a large set of images and their rotations we present here an efficient algorithm to compute the principal component analysis pca of a large image set consisting of images and for each image the set of its uniform rotations in the plane we do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors we also demonstrate the advantages of this algorithm over similar ones with numerical experiments although it is useful in many settings we illustrate the specific application of the algorithm to the problem of cryo electron microscopy

training less color object recognition for autonomous robotics abstract this paper looks at the challenge of object recognition from the perspective of achieving the final goals of practical real world autonomous robot vision applications that of identifying a target of interest in the robot s field of view and properly localizing its position in preparation for the higher level goal of tracking and navigation a unified framework is introduced that combines a multidimensional feature histogram approach with a multiscale pyramid approach for training less color object recognition and localization with direct application to autonomous robotic agents this framework addresses the high computational cost associated with multidimensional processing by deriving the multidimensional laplacian feature histogram pyramid a novel approach to a unified multidimensional multiscale histogram representation furthermore a taylor series formulation is employed to combine the multiscale levels of the multidimensional laplacian feature histogram pyramid into one efficient multidimensional multiscale laplacian taylor feature histogram for rapid object recognition and localization the paper describes the criteria for target detection and localization by autonomous robots and how this newly developed framework fits these needs comparative results demonstrate the robustness of this recognition framework to noise and localization of target objects in cluttered scenes

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

generalized sampling expansion for functions on the sphere functions on the sphere appear in several applications including geodesics imaging and acoustics sampling of these functions may result in aliasing if the sampling condition is not met the generalized sampling expansion introduced by papoulis enables the reconstruction of a band limited function sampled at a frequency lower than the nyquist frequency using the outputs of several linear time invariant systems this paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition facilitating sub nyquit sampling without aliasing error an analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented examples demonstrating the performance of the method and its limitations are studied

two view line matching algorithm based on context and appearance in low textured images a novel approach for line detection and matching is proposed aimed at achieving good performance with low textured scenes under uncontrolled illumination conditions line detection is performed by means of phase based edge detector over gaussian scale space followed by a multi scale fusion stage which has been proven to be profitable in minimizing the number of fragmented and overlapped segments line matching is performed by an iterative process that uses structural information collected through the use of different line neighborhoods making the set of matched lines grow robustly at each iteration results show that this approach is suitable to deal with low textured scenes and also robust under a wide variety of image transformations highlightsa novel approach for line detection and matching is proposed lines are detected through a fusion process over the gaussian scale space lines are matched based on their appearance geometric properties and neighborhoods our proposal minimizes the number of fragmented and overlapped segments our proposal is suitable for low textured scenes under uncontrolled illumination

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

common polynomial lyapunov functions for linear switched systems in this paper we consider linear switched systems dot x t a u t x t x in r n u in u a u u in u compact and the problem of asymptotic stability for arbitrary switching functions uniform with respect to switching uas given a uas system it is always possible to build a common polynomial lyapunov function our main result is that the degree of that common polynomial lyapunov function is not uniformly bounded over all the uas systems this result answers a question raised by dayawansa and martin a generalization to a class of piecewise polynomial lyapunov functions is given

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

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

discriminative learning of local image descriptors in this paper we explore methods for learning local image descriptors from training data we describe a set of building blocks for constructing descriptors which can be combined together and jointly optimized so as to minimize the error of a nearest neighbor classifier we consider both linear and nonlinear transforms with dimensionality reduction and make use of discriminant learning techniques such as linear discriminant analysis lda and powell minimization to solve for the parameters using these techniques we obtain descriptors that exceed state of the art performance with low dimensionality in addition to new experiments and recommendations for descriptor learning we are also making available a new and realistic ground truth data set based on multiview stereo data

noise analysis of a new singularity index we analyze the noise sensitivity of a new singularity index that was designed to detect impulse singularities in signals of arbitrary dimensionality while rejecting step like singularities see muralidhar ieee signal process lett vol 20 no 1 pp 7 10 2013 and muralidhar proc ieee int conf image process 2012 for example the index responds strongly to curvilinear masses ridges in images while weakly to jump discontinuities edges we analyze the detection power of the index in the presence of noise our analysis is geared towards answering the following questions a in the presence of noise only what is the probability of falsely detecting an impulse given a threshold b given an impulse submerged in noise what is the probability of detecting it given a threshold and c since the index is designed to be edge suppressing what is the probability of incorrectly detecting an edge submerged in noise given a threshold we compare the detection power of the index with that of a nominal impulse detector the second derivative operator simulations and example applications in 1 d and 2 d reveal the efficacy of the new singularity index for correctly detecting impulses submerged in noise while suppressing edges a software version of the 2 d singularity index can be downloaded from http live ece utexas edu research singularityindex singularityindexcode zip

lapb locally adaptive patch based wavelet domain edge preserving image denoising abstract image denoising is one of the most diversified research areas in the field of image processing and computer vision it is highly desirable for a denoising technique to preserve important image features such as edges corners and other sharp structures of an image after denoising wavelet transforms show excellent proficiency in providing efficient edge preserving image denoising due to their capability of suppressing noisy signals from an image this paper presents a novel edge preserving image denoising technique based on wavelet transforms the multi level decomposition of the noisy image is carried out to transform the data into the wavelet domain a locally adaptive patch based lapb thresholding scheme is used to effectively reduce noise while preserving relevant features of the original image experimental results on benchmark test images demonstrate that the proposed method achieves competitive denoising performance in comparison to various state of the art algorithms

comments on optimal approximation of uniformly rotated images relationship between karhumen loeve expansion and discrete cosine transform this paper points out the incorrect expressions of uenohara and kanade see ibid vol 7 p 116 19 1998 in the context of the representation of the eigenvectors based on the discrete cosine transform dct with the repeated eigenvalues the eigenvector matrix of the p spl times p real symmetric circulant matrix can be constructed using the singular value decomposition svd where p denotes the number of uniformly rotated images or equivalently it can be formulated in terms of the discrete hartley transform dht an example with p 4 is presented to show the correctness of our analysis

stabilization of planar switched systems this paper considers the problem of stabilization of single input planar switched systems we assume the switching law is observable a formula is presented which provides a necessary and sufficient condition for the system to be quadratically stabilizable a set of linear inequalities are given to describe the set of all quadratic lyapunov functions the solvability and the control design technique are clearly described in a straightforward computation algorithm

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

noise reduction procedures for gravity gradiometer data abstractnoise suppression of airborne gravity gradiometer data is a crucial part of the data processing stream we considered two approaches to removing noise kriging and directional filtering kriging is an estimation procedure for the interpolation of spatial data the estimator is calculated from the data variogram which characterizes the noise level and correlation length of the measurements directional filtering uses a user defined operator that is oriented to preferentially smooth the data along the strike but it leaves short wavelength components in the cross strike direction for definition of the trend edges both methods were applied to a recently collected offshore gravity gradient survey the kriging and directional filtering results revealed a similar level of smoothness but the main difference between them was the extra smoothing along the strike for the directionally filtered data because kriging is a data driven procedure it provides an objective estimate of the data noise level and

a least squares framework for component analysis over the last century component analysis ca methods such as principal component analysis pca linear discriminant analysis lda canonical correlation analysis cca locality preserving projections lpp and spectral clustering sc have been extensively used as a feature extraction step for modeling classification visualization and clustering ca techniques are appealing because many can be formulated as eigen problems offering great potential for learning linear and nonlinear representations of data in closed form however the eigen formulation often conceals important analytic and computational drawbacks of ca techniques such as solving generalized eigen problems with rank deficient matrices e g small sample size problem lacking intuitive interpretation of normalization factors and understanding commonalities and differences between ca methods this paper proposes a unified least squares framework to formulate many ca methods we show how pca lda cca lpp sc and its kernel and regularized extensions correspond to a particular instance of least squares weighted kernel reduced rank regression ls wkrrr the ls wkrrr formulation of ca methods has several benefits 1 provides a clean connection between many ca techniques and an intuitive framework to understand normalization factors 2 yields efficient numerical schemes to solve ca techniques 3 overcomes the small sample size problem 4 provides a framework to easily extend ca methods we derive weighted generalizations of pca lda sc and cca and several new ca techniques

space time coupled spectral hp least squares finite element formulation for the incompressible navier stokes equations we consider least squares finite element models for the numerical solution of the non stationary navier stokes equations governing viscous incompressible fluid flows the paper presents a formulation where the effects of space and time are coupled resulting in a true space time least squares minimization procedure as opposed to a space time decoupled formulation where a least squares minimization procedure is performed in space at each time step the formulation is first presented for the linear advection diffusion equation and then extended to the navier stokes equations the formulation has no time step stability restrictions and is spectrally accurate in both space and time to allow the use of practical c0 element expansions in the resulting finite element model the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity as an additional independent variable and the least squares method is used to develop the finite element model of the governing equations high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix free form spectral convergence of the l2 least squares functional and l2 error norms in space time is verified using a smooth solution to the two dimensional non stationary incompressible navier stokes equations numerical results are presented for impulsively started lid driven cavity flow oscillatory lid driven cavity flow transient flow over a backward facing step and flow around a circular cylinder the results demonstrate the predictive capability and robustness of the proposed formulation even though the space time coupled formulation is emphasized we also present the formulation and numerical results for least squares space time decoupled finite element models the numerical results show that the space time coupled formulation has superior predictive capabilities for flows demanding high space time resolution exemplified here by the transient flow over a backward facing step

accurate image rotation using hermite expansions in this paper we propose an approach for the accurate rotation of a digital image using hermite expansions this exploits the fact that if a 2 d continuous bandlimited hermite expansion is rotated the resulting function can be expressed as a hermite expansion with the same bandlimit furthermore the hermite coefficients of the initial 2 d expansion and the rotated expansion are mapped through an invertible linear relationship two efficient methods to compute the mapping between hermite coefficients during rotation are proposed we also propose a method for connecting the hermite expansion and a discrete image using this method we can obtain the hermite expansion from a discrete image and vice versa combining these techniques we propose new methods for the rotation of discrete images we assess the accuracy of our methods and compare them with an existing fft based method implementing three shears we find that the method proposed here consistently has better accuracy than the fft based method

rotation and illumination invariant interleaved intensity order based local descriptor the region descriptors using local intensity ordering patterns have become more popular recent years for image matching due to its enhanced discriminative ability however the dimension of these descriptors increases rapidly with the slight increase in the number of local neighbors under consideration and becomes unreasonable for image matching due to time constraint in this paper we reduce the dimension of the descriptor and matching time significantly while keeping up the comparable performance by considering the number of neighboring sample points in an interleaved manner the proposed interleaved order based local descriptor iold considers the local neighbors of a pixel as a set of interleaved neighbors and constructs the descriptor over each set separately and finally combines them to produce a single pattern we extract the local ordering pattern to cope up with the illumination effect in an inherent rotation invariant manner the novelty lies with using multiple neighboring sets in an interleaved fashion we also explored the local intensity order pattern in a multisupport region scenario results are compared over three challenging and widely adopted image matching data sets with other prominent descriptors under various image transformations results based on experiments suggest that the proposed iold descriptor outperforms in terms of both improved matching performance and reduced matching time we also found that the amount of improvement is significant under complex illumination difference while showing more robustness toward noise

asymmetric pulse modeling for fri sampling we consider sampling and reconstruction of finite rate of innovation fri signals such as a train of pulses where the pulses have varying degrees of asymmetry we address the problem of asymmetry modeling starting from a given symmetric prototype we show that among the class of unitary operators that are linear and invariant to translation and scale the fractional hilbert frh operator is unique for parametrically modeling pulse asymmetry the frh operator is obtained by a trigonometric interpolation between the standard hilbert and identity operators where the interpolation weights are determined by the degree of asymmetry the frh operators are also steerable which allows for estimation of the asymmetry factors in addition to the delays and amplitudes using the high resolution spectral estimation techniques that are used for solving standard fri problems we also develop the discrete counterpart using discrete frh operators and show that all the desirable properties carry over smoothly to the discrete setting as well we derive closed form expressions for the cramer rao bounds and hammersley chapman robbins bound on the variances of the estimators for continuous and discrete parameters respectively experimental results show that the proposed estimators have variances that meet the lower bounds we demonstrate an application of the proposed discrete frh methodology on real electrocardiogram ecg signals in the presence of noise specifically we show how the asymmetry of qrs complexes in various channels of an ecg signal could be modeled accurately

optimal approximation of uniformly rotated images relationship between karhunen loeve expansion and discrete cosine transform we present the concept that for uniformly rotated images the optimal approximation of the images can be obtained by computing the basis vectors for the discrete cosine transform dct of the original image in polar coordinates and that the images can be represented as linear combinations of the basis vectors

stability and stabilisation of planar switched linear systems via lasalle s invariance principle this paper investigates the problem of uniformly asymptotical stability uas and stabilisation of planar switched linear systems using lasalle s invariance principle of switched systems first we show that a common weak quadratic lyapunov function wqlf is enough to assure the uas of a switched linear system with stable modes then the necessary and sufficient conditions for the existence of common wqlf are obtained secondly we consider the problem of uniformly asymptotical stabilisation uasz of single input planar switched linear systems necessary and sufficient conditions for the closed loop system with proper feedback to share a common wqlf are presented it is also proved that a common wqlf is enough to assure the uas of the closed loop system

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

steerable wavelet frames based on the riesz transform we consider an extension of the 1 d concept of analytical wavelet to n d which is by construction compatible with rotations this extension called a monogenic wavelet yields a decomposition of the wavelet coefficients into amplitude phase and phase direction the monogenic wavelet is based on the hypercomplex monogenic signal which is defined using riesz transforms and perfectly isotropic wavelets frames employing the new concept of clifford frames we can show that the monogenic wavelet generates a wavelet frame furthermore this approach yields wavelet frames that are steerable with respect to direction applications to descreening and contrast enhancement illustrate the versatility of this approach to image analysis and reconstruction

using basic image features for texture classification representing texture images statistically as histograms over a discrete vocabulary of local features has proven widely effective for texture classification tasks images are described locally by vectors of for example responses to some filter bank and a visual vocabulary is defined as a partition of this descriptor response space typically based on clustering in this paper we investigate the performance of an approach which represents textures as histograms over a visual vocabulary which is defined geometrically based on the basic image features of griffin and lillholm proc spie 6492 09 1 11 2007 rather than by clustering bifs provide a natural mathematical quantisation of a filter response space into qualitatively distinct types of local image structure we also extend our approach to deal with intra class variations in scale our algorithm is simple there is no need for a pre training step to learn a visual dictionary as in methods based on clustering and no tuning of parameters is required to deal with different datasets we have tested our implementation on three popular and challenging texture datasets and find that it produces consistently good classification results on each including what we believe to be the best reported for the kth tips and equal best reported for the uiuctex databases

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

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

3d steerable wavelets in practice we introduce a systematic and practical design for steerable wavelet frames in 3d our steerable wavelets are obtained by applying a 3d version of the generalized riesz transform to a primary isotropic wavelet frame the novel transform is self reversible tight frame and its elementary constituents riesz wavelets can be efficiently rotated in any 3d direction by forming appropriate linear combinations moreover the basis functions at a given location can be linearly combined to design custom and adaptive steerable wavelets the features of the proposed method are illustrated with the processing and analysis of 3d biomedical data in particular we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3d monogenic analysis we also propose a new inverse problem formalism along with an optimization algorithm for reconstructing 3d images from a sparse set of wavelet domain edges the scheme results in high quality image reconstructions which demonstrate the feature reduction ability of the steerable wavelets as well as their potential for solving inverse problems

spatially adaptive estimation via fitted local likelihood techniques this paper offers a new technique for spatially adaptive estimation the local likelihood is exploited for nonparametric modeling of observations and estimated signals the approach is based on the assumption of a local homogeneity of the signal for every point there exists a neighborhood in which the signal can be well approximated by a constant the fitted local likelihood statistics are used for selection of an adaptive size and shape of this neighborhood the algorithm is developed for a quite general class of observations subject to the exponential distribution the estimated signal can be uni and multivariable we demonstrate a good performance of the new algorithm for image denoising and compare the new method versus the intersection of confidence interval ici technique that also exploits a selection of an adaptive neighborhood for estimation

deformable kernels for early vision early vision algorithms often have a first stage of linear filtering that extracts from the image information at multiple scales of resolution and multiple orientations a common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs a technique is presented that allows 1 computing the best approximation of a given family using linear combinations of a small number of basis functions and 2 describing all finite dimensional families i e the families of filters for which a finite dimensional representation is possible with no error the technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations the relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi scale 2d edge detection kernels the implementation issues are also discussed

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

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

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

the hermite transform theory the author introduces a scheme for the local processing of visual information called the hermite transform the problem is addressed from the point of view of image coding and therefore the scheme is presented as an analysis resynthesis system the objectives of the present work however are not restricted to coding the analysis part is designed so that it can also serve applications in the area of computer vision indeed derivatives of gaussians which have found widespread application in feature detection over the past few years play a central role in the hermite analysis it is also argued that the proposed processing scheme is in close agreement with current insight into the image processing that is carried out by the human visual system in particular it is demonstrated that the hermite transform is in better agreement with human visual modeling than gabor expansions

signal denoising and ultrasonic flaw detection via overcomplete and sparse representations sparse signal representations from overcomplete dictionaries are the most recent technique in the signal processing community applications of this technique extend into many fields in this paper this technique is utilized to cope with ultrasonic flaw detection and noise suppression problem in particular a noisy ultrasonic signal is decomposed into sparse representations using a sparse bayesian learning algorithm and an overcomplete dictionary customized from a gabor dictionary by incorporating some a priori information of the transducer used nonlinear postprocessing including thresholding and pruning is then applied to the decomposed coefficients to reduce the noise contribution and extract the flaw information because of the high compact essence of sparse representations flaw echoes are packed into a few significant coefficients and noise energy is likely scattered all over the dictionary atoms generating insignificant coefficients this property greatly increases the efficiency of the pruning and thresholding operations and is extremely useful for detecting flaw echoes embedded in background noise the performance of the proposed approach is verified experimentally and compared with the wavelet transform signal processor experimental results to detect ultrasonic flaw echoes contaminated by white gaussian additive noise or correlated noise are presented in the paper

a differential model of the complex cell the receptive fields of simple cells in the visual cortex can be understood as linear filters these filters can be modeled by gabor functions or gaussian derivatives gabor functions can also be combined in an energy model of the complex cell response this letter proposes an alternative model of the complex cell based on gaussian derivatives it is most important to account for the insensitivity of the complex response to small shifts of the image the new model uses a linear combination of the first few derivative filters at a single position to approximate the first derivative filter at a series of adjacent positions the maximum response over all positions gives a signal that is insensitive to small shifts of the image this model unlike previous approaches is based on the scale space theory of visual processing in particular the complex cell is built from filters that respond to the 2d differential structure of the image the computational aspects of the new model are studied in one and two dimensions using the steerability of the gaussian derivatives the response of the model to basic images such as edges and gratings is derived formally the response to natural images is also evaluated using statistical measures of shift insensitivity the neural implementation and predictions of the model are discussed

focus of attention from local color symmetries in this paper a continuous valued measure for local color symmetry is introduced the new algorithm is an extension of the successful gray value based symmetry map proposed by reisfeld et al the use of color facilitates the detection of focus points fps on objects that are difficult to detect using gray value contrast only the detection of fps is aimed at guiding the attention of an object recognition system therefore fps have to fulfill three major requirements stability distinctiveness and usability the proposed algorithm is evaluated for these criteria and compared with the gray value based symmetry measure and two other methods from the literature stability is tested against noise object rotation and variations of lighting as a measure for the distinctiveness of fps the principal components of fp centered windows are compared with those of windows at randomly chosen points on a large database of natural images finally usability is evaluated in the context of an object recognition task

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

an algorithm for calculation of the discrete cosine transform by paired transform a new algorithm for splitting the one dimensional 1 d 2 sup r point discrete cosine transform dct into a set of short 2 sup k point type iv dcts k 1 r 1 is introduced the splitting is performed by means of paired transformation that is defined by the paired representation of signals with respect to the cosine transform a proposed method of calculating the 2 sup r point cosine transform requires 2 sup r 1 r multiplications and 2 sup r 1 3r 2 1 additions when r spl ges 2

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