local and global controllability for nonlinear systems a technique to study local and global controllability properties for a wide class of nonlinear systems is presented in addition to an extensive study of systems on r2 we propose as an application of our method a new criterion for global controllability of systems with polynomial drift term defined on rn in the case of linear systems the criterion reduces to the classical kalman condition a study of local controllability at the equilibrium point of the drift term of systems defined on r2 enables us not only to rederive a local controllability result derived by hermes 4 5 but also to extend this result when no assumptions are made on the boundedness of the controls

fuzzy edge detection for omnidirectional images the use of omnidirectional vision has increased during these past years it provides a very large field of view nevertheless omnidirectional images contain significant radial distortions and conventional image processing is not adapted to these specific images this paper presents an edge detector adapted to the image geometry fuzzy sets will be used to take into account all imprecisions introduced by the sampling process the prewitt filter applied to omnidirectional image will be studied to illustrate this paper

structured condition numbers and small sample condition estimation of symmetric algebraic riccati equations abstract this paper is devoted to a structured perturbation analysis of the symmetric algebraic riccati equations by exploiting the symmetry structure based on the analysis the upper bounds for the structured normwise mixed and componentwise condition numbers are derived due to the exploitation of the symmetry structure our results are improvements of the previous work on the perturbation analysis and condition numbers of the symmetric algebraic riccati equations our preliminary numerical experiments demonstrate that our condition numbers provide accurate estimates for the change in the solution caused by the perturbations on the data moreover by applying the small sample condition estimation method we propose a statistical algorithm for practically estimating the condition numbers of the symmetric algebraic riccati equations

approximation of an arbitrary filter and its recursive implementation abstract filtering is one of the important techniques in computer vision it has been widely used in edge detection image restoration range image segmentation etc however the efficient implementation of an arbitrary filter has been a challenging problem until now in this paper a novel method is proposed to implement an arbitrary filter firstly an efficient recursive structure is proposed to implement any polynomial exponential type pet filter the computational complexity and structure are independent of its filter mask size or its bandwidth secondly a new method is proposed lagurre spectrum decomposition method to obtain the pet approximation of any filters as an example the above method is applied to the approximation and implementation of gaussian filters and experiments have shown that a perfect approximation can be obtained with only third order lagurre bases and therefore only a fourth order recursive filter is needed to implement gaussian filters finally the comparison of the present method with the known ones shows that 1 lagurre polynomial bases are orthogonal with each other so the filter approximation is simple 2 the bases are complete and the completeness guarantees the approximation error can be reduced to zero 3 the method can be used to design both gaussian and any other filters

on the inter conversion between hermite and laguerre local image expansions the nice relationship existing among the hermite gauss and the laguerre gauss image expansions whose basis functions span the same signal space is investigated as a result a novel efficient method for cartesian to polar coordinate inter conversion especially suited for dedicated hardware realization is proposed applications to local image rotation based on the simple steerability of the laguerre gauss expansion and to local image analysis based on gaussian derivatives are considered in detail a possible fixed point realization of the proposed inter conversion scheme is discussed

the matrix sign function a survey of the matrix sign function is presented including some historical background definitions and properties approximation theory and computational methods and condition theory and estimation procedures applications to areas such as control theory eigendecompositions and roots of matrices are outlined and some new theoretical results are also given

fast algorithms for low level vision a recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing performing the first and second directional derivatives and carrying out the laplacian of an image these operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered the key to the approach is first the use of an exponentially based filter family and second the use of the recursive filtering applications to edge detection problems and multiresolution techniques are considered and an edge detector allowing the extraction of zero crossings of an image with only 14 operations per output element at any resolution is proposed various experimental results are shown

a flexible condition number for weighted linear least squares problem and its statistical estimation in this paper we mainly focus on the derivation of a flexible condition number for weighted linear least squares problem and its estimation with frechet derivative and kronecker product the explicit expression of the condition number is obtained when the coefficient matrices are large and dense considering the difficulties of explicitly forming the expression of condition number in computer we also present its simplified form through a simple and easy to operate method two different condition estimation methods are introduced and the numerical experiments are also performed to show the efficiency of the condition estimators

a representation for shape based on peaks and ridges in the difference of low pass transform this paper defines a multiple resolution representation for the two dimensional gray scale shapes in an image this representation is constructed by detecting peaks and ridges in the difference of lowpass dolp transform descriptions of shapes which are encoded in this representation may be matched efficiently despite changes in size orientation or position motivations for a multiple resolution representation are presented first followed by the definition of the dolp transform techniques are then presented for encoding a symbolic structural description of forms from the dolp transform this process involves detecting local peaks and ridges in each bandpass image and in the entire three dimensional space defined by the dolp transform linking adjacent peaks in different bandpass images gives a multiple resolution tree which describes shape peaks which are local maxima in this tree provide landmarks for aligning manipulating and matching shapes detecting and linking the ridges in each dolp bandpass image provides a graph which links peaks within a shape in a bandpass image and describes the positions of the boundaries of the shape at multiple resolutions detecting and linking the ridges in the dolp three space describes elongated forms and links the largest peaks in the tree the principles for determining the correspondence between symbols in pairs of such descriptions are then described such correspondence matching is shown to be simplified by using the correspondence at lower resolutions to constrain the possible correspondence at higher resolutions

on local region models and a statistical interpretation of the piecewise smooth mumford shah functional the mumford shah functional is a general and quite popular variational model for image segmentation in particular it provides the possibility to represent regions by smooth approximations in this paper we derive a statistical interpretation of the full piecewise smooth mumford shah functional by relating it to recent works on local region statistics moreover we show that this statistical interpretation comes along with several implications firstly one can derive extended versions of the mumford shah functional including more general distribution models secondly it leads to faster implementations finally thanks to the analytical expression of the smooth approximation via gaussian convolution the coordinate descent can be replaced by a true gradient descent

bi exponential edge preserving smoother edge preserving smoothers need not be taxed by a severe computational cost we present in this paper a lean algorithm that is inspired by the bi exponential filter and preserves its structure a pair of one tap recursions by a careful but simple local adaptation of the filter weights to the data we are able to design an edge preserving smoother that has a very low memory and computational footprint while requiring a trivial coding effort we demonstrate that our filter a bi exponential edge preserving smoother or beeps has formal links with the traditional bilateral filter on a practical side we observe that the beeps also produces images that are similar to those that would result from the bilateral filter but at a much reduced computational cost the cost per pixel is constant and depends neither on the data nor on the filter parameters not even on the degree of smoothing

higher order numerical discretizations for exterior and biharmonic type pdes a higher order numerical discretization technique based on minimum sobolev norm msn interpolation was introduced in our previous work in this article the discretization technique is presented as a tool to solve two hard classes of pdes namely the exterior laplace problem and the biharmonic problem the exterior laplace problem is compactified and the resultant near singular pde is solved using this technique this finite difference type method is then used to discretize and solve biharmonic type pdes a simple book keeping trick of using ghost points is used to obtain a perfectly constrained discrete system numerical results such as discretization error condition number estimate and solution error are presented for both classes of pdes variable coefficient examples on complicated geometries and irregular grids are considered the method is seen to have high order of convergence in all these cases through numerical evidence perhaps for the first time such a systematic higher order procedure for irregular grids and variable coefficient cases is now available though not discussed in the paper the idea seems to be easily generalizable to finite element type techniques as well

stochastic perturbation theory in this paper classical matrix perturbation theory is approached from a probabilistic point of view the perturbed quantity is approximated by a first order perturbation expansion in which the perturbation is assumed to be random this permits the computation of statistics estimating the variation in the perturbed quantity up to the higher order terms that are ignored in the expansion these statistics tend to be more realistic than perturbation bounds obtained in terms of norms the technique is applied to a number of problems in matrix perturbation theory including least squares and the eigenvalue problem

global controllability for smooth nonlinear systems a geometric approach the paper consists of two parts in part i a global controllability theory is constructed local controllability criteria are integrated by means of the qualitative behavior of the dynamics involved leading to a global result the relation with global observability is discussed part ii is concerned with controllability by means of two vectorfields it is well known that each connected paracompact manifold of class c k 2 leqq k leqq infty or k omega carries a globally controllable set of two c k 1 vectorfields as an application of part i we construct control systems of the form dot x x uy defined on a compact manifold with the property that for x a morse smale vectorfield with no periodic orbits there exists a large class of vectorfields y such that the system is globally controllable by means of a bang bang two valued control it is stressed that the techniques applied imply the existence of a multitude of basically different globally controllable systems with two

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

a survey of condition number estimation for triangular matrices we survey and compare a wide variety of techniques for estimating the condition number of a triangular matrix and make recommendations concerning the use of the estimates in applications each of the methods is shown to bound the condition number the bounds can broadly be categorised as upper bounds from matrix theory and lower bounds from heuristic or probabilistic algorithms for each bound we examine by how much at worst it can overestimate or underestimate the condition number numerical experiments are presented in order to illustrate and compare the practical performance of the condition estimators

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

a new variational approach for restoring images with multiplicative noise this paper proposes a novel variational model for restoration of images corrupted with multiplicative noise it combines a fractional order total variational filter with a high order pde laplacian norm the combined approach is able to preserve edges while avoiding the blocky effect in smooth regions this strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori map semi implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional to improve the numerical results we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial and error method the existence and uniqueness of a solution to the proposed variational model is established in this study parameter dependence is also discussed experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding pde methods

a class of constrained clustering algorithms for object boundary extraction boundary extraction is a key task in many image analysis operations this paper describes a class of constrained clustering algorithms for object boundary extraction that includes several well known algorithms proposed in different fields deformable models constrained clustering data ordering and traveling salesman problems the algorithms belonging to this class are obtained by the minimization of a cost function with two terms a quadratic regularization term and an image dependent term defined by a set of weighting functions the minimization of the cost function is achieved by lowpass filtering the previous model shape and by attracting the model units toward the centroids of their attraction regions to define a new algorithm belonging to this class the user has to specify a regularization matrix and a set of weighting functions that control the attraction of the model units toward the data the usefulness of this approach is twofold it provides a unified framework for many existing algorithms in pattern recognition and deformable models and allows the design of new recursive schemes

parametric oriented fitting for local contrast enhancement local image contrast enhancement methods extract more informative details comparing with the global methods yet the traditional schemes require to access all of the pixels in a local region to obtain the cumulative distribution function cdf for further enhancement i e adaptive histogram equalization ahe and thus the time complexity drastically increases accordingly when the block size increases consequently some speed up ingenuities such as block wise strategy and simple proportionally averaging manner are employed to cope with this issue yet serious blocking artifact or low contrast issues are accompanied in this study a local enhancement method namely corrected parametric oriented histogram equalization cpohe is proposed to effectively yield enhanced results with high contrast and artifact free texture using the concept of integral image and further correct the accompanied distortion as documented in the experimental results the proposed method provides a high practical value for applied in visual perception biometric and tracking detection applications

controllability in codimension one abstract local and global controlability of analytic affine control systems with an arbitrary number of controls are studied assuming strong accessibility of and codimension one of the lie algebra t generated by the input vector fields i e dim t p n 1 at every p m controls are assumed to have no a priori bound from the study of the set h where a necessary condition for local controllability at a point is verified and assuming some transversality relations an easy to verify geometric condition is proved h is a submanifold and is locally controllable at every point of h outside a codimension one submanifold a geometric sufficient condition for global controllability on simply connected manifolds is then obtained if every leaf of t intersects the manifold h and some transversality relations including those involved in the local condition are verified is globally controllable

fast convolution with laplacian of gaussian masks we present a technique for computing the convolution of an image with log laplacian of gaussian masks it is well known that a log of variance a can be decomposed as a gaussian mask and a log of variance 1 we take advantage of the specific spectral characteristics of these filters in our computation the log is a bandpass filter we can therefore fold the spectrum of the image after low pass filtering without loss of information which is equivalent to reducing the resolution we present a complete evaluation of the parameters involved together with a complexity analysis that leads to the paradoxical result that the computation time decreases when increases we illustrate the method on two images

further results on global controllability of planar nonlinear systems the global controllability of a class of planar affine nonlinear systems with perturbation is investigated it has been proven that the systems can still hold their global controllability under the perturbation which can be dominated by a function of state and vanishes when control input is zero

small sample statistical condition estimation of large scale generalized eigenvalue problems we consider the evaluation of the sensitivity or condition number of generalized eigenvalue problems for a large and sparse real matrix or matrix pair in r n n through some coupled sylvester equation using newton s method the technique of the statistical condition estimation has been adapted to the sensitivity of symmetric matrices as well as general matrices with special structures under some assumptions on various types of perturbations

error estimation for reduced order models of dynamical systems the use of reduced order models to describe a dynamical system is pervasive in science and engineering often these models are used without an estimate of their error or range of validity in this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition we show how to compute estimates and bounds for these errors by a combination of small sample statistical condition estimation and error estimation using the adjoint method most important the proposed approach allows the assessment of regions of validity for reduced models i e ranges of perturbations in the original system over which the reduced model is still appropriate numerical examples validate our approach the error norm estimates approximate well the forward error while the derived bounds are within an order of magnitude

fast anisotropic gauss filtering we derive the decomposition of the anisotropic gaussian in a one dimensional 1 d gauss filter in the x direction followed by a 1 d filter in a nonorthogonal direction spl phi so also the anisotropic gaussian can be decomposed by dimension this appears to be extremely efficient from a computing perspective an implementation scheme for normal convolution and for recursive filtering is proposed also directed derivative filters are demonstrated for the recursive implementation filtering an 512 spl times 512 image is performed within 40 msec on a current state of the art pc gaining over 3 times in performance for a typical filter independent of the standard deviations and orientation of the filter accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error the anisotropic gaussian filtering method allows fast calculation of edge and ridge maps with high spatial and angular accuracy for tracking applications the normal anisotropic convolution scheme is more advantageous with applications in the detection of dashed lines in engineering drawings the recursive implementation is more attractive in feature detection applications for instance in affine invariant edge and ridge detection in computer vision the proposed computational filtering method enables the practical applicability of orientation scale space analysis

well posedness of two nonrigid multimodal image registration methods image registration methods may be designed as solutions of minimization problems on a set of geometric deformations in the nonrigid case solving these problems often means computing the steady state of a system of evolution equations involving the gradient of the error criterion defined from the euler lagrange equations of the corresponding minimization problem the well posedness of the registration methodrequires showing the existence of a solution to the minimization problem as well as that of a stable solution of the evolution equations derived from it we provide such proofs in the case where the error criterion is derived from two different statistical similarity measures global mutual information and local cross covariance we also describe our numerical implementation for solving the corresponding evolution equations and show examples of registrations of real 2d and 3d images achieved with these algorithms the proofs are quite general and can be applied to most of the known nonrigid image

a discrete expression of canny s criteria for step edge detector performances evaluation optimal filters for edge detection are usually developed in the continuous domain and then transposed by sampling to the discrete domain simpler filters are directly defined in the discrete domain we define criteria to compare filter performances in the discrete domain canny has defined 1983 1986 three criteria to derive the equation of an optimal filter for step edge detection good detection good localization and low responses multiplicity these criteria seem to be good candidates for filter comparison unfortunately they have been developed in the continuous domain and their analytical expressions cannot be used in the discrete domain we establish three criteria with the same meaning as canny s some comparisons with experimental results confirm the validity of our approach this study highlights the existence of two classes of derivative operators that are distinguished by whether or not the impulse response of the filter in continuous space domain is continuous on its center these classes exhibit very different properties for the second and third criteria we extend the use of the first and third criteria to the smoothing filters we also define an optimal continuous filter according to the continuous third criterion and an optimal discrete filter according to the discrete third criterion we compare the performances of the sampled version of the continuous filter to those of the optimal discrete filter

frequency response computation via rational interpolation a simple rational interpolation method is given for estimating a frequency response matrix the method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the subtraction of nearly equal values in the calculation of the difference terms when coupled with a pole cancellation method the resulting interpolation algorithm is accurate and efficient the error in this procedure has the form of a modified response matrix which means that the interpolation algorithm can be used to approximate both the response matrix and the error

fast space variant elliptical filtering using box splines the efficient realization of linear space variant non convolution filters is a challenging computational problem in image processing in this paper we demonstrate that it is possible to filter an image with a gaussian like elliptic window of varying size elongation and orientation using a fixed number of computations per pixel the associated algorithm which is based upon a family of smooth compactly supported piecewise polynomials the radially uniform box splines is realized using preintegration and local finite differences the radially uniform box splines are constructed through the repeated convolution of a fixed number of box distributions which have been suitably scaled and distributed radially in an uniform fashion the attractive features of these box splines are their asymptotic behavior their simple covariance structure and their quasi separability they converge to gaussians with the increase of their order and are used to approximate anisotropic gaussians of varying covariance simply by controlling the scales of the constituent box distributions based upon the second feature we develop a technique for continuously controlling the size elongation and orientation of these gaussian like functions finally the quasi separable structure along with a certain scaling property of box distributions is used to efficiently realize the associated space variant elliptical filtering which requires o 1 computations per pixel irrespective of the shape and size of the filter

structured condition numbers of structured tikhonov regularization problem and their estimations both structured componentwise and structured normwise perturbation analysis of the tikhonov regularization are presented the structured matrices under consideration include toeplitz hankel vandermonde and cauchy matrices structured normwise mixed and componentwise condition numbers for the tikhonov regularization are introduced and their explicit expressions are derived for the general linear structure based on the derived expressions we prove structured condition numbers are smaller than their corresponding unstructured counterparts by means of the power method and small sample statistical condition estimation sce fast condition estimation algorithms are proposed our estimation methods can be integrated into tikhonov regularization algorithms that use the generalized singular value decomposition gsvd for large scale linear structured tikhonov regularization problems we show how to incorporate the sce into the preconditioned conjugate gradient pcg method to get the posterior error estimations the structured condition numbers and perturbation bounds are tested on some numerical examples and compared with their unstructured counterparts our numerical examples demonstrate that the structured mixed condition numbers give sharper perturbation bounds than existing ones and the proposed condition estimation algorithms are reliable also an image restoration example is tested to show the effectiveness of the sce for large scale linear structured tikhonov regularization problems

condition numbers for the nonlinear matrix equation and their statistical estimation abstract in this paper we consider four different types of condition numbers i e two normwise ones mixed and componentwise ones for the nonlinear matrix equation x a f x a q and derive their explicit expressions using the probabilistic spectral norm estimator and the statistical condition estimation method these condition numbers can be estimated with high reliability two numerical examples are provided to illustrate the difference between the normwise condition numbers and the mixed and componentwise condition numbers and the efficiency of the estimators respectively

on optimal linear filtering for edge detection in this paper we revisit the analytical expressions of the three canny s 1983 criteria for edge detection quality good detection good localization and low multiplicity of false detections our work differs from canny s work on two essential points here the criteria are given for discrete sampled signals i e for the real implemented filters instead of a single step edge as input signal we use pulses of various width the proximity of other edges affects the quality of the detection process this is taken into account in the new expressions of these criteria we derive optimal filters for each of the criteria and for any combination of them in particular we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria the upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter exponential deriche 1987 and first derivative of gaussian filters are evaluated our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed

a new generalised α scale spaces quadrature filters abstract the scale spaces is a recent theory that open new possibilities of phase based image processing it is a parameterised class 0 1 of linear scale space representations which allows a continuous connection beyond the well known gaussian scale space 1 in this paper we make use of this unified representation to derive new families of band pass quadrature filters built from derivatives and difference of the scale space generating kernels this construction leads to generalised kernel filters including the commonly known families derived from the gaussian and the poisson kernels the properties of each family are first studied and then experiments on one and two dimensional signals are shown to exemplify how the suggested filters can be used for edge detection this work is complemented by an experimental evaluation which demonstrates that the new proposed filters are a good alternative to the commonly used log gabor filter

a new adaptive framework for unbiased orientation estimation in textured images this paper focuses on directional texture analysis we propose a new approach for orientation estimation this approach hinges on two classes of convolution masks i e the gradient and the valleyness operators we provide a framework for their optimization regarding bias reduction and noise robustness as the gradient and the valleyness operators are complementary we propose a combination named gv joe this combination consists in using the gradient on inflexion pixels the valleyness on crests and valleys and a linear mixture of both elsewhere we implement an adaptive selection of the size of our operators in order to take into account the variations of the texture scale in the image we apply our approach both on synthetic and natural textures these experiments show that when used separately both classes of operators are more accurate than classical derivative approaches in noisy cases the gv joe implementation improves the robustness of our operators without affecting their accuracy moreover compared to well known orientation estimators it gives the best estimates in the most difficult cases i e for high frequency textures and low snr

compressed sensing with wavelet domain dependencies for coronary mri a retrospective study coronary magnetic resonance imaging mri is a noninvasive imaging modality for diagnosis of coronary artery disease one of the limitations of coronary mri is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions compressed sensing cs has been recently utilized to accelerate image acquisition in mri in this paper we develop an improved cs reconstruction method bayesian least squares gaussian scale mixture bls gsm that uses dependencies of wavelet domain coefficients to reduce the observed blurring and reconstruction artifacts in coronary mri using traditional l1 regularization images of left and right coronary mri was acquired in 7 healthy subjects with fully sampled k space data the data was retrospectively undersampled using acceleration rates of 2 4 6 and 8 and reconstructed using l1 thresholding l1 minimization and bls gsm thresholding reconstructed right and left coronary images were compared with fully sampled reconstructions in vessel sharpness and subjective image quality 1 4 for poor excellent mean square error mse was also calculated for each reconstruction there were no significant differences between the fully sampled image score versus rate 2 4 or 6 for bls gsm for both right and left coronaries n s however for l1 thresholding significant differences p 0 05 were observed for rates higher than 2 and 4 for right and left coronaries respectively l1 minimization also yields images with lower scores compared to the reference for rates higher than 4 for both coronaries these results were consistent with the quantitative vessel sharpness readings bls gsm allows acceleration of coronary mri with acceleration rates beyond what can be achieved with l1 regularization

estimating extremal eigenvalues and condition numbers of matrices the paper describes probabilistic algorithms which may be used to make rough estimates of the largest and smallest eigenvalues of a positive definite matrix and the condition number of a nonsingular matrix in the 2 norm given varepsilon 0 and a prescribed relative error the algorithms compute estimates which with probability at least 1 varepsilon have relative errors less than that prescribed in particular the method gives a reliable way to estimate the condition number of a matrix of large degree

statistical condition estimation for the roots of polynomials this paper presents fast and reliable condition estimates for the roots of a real polynomial based on the method of statistical condition estimation sce by kenney and laub using relative perturbations we provide both a basic implementation of sce and an advanced one via the condition of the eigenvalues of the corresponding companion matrix new results for estimating the condition of eigenvalues are given fast structured calculations of the eigenvalues of the companion matrix are used and fast structured manipulations of the schur decomposition and the invariant subspaces of the companion matrix are presented the overall process is based on fast operations for sequentially semiseparable structures with small off diagonal ranks the cost of obtaining the condition estimates for all of the roots is o n 2 where n is the degree of the polynomial numerical examples are used to demonstrate the accuracy and efficiency of the proposed methods

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

compressive bilateral filtering this paper presents an efficient constant time bilateral filter that produces a near optimal performance tradeoff between approximate accuracy and computational complexity without any complicated parameter adjustment called a compressive bilateral filter cblf the constant time means that the computational complexity is independent of its filter window size although many existing constant time bilateral filters have been proposed step by step to pursue a more efficient performance tradeoff they have less focused on the optimal tradeoff for their own frameworks it is important to discuss this question because it can reveal whether or not a constant time algorithm still has plenty room for improvements of performance tradeoff this paper tackles the question from a viewpoint of compressibility and highlights the fact that state of the art algorithms have not yet touched the optimal tradeoff the cblf achieves a near optimal performance tradeoff by two key ideas 1 an approximate gaussian range kernel through fourier analysis and 2 a period length optimization experiments demonstrate that the cblf significantly outperforms state of the art algorithms in terms of approximate accuracy computational complexity and usability

estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse abstract a number of applications require the computation of the trace of a matrix that is implicitly available through a function a common example of a function is the inverse of a large sparse matrix which is the focus of this paper when the evaluation of the function is expensive the task is computationally challenging because the standard approach is based on a monte carlo method which converges slowly we present a different approach that exploits the pattern correlation if present between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively we leverage various sampling and fitting techniques to fit the diagonal of the approximation to the diagonal of the inverse depending on the quality of the approximate inverse our method may serve as a standalone kernel for providing a fast trace estimate with a small number of samples furthermore the method can be used as a variance reduction method for monte carlo in some cases this is decided dynamically by our algorithm an extensive set of experiments with various technique combinations on several matrices from some real applications demonstrate the potential of our method

fast computation of unbiased intensity derivatives in images using separable filters in this paper we prove that all high order non biased spatial intensity derivative operators in images can be computed using linear combinations of separable filters the separable filters are the same as those used by haralick 1984 but different linear combinations are taken a comparison of the number of operations necessary to compute the derivatives using separable and non separable filters is made the conclusion of our analysis is that the optimal way to compute the needed derivatives depends on which derivatives we have to compute on the size of the window and on the order of expansion finally we discuss the performance of an edge detector using these derivatives for unsmoothed and smoothed step edges

perturbation analysis of generalized saddle point systems we discuss the perturbation analysis of generalized saddle point systems in this paper we give the nonlinear perturbation bounds then derive the condition numbers and analyze the sensitivity of the computed solutions

some defects in finite difference edge finders this work illustrates and explains various artifacts in the output of five finite difference edge finders those of j f canny 1983 1986 r a boie et al 1986 and r a boie and i j cox 1987 and three variations on that of d marr and e c hildreth 1980 reimplemented with a common output format and method of noise suppression these artifacts include gaps in boundaries spurious boundaries and deformation of region shape

a multi scale edge detector abstract a multi scale edge detector with subpixel accuracy is described a subpixel laplacian edge detector recursively implemented is run at different scales and the recovered edge information is combined the multi scale edge detection is based on the behavior of edges in scale space and takes into account their physical phenomena with this purpose in mind four step edge models are considered the ideal the blurred the pulse and the staircase it is emphasized that the use of two scales the larger and the smaller is sufficient for good edge detection furthermore a set of rules is derived for combining edge information obtained from a laplacian detector which has some special properties however this type of edge detector gives at least two classes of false edges one of which cannot be eliminated by the usual thresholding methods an appropriate thresholding algorithm is given taking into account the origin of the false edges and their behavior in scale space

randomized algorithms for estimating the trace of an implicit symmetric positive semi definite matrix we analyze the convergence of randomized trace estimators starting at 1989 several algorithms have been proposed for estimating the trace of a matrix by 1 m i 1m zit azi where the zi are random vectors different estimators use different distributions for the zis all of which lead to e 1 m i 1m zit azi trace a these algorithms are useful in applications in which there is no explicit representation of a but rather an efficient method compute ztaz given z existing results only analyze the variance of the different estimators in contrast we analyze the number of samples m required to guarantee that with probability at least 1 the relative error in the estimate is at most we argue that such bounds are much more useful in applications than the variance we found that these bounds rank the estimators differently than the variance this suggests that minimum variance estimators may not be the best we also make two additional contributions to this area the first is a specialized bound for projection matrices whose trace rank needs to be computed in electronic structure calculations the second is a new estimator that uses less randomness than all the existing estimators

automatic parameter selection for multimodal image registration over the past ten years similarity measures based on intensity distributions have become state of the art in automatic multimodal image registration an implementation for clinical usage has to support a plurality of images however a generally applicable parameter configuration for the number and sizes of histogram bins optimal parzen window kernel widths or background thresholds cannot be found this explains why various research groups present partly contradictory empirical proposals for these parameters this paper proposes a set of data driven estimation schemes for a parameter free implementation that eliminates major caveats of heuristic trial and error we present the following novel approaches a new coincidence weighting scheme to reduce the influence of background noise on the similarity measure in combination with max lloyd requantization and a tradeoff for the automatic estimation of the number of histogram bins these methods have been integrated into a state of the art rigid registration that is based on normalized mutual information and applied to ct mr pet mr and mr mr image pairs of the rire 2 0 database we compare combinations of the proposed techniques to a standard implementation using default parameters which can be found in the literature and to a manual registration by a medical expert additionally we analyze the effects of various histogram sizes sampling rates and error thresholds for the number of histogram bins the comparison of the parameter selection techniques yields 25 approaches in total with 114 registrations each the number of bins has no significant influence on the proposed implementation that performs better than both the manual and the standard method in terms of acceptance rates and target registration error tre the overall mean tre is 2 34 mm compared to 2 54 mm for the manual registration and 6 48 mm for a standard implementation our results show a significant tre reduction for distortion corrected magnetic resonance images

small sample statistical condition estimates for general matrix functions a new condition estimation procedure for general matrix functions is presented that accurately gauges sensitivity by measuring the effect of random perturbations at the point of evaluation in this procedure the number of extra function evaluations used to evaluate the condition estimate determines the order of the estimate that is the probability that the estimate is off by a given factor is inversely proportional to the factor raised to the order of the method the transpose free nature of this new method allows it to be applied to a broad range of problems in which the function maps between spaces of different dimensions this is in sharp contrast to the more common power method condition estimation procedure that is limited in the usual case where the frechet derivative is known only implicitly to maps between spaces of equal dimension a group of examples illustrates the flexibility of the new estimation procedure in handling a variety of problems and types of sensitivity estimates such as mix

robust and fast computation of edge characteristics in image sequences in this paper we consider a non parametric analytical model of the intensity for a curved edge and derive the relations between the image data and some local characteristics of the edge in the discrete case in order to identify this model we also study how to develop high order non biased spatial derivative operators with subpixel accuracy in fact this discrete approach corresponds to the notion of spatio temporal surfaces in the continuous case and provides a way to obtain some of the spatio temporal parameters from an image sequence an implementation is proposed and experimental data are provided

statistical condition estimation for linear systems the standard approach to measuring the condition of a linear system compresses all sensitivity information into one number thus a loss of information can occur in situations in which the standard condition number with respect to inversion does not accurately reflect the actual sensitivity of a solution or particular entries of a solution it is shown that a new method for estimating the sensitivity of linear systems addresses these difficulties the new procedure measures the effects on the solution of small random changes in the input data and by properly scaling the results obtains reliable condition estimates for each entry of the computed solution moreover this approach which is referred to as small sample statistical condition estimation is no more costly than the standard 1 norm or power method 2 norm condition estimates and it has the advantage of considerable flexibility for example it easily accommodates restrictions on or structure associated with allowable perturbations the method also has a rigorous statistical theory available for the probability of accuracy of the condition estimates however it gives no estimate of an approximate null vector for nearly singular systems the theory of this approach is discussed along with several illustrative examples

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data