image denoising with edge preserving and segmentation based on mask nha in this paper we propose a zero mean white gaussian noise removal method using a high resolution frequency analysis it is difficult to separate an original image component from a noise component when using discrete fourier transform or discrete cosine transform for analysis because sidelobes occur in the results the 2d non harmonic analysis 2d nha is a high resolution frequency analysis technique that improves noise removal accuracy because of its sidelobe reduction feature however spectra generated by nha are distorted because of which the signal of the image is non stationary in this paper we analyze each region with a homogeneous texture in the noisy image non uniform regions that occur due to segmentation are analyzed by an extended 2d nha method called mask nha we conducted an experiment using a simulation image and found that mask nha denoising attains a higher peak signal to noise ratio psnr value than the state of the art methods if a suitable segmentation result can be obtained from the input image even though parameter optimization was incomplete this experimental result exhibits the upper limit on the value of psnr in our mask nha denoising method the performance of mask nha denoising is expected to approach the limit of psnr by improving the segmentation method

further results on incremental input to state stability incremental stability notions defined by means of comparison functions in a state space framework are further investigated in particular we provide a continuous converse lyapunov theorem for incremental integral iss and show that the incremental integral property is at least as strong as incremental iss

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

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

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

a joint inter and intrascale statistical model for bayesian wavelet based image denoising this paper presents a new wavelet based image denoising method which extends a geometrical bayesian framework the new method combines three criteria for distinguishing supposedly useful coefficients from noise coefficient magnitudes their evolution across scales and spatial clustering of large coefficients near image edges these three criteria are combined in a bayesian framework the spatial clustering properties are expressed in a prior model the statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model the three main novelties with respect to related approaches are 1 the interscale ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated 2 a joint conditional model is introduced and 3 a novel anisotropic markov random field prior model is proposed the results demonstrate an improved denoising performance over related earlier techniques

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

a non quadratic criterion for stability of forced oscillations abstract a new test for stability of forced oscillations in nonlinear systems is proposed the result is illustrated by an example of a saturated pi control of an integrator with a harmonic reference signal the range of frequencies and amplitudes that guarantee stability of the corresponding oscillations is found

wavelet threshold estimators for data with correlated noise wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level dependent soft threshold to the coefficients in the wavelet transform a variety of threshold choices is proposed including one based on an unbiased estimate of mean squared error the practical performance of the method is demonstrated on examples including data from a neurophysiological context the theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable bench mark that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity and more generally is obtained by the use of an oracle that provides information that is not actually available in the data it is shown that the level dependent threshold estimator performs well relative to the bench mark risk and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator the wavelet domain structure of both short and long range dependent noise is considered and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes adapting automatically to the regularity properties of the underlying model the proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem

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

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

empirical bayes approach to improve wavelet thresholding for image noise reduction wavelet threshold algorithms replace small magnitude wavelet coefficients with zero and keep or shrink the other coefficients this is basically a local procedure because wavelet coefficients characterize the local regularity of a function although a wavelet transform has decorrelating properties structures in images like edges are never decorrelated completely and these structures appear in the wavelet coefficients a classification based on a local criterion like coefficient magnitude is not the perfect method to distinguish important uncorrupted coefficients from coefficients dominated by noise we therefore introduce a geometrical prior model for configurations of important wavelet coefficients and combine this with local characterization of a classical threshold procedure into a bayesian framework the local characterization is incorporated into the conditional model whereas the prior model describes only configurations not coefficient values more precisely local characterization favors co

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

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

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

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

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

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

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

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

brief paper stability and robustness analysis of nonlinear systems via contraction metrics and sos programming a wide variety of stability and performance questions about linear dynamical systems can be reformulated as convex optimization problems involving linear matrix inequalities lmis these techniques have been recently extended to nonlinear systems with polynomial or rational dynamics through the use of sum of squares sos programming in this paper we further extend the class of systems that can be analyzed with convexity based methods we show how to analyze the robust stability properties of uncertain nonlinear systems with polynomial or rational dynamics via contraction analysis and sos programming since the existence of a global contraction metric is a sufficient condition for global stability of an autonomous system we develop an algorithm for finding such contraction metrics using sos programming the search process is made computationally tractable by relaxing matrix definiteness constraints the feasibility of which indicates the existence of a contraction metric to sos constraints on polynomial matrices we illustrate our results through examples from the literature and show how our contraction based approach offers advantages when compared with traditional lyapunov analysis

from local kernel to nonlocal multiple model image denoising we review the evolution of the nonparametric regression modeling in imaging from the local nadaraya watson kernel estimate to the nonlocal means and further to transform domain filtering based on nonlocal block matching the considered methods are classified mainly according to two main features local nonlocal and pointwise multipoint here nonlocal is an alternative to local and multipoint is an alternative to pointwise these alternatives though obvious simplifications allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques within this framework we introduce a novel single and multiple model transform domain nonlocal approach the block matching and 3 d filtering bm3d algorithm which is currently one of the best performing denoising algorithms is treated as a special case of the latter approach

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

commensurability of 1 cusped hyperbolic 3 manifolds we give examples of non fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres in fact we give many examples of knot complements in homology spheres where every commensurable knot complement in a homology sphere has non monic alexander polynomial

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

some results on exponential synchronization of nonlinear systems based on recent works on transverse exponential stability we establish some necessary and sufficient conditions for the existence of a locally exponential synchronizing control law we show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems on the synchronization manifold by a linear state feedback this in turn is also equivalent to the existence of a symmetric covariant tensor field which satisfies a control matrix function inequality based on this result we provide the construction of such a synchronizer via backstepping approach in some particular cases we show how global exponential synchronization may be obtained

the bieri neumann strebel invariants via newton polytopes we study the newton polytopes of determinants of square matrices defined over rings of twisted laurent polynomials we prove that such newton polytopes are single polytopes rather than formal differences of two polytopes this result can be seen as analogous to the fact that determinants of matrices over commutative laurent polynomial rings are themselves polynomials rather than rational functions we also exhibit a relationship between the newton polytopes and invertibility of the matrices over novikov rings thus establishing a connection with the invariants of bieri neumann strebel bns via a theorem of sikorav we offer several applications we reprove thurston s theorem on the existence of a polytope controlling the bns invariants of a 3 manifold group we extend this result to free by cyclic groups and the more general descending hnn extensions of free groups we also show that the bns invariants of poincare duality groups of type mathtt f in dimension 3 and groups of deficiency one are determined by a polytope when the groups are assumed to be agrarian that is their integral group rings embed in skew fields the latter result partially confirms a conjecture of friedl we also deduce the vanishing of the newton polytopes associated to elements of the whitehead groups of many groups satisfying the atiyah conjecture we use this to show that the l 2 torsion polytope of friedl luck is invariant under homotopy we prove the vanishing of this polytope in the presence of amenability thus proving a conjecture of friedl luck tillmann

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

convergent dynamics a tribute to boris pavlovich demidovich we review and pay tribute to a result on convergent systems by the russian mathematician boris pavlovich demidovich in a sense demidovich s approach forms a prelude to a field which is now called incremental stability of dynamical systems developments on incremental stability are reviewed from a historical perspective

contraction theory on riemannian manifolds abstract contraction theory is a methodology for assessing the stability of trajectories of a dynamical system with respect to one another in this work we present the fundamental results of contraction theory in an intrinsic coordinate free setting with the presentation highlighting the underlying geometric foundation of contraction theory and the resulting stability properties we provide coordinate free proofs of the main results for autonomous vector fields and clarify the assumptions under which the results hold we state and prove several interesting corollaries to the main result study cascade and feedback interconnections of contracting systems study some simple examples and highlight how contraction theory has arisen independently in other scientific disciplines we conclude by illustrating the developed theory for the case of gradient dynamics

multiresolution bilateral filtering for image denoising the bilateral filter is a nonlinear filter that does spatial averaging without smoothing edges it has shown to be an effective image denoising technique an important issue with the application of the bilateral filter is the selection of the filter parameters which affect the results significantly there are two main contributions of this paper the first contribution is an empirical study of the optimal bilateral filter parameter selection in image denoising applications the second contribution is an extension of the bilateral filter multiresolution bilateral filter where bilateral filtering is applied to the approximation low frequency subbands of a signal decomposed using a wavelet filter bank the multiresolution bilateral filter is combined with wavelet thresholding to form a new image denoising framework which turns out to be very effective in eliminating noise in real noisy images experimental results with both simulated and real data are provided

joint image denoising using adaptive principal component analysis and self similarity the non local means nlm has attracted enormous interest in image denoising problem in recent years in this paper we propose an efficient joint denoising algorithm based on adaptive principal component analysis pca and self similarity that improves the predictability of pixel intensities in reconstructed images the proposed algorithm consists of two successive steps without iteration the low rank approximation based on parallel analysis and the collaborative filtering first for a pixel and its nearest neighbors the training samples in a local search window are selected to form the similar patch group by the block matching method next it is factorized by singular value decomposition svd whose left and right orthogonal basis denote local and non local image features respectively the adaptive pca automatically chooses the local signal subspace dimensionality of the noisy similar patch group in the svd domain by the refined parallel analysis with monte carlo simulation thus image features can be well preserved after dimensionality reduction and simultaneously the noise is almost eliminated then after the inverse svd transform the denoised image is reconstructed from the aggregate filtered patches by the weighted average method finally the collaborative wiener filtering is used to further remove the noise the experimental results validate its generality and effectiveness in a wide range of the noisy images the proposed algorithm not only produces very promising denoising results that outperforms the state of the art methods in most cases but also adapts to a variety of noise levels

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

skinning maps are finite to one we show that thurston s skinning maps of teichmuller space have finite fibers the proof centers around a study of two subvarieties of the rm sl 2 mathbb c character variety of a surface one associated with complex projective structures and the other associated with a 3 manifold using the morgan shalen compactification of the character variety and author s results on holonomy limits of complex projective structures we show that these subvarieties have only a discrete set of intersections

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

image restoration using space variant gaussian scale mixtures in overcomplete pyramids in recent years bayes least squares gaussian scale mixtures bls gsm has emerged as one of the most powerful methods for image restoration its strength relies on providing a simple and yet very effective local statistical description of oriented pyramid coefficient neighborhoods via a gsm vector this can be viewed as a fine adaptation of the model to the signal variance at each scale orientation and spatial location here we present an enhancement of the model by introducing a coarser adaptation level where a larger neighborhood is used to estimate the local signal covariance within every subband we formulate our model as a bls estimator using space variant gsm the model can be also applied to image deconvolution by first performing a global blur compensation and then doing local adaptive denoising we demonstrate through simulations that the proposed method besides being model based and noniterative it is also robust and efficient its performance measured visually and in l2 norm terms is significantly higher than the original bls gsm method both for denoising and deconvolution

image denoising using total least squares in this paper we present a method for removing noise from digital images corrupted with additive multiplicative and mixed noise an image patch from an ideal image is modeled as a linear combination of image patches from the noisy image we propose to fit this model to the real world image data in the total least square tls sense because the tls formulation allows us to take into account the uncertainties in the measured data we develop a method to reduce the contribution from the irrelevant image patches which will sharpen the edges and reduce edge artifacts at the same time although the proposed algorithm is computationally demanding the image quality of the output image demonstrates the effectiveness of the tls algorithms

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

image denoising using trivariate shrinkage filter in the wavelet domain and joint bilateral filter in the spatial domain this correspondence proposes an efficient algorithm for removing gaussian noise from corrupted image by incorporating a wavelet based trivariate shrinkage filter with a spatial based joint bilateral filter in the wavelet domain the wavelet coefficients are modeled as trivariate gaussian distribution taking into account the statistical dependencies among intrascale wavelet coefficients and then a trivariate shrinkage filter is derived by using the maximum a posteriori map estimator although wavelet based methods are efficient in image denoising they are prone to producing salient artifacts such as low frequency noise and edge ringing which relate to the structure of the underlying wavelet on the other hand most spatial based algorithms output much higher quality denoising image with less artifacts however they are usually too computationally demanding in order to reduce the computational cost we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain this filter could suppress the noise while preserve image details with small computational cost extension to color image denoising is also presented we compare our denoising algorithm with other denoising techniques in terms of psnr and visual quality the experimental results indicate that our algorithm is competitive with other denoising techniques

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

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

asymptotic stability and smooth lyapunov functions abstract we establish that differential inclusions corresponding to upper semicontinuous multifunctions are strongly asymptotically stable if and only if there exists a smooth lyapunov function since well known concepts of generalized solutions of differential equations with discontinuous right hand side can be described in terms of solutions of certain related differential inclusions involving upper semicontinuous multifunctions this result gives a lyapunov characterization of asymptotic stability of either filippov or krasovskii solutions for differential equations with discontinuous right hand side in the study of weak as opposed to strong asymptotic stability the existence of a smooth lyapunov function is rather exceptional however the methods employed in treating the strong case of asymptotic stability are applied to yield a necessary condition for the existence of a smooth lyapunov function for weakly asymptotically stable differential inclusions this is an extension to the context of lyapunov functons of brockett s celebrated covering condition from continuous feedback stabilization theory

sensitivity to cumulative perturbations for a class of piecewise constant hybrid systems we consider a class of continuous time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces and which includes the fluid level dynamics of the max weight scheduling policy as a special case we study the effect of an external disturbance perturbation on the state trajectory and establish that the magnitude of this effect can be bounded by a constant multiple of the integral of the perturbation

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

transverse exponential stability and applications we investigate how the following properties are related to each other i a manifold is transversally exponentially stable ii the transverse linearization along any solution in the manifold is exponentially stable and iii there exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow we illustrate their relevance with the study of exponential incremental stability finally we apply these results to two control design problems nonlinear observer design and synchronization in particular we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property

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

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

norms on the cohomology of hyperbolic 3 manifolds we study the relationship between two norms on the first cohomology of a hyperbolic 3 manifold the purely topological thurston norm and the more geometric harmonic norm refining recent results of bergeron engun and venkatesh as well as older work of kronheimer and mrowka we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3 manifold itself moreover we give families of examples showing that some but not all qualitative aspects of our estimates are sharp finally we exhibit closed hyperbolic 3 manifolds where the thurston norm grows exponentially in terms of the volume and yet there is a uniform lower bound on the injectivity radius

a differential lyapunov framework for contraction analysis lyapunov s second theorem is an essential tool for stability analysis of differential equations the paper provides an analog theorem for incremental stability analysis by lifting the lyapunov function to the tangent bundle the lyapunov function endows the state space with a finsler structure incremental stability is inferred from infinitesimal contraction of the finsler metrics through integration along solutions curves

bayesian tree structured image modeling using wavelet domain hidden markov models wavelet domain hidden markov models have proven to be useful tools for statistical signal and image processing the hidden markov tree hmt model captures the key features of the joint probability density of the wavelet coefficients of real world data one potential drawback to the hmt framework is the need for computationally expensive iterative training to fit an hmt model to a given data set e g using the expectation maximization algorithm we greatly simplify the hmt model by exploiting the inherent self similarity of real world images the simplified model specifies the hmt parameters with just nine meta parameters independent of the size of the image and the number of wavelet scales we also introduce a bayesian universal hmt uhmt that fixes these nine parameters the uhmt requires no training of any kind while extremely simple we show using a series of image estimation denoising experiments that these new models retain nearly all of the key image structure modeled by the full hmt finally we propose a fast shift invariant hmt estimation algorithm that outperforms other wavelet based estimators in the current literature both visually and in mean square error

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

holonomy limits of complex projective structures abstract we study the limits of holonomy representations of complex projective structures on a compact riemann surface in the morgan shalen compactification of the character variety we show that the dual r trees of the quadratic differentials associated to a divergent sequence of projective structures determine the morgan shalen limit points up to a natural folding operation for quadratic differentials with simple zeros no folding is possible and the limit of holonomy representations is isometric to the dual tree we also derive an estimate for the growth rate of the holonomy map in terms of a norm on the space of quadratic differentials

asymptotic properties of incrementally stable systems it is shown that incremental stability of an input output operator ensures asymptotic stability of any equilibrium pair x sub e u sub e of its state representation if suitable minimality assumptions hold

derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises this paper addresses the problem of estimating signals from observation models with multiplicative and additive noises assuming that the state space model is unknown the multiplicative noise is non white and the signal and additive noise are correlated recursive algorithms are derived for the least squares linear filter and fixed point smoother the proposed algorithms are obtained using an innovation approach and taking into account the information provided by the covariance functions of the process involved

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

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