robust stability parameter dependent perturbations conditions for a system to be robustly stable with respect to a set of perturbations parametrized by possibly uncertain parameters are given in terms of some worst case estimates of the perturbations making use of the hadamard product of matrices a new way of formulating perturbations is introduced the advantage of representing the perturbations in this way is that the magnitude structure of the system can be taken into robustness considerations

relative canonical sheaves of a family of curves abstract in this paper we study the relative canonical sheaf of a relatively minimal fibration of curves of genus g 2 over a one dimensional regular scheme using the configurations of 2 chains we show that its m tensored product is base point free for any m 2 we utilize koszul cohomology to prove that the relative canonical algebra of the fibration is generated in degree up to five it is a generalization of k konno s work on the 1 2 3 conjecture of m reid

breakpoint detection using covariance propagation presents a statistical approach for detecting breakpoints from chain encoded digital arcs an arc point is declared as a breakpoint if the estimated orientations of the two fitted lines of the two arc segments immediately to the right and left of the arc point are significantly statistically different the major contributions of this research include developing a method for analytically estimating the covariance matrix of the fitted line parameters and proposing a perturbation model to characterize the perturbation associated with each arc point

on the stabilization of nonlinear systems we extend the applicability of the global q parametrization method of controller design to a large class of unstable nonlinear plants the main result is a two step compensation theorem analogous to that of zames for unstable linear plants if p l e2 rightarrow l e1 is a nonlinear possibly unstable plant and f 0 is any incrementally stable controller such that p 1 p i f 0 p 1 is incrementally stable then the class of controllers f which yields an f g stable closed loop system in the unity feedback configuration for p is globally parametrized by finite gain stable maps q l e1 rightarrow l e2 with f f 0 q i p 1 q 1

minimax linear observers and regulators for stochastic systems with uncertain second order statistics the problem of minimax design of linear observers and regulators for linear time varying multivariable stochastic systems with uncertain models of their second order statistics is treated in this paper general classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered a game formulation of the problem is adopted and it is shown that the optimal filter for the least favorable set of covariances is minimax robust for each of the filtering situations analyzed conditions satisfied by the saddle point solutions are given and their utility for finding the worst case covariances is illustrated by way of several examples of uncertainty classes of practical interest

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

segmentation of two dimensional curve contours abstract segmentation of digitized planar curves is one of the most important elements in early image processing because a segmented image can describe the object profile in a compact form to facilitate higher level vision processing in many applications it is necessary to decompose an object boundary contour into several primitives such as segments and curves in this paper a two stage hybrid technique for the segmentation of two dimensional 2d curves is presented in which the number of segments is assumed to be known first the boundary is iteratively approximated using a split and merge method next an end point adjustment procedure is applied to reach the best fitting polygonal approximation a computational comparison with two existing methods shows that the proposed technique is fast and accurate an application of the new segmentation technique to industrial part inspection is also provided

optimization models for shape matching of nonconvex polygons abstract the shape matching problem is concerned with fitting an input shape represented by a set of discrete boundary data to a defect free reference shape two aspects of the problem must be considered 1 shape modeling and 2 matching algorithm in this paper two shape modeling schemes are proposed to represent the reference shape by a set of primitives in which the object geometric configuration is encoded the primitives uniquely define the pose and dimension of a given polygonal object based on these models optimization matching procedures that use the least squares criterion to find the best fitting between the set of scene data and the reference shape are developed the complexity analysis and computational results show our shape matching approaches to be extremely fast

reduced resolution and scale space for dominant feature detection in contours abstract analysis of contours or curves at various scales or levels of smoothing scale space is an important tool in curve segmentation and feature detection in this paper we propose the application of the hierarchical discrete correlation algorithm for efficiently calculating and creating a scale space of curves in conjunction with this procedure we also investigate the use of the reduced resolution or gaussian pyramid representation of the set of smoothed curves as the basis for initially localizing and detecting features we also create an approximation to the above algorithms that is computationally less expensive finally we propose a new inter scale method for curve segmentation and feature detection based on the motion of a curve through scale space

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

measures of acutance and shape for classification of breast tumors most benign breast tumors possess well defined sharp boundaries that delineate them from surrounding tissues as opposed to malignant tumors computer techniques proposed to date for tumor analysis have concentrated on shape factors of tumor regions and texture measures while shape measures based on contours of tumor regions can indicate differences in shape complexities between circumscribed and spiculated tumors they are not designed to characterize the density variations across the boundary of a tumor here the authors propose a region based measure of image edge profile acutance which characterizes the transition in density of a region of interest roi along normals to the roi at every boundary pixel the authors investigate the potential of acutance in quantifying the sharpness of the boundaries of tumors and propose its application to discriminate between benign and malignant mammographic tumors in addition they study the complementary use of various shape factors based upon the shape of the roi such as compactness fourier descriptors moments and chord length statistics to distinguish between circumscribed and spiculated tumors thirty nine images from the mammographic image analysis society mias database and an additional set of 15 local cases were selected for this study the cases included 16 circumscribed benign 7 circumscribed malignant 12 spiculated benign and 19 spiculated malignant lesions all diagnoses were proven by pathologic examinations of resected tissue the contours of the lesions were first marked by an expert radiologist using x paint and x windows on a sun sparcstation 2 workstation for computation of acutance the roi boundaries were iteratively approximated using a split merge and end point adjustment technique to obtain the best fitting polygonal approximation the jackknife method using the mahalanobis distance measure in the bmdp biomedical programs package was used for classification of the lesions using acutance and the shape factors as features in various combinations acutance alone resulted in a benign malignant classification accuracy of 95 the mias cases compactness alone gave a circumscribed spiculated classification rate of 92 3 with the mias cases acutance in combination with a moment based shape measure and a fourier descriptor based measure gave four group classification rate of 95 with the mias cases the results indicate the importance of including lesion edge definition with shape information for classification of tumors and that the proposed measure of acutance fills this need

an adaptive reduction procedure for the piecewise linear approximation of digitized curves a new algorithm is presented for the piecewise linear approximation of two dimensional digitized curves against a square grid the algorithm utilizes an adaptive reduction procedure in two approximation phases to select the critical points of a digitized curve such that the deviation from the digitized curve to its final approximated curve is bounded by a uniform error tolerance the time complexity of this algorithm is o m sup 2 rather than o n sup 2 on the theoretical plane in the experiments of fixing the initial and the final processing points the performance of the algorithm has been compared to those of three prominent other algorithms regarding the required number of critical points and the total execution time of the program of the four algorithms compared the present algorithm consistently has the shortest execution time of the program and it tends most to require as few critical points as the optimum algorithm that was tested

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

gradient and texture analysis for the classification of mammographic masses computer aided classification of benign and malignant masses on mammograms is attempted in this study by computing gradient based and texture based features features computed based on gray level co occurrence matrices gcms are used to evaluate the effectiveness of textural information possessed by mass regions in comparison with the textural information present in mass margins a method involving polygonal modeling of boundaries is proposed for the extraction of a ribbon of pixels across mass margins two gradient based features are developed to estimate the sharpness of mass boundaries in the ribbons of pixels extracted from their margins a total of 54 images 28 benign and 26 malignant containing 39 images from the mammographic image analysis society mias database and 15 images from a local database are analyzed the best benign versus malignant classification of 82 1 with an area a sub z of 0 85 under the receiver operating characteristics roc curve was obtained with the images from the mias database by using gcm based texture features computed from mass margins the classification method used is based on posterior probabilities computed from mahalanobis distances the corresponding accuracy using jack knife classification was observed to be 74 4 with a sub x 0 67 gradient based features achieved a sub x 0 6 on the mias database and a sub z 0 76 on the combined database the corresponding values obtained using jack knife classification were observed to be 0 52 and 0 73 for the mias and combined databases respectively

restricted risk bayes linear state estimation the problem of state estimation with stochastic uncertainties in the initial state model noise and measurement noise is considered using the restricted risk bayes approach it is assumed that the a priori distributions of these quantities are not perfectly known but that some information about them may be available while offering robustness the restricted risk bayes approach incorporates the available a priori information to give less conservative state estimators than the gamma minimax approach popular in the literature when attention is restricted to linear estimators based on a quadratic loss function a systematic method to derive restricted risk bayes estimators is proposed applying to the filtering problem the restricted risk bayes approach provides us with a robust method to calibrate the kalman filter kf considering the presence of stochastic uncertainties this method is illustrated with a target tracking example and a wireless channel tracking example for which the bayes minimax and restricted risk bayes estimators are derived and their performance is compared

minimax control of linear stochastic systems with noise uncertainty the problem of linear quadratic gaussian control of multivariable linear stochastic systems with uncertain second order statistical properties is considered uncertainty is modeled by allowing process and observation noise spectral density matrices to vary arbitrarily within given classes and a minimax control formulation is applied to the quadratic objective functional general theorems proving the existence and characterization of saddle point solutions to this problem are presented and the relationship of these results to earlier results on minimax state estimation are discussed to illustrate the analytical results the specific example of regulating a double integrator plant is treated in detail

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

robust filtering and prediction for linear systems with uncertain dynamics a game theoretic approach we examine the existence and behavior of game theoretic solutions for robust linear filters and predictors our basic uncertainty class includes m th order time varying discrete time systems with uncertain dynamics uncertain initial state covariance and uncertain nonstationary input and observation noise covariance our results include recursive kalman filter predictor realizations for the resulting robust procedures our approach is based on saddle point theory we emphasize the notion of a least favorable prior distribution for the uncertain parameter values to obtain a worst case design technique in this paper we highlight the role such distributions with finite support play in these decision models in particular we demonstrate that in these decision models the least favorable prior distribution is always discrete

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

techniques for assessing polygonal approximations of curves given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines instead we suggest assessing an algorithm s results relative to an optimal polygon and describe a measure which combines the relative fidelity and efficiency of a curve segmentation we use this measure to compare the application of 23 algorithms to a curve first used by teh and chin 1989 their integral square errors ises are assessed relative to the optimal ise in addition using an example of pose estimation it is shown how goal directed evaluation can be used to select an appropriate assessment criterion

fast polygonal approximation of digital curves using relaxed straightness properties several existing digital straight line segment dss recognition algorithms can be used to determine the digital straightness of a given one pixel thick digital curve because of the inherent geometric constraints of digital straightness these algorithms often produce a large number of segments to cover a given digital curve representing a real life object image thus a curve segment which is not exactly digitally straight but appears to be visually straight is fragmented into multiple dss when these algorithms are run in this paper a new concept of approximate straightness is introduced by relaxing certain conditions of dss and an algorithm is described to extract those segments from a digital curve the number of such segments required to cover the curve is found to be significantly fewer than that of the exact dss cover as a result the data set required for representing a curve also reduces to a large extent the extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance the proposed algorithm involves only primitive integer operations and thus runs very fast compared to those based on exact dss the overall time complexity becomes linear in the number of points present in the representative set experimental results on several digital curves demonstrate the speed elegance and efficacy of the proposed method

optimum uniform piecewise linear approximation of planar curves two dimensional digital curves are often uniformly approximated by polygons or piecewise linear curves several algorithms have been proposed in the literature to find such curves we present an algorithm that finds a piecewise linear curve with the minimal number of segments required to approximate a curve within a uniform error with fixed initial and final points we compare our optimal algorithm to several suboptimal algorithms with respect to the number of linear segments required in the approximation and the execution time of the algorithm

lqg controller synthesis with plant and noise spectral uncertainties in this paper we consider the problem of robust controller synthesis with plant and noise spectral uncertainties in lqg optimal systems we frame an algorithm for synthesizing the robust controller to minimize the least favourable cost functional j via specifying the weighting matrices q and r the wiener hopf technique in the lqg optimal system the saddle point theory and a property of the contractive operator are employed to solve this problem

segmentation of two dimensional boundaries using the chain code abstract we divide the boundary of a two dimensional object into segments each of which is either straight or a circular arc associated with the segment end points are angle measures that can be used to match an object with a transformed rotated scaled version of itself the chain code easily extracted from the boundary pixels is the basis of this division the approach avoids problems common to many of the existing methods for identification of curvature extrema sensitivity to noise and dependence on parameters that are chosen empirically to each section of the boundary we assign a code that represents the change in slope between it and the previous section this set of codes is integrated and thus provides a measure of the total directional change relative to the first section for a closed object the sequence of these sums is periodic and one cycle can be plotted as a function of arc length s such a plot can be shown to contain only straight lines those that are not parallel to the s axis representing circular arcs on the original boundary of the object and those that are representing straight sections on the boundary this paper describes a recursive procedure for dividing the digital version of the curve described above into its linear segments each segment represents an arc that is the best fit to a portion of the original boundary the angle which is defined by the arc is identical to the angle change of the edge in the same section and the length of the arc is identical to that of the edge the recursive procedure measures the error for each value of arc length between a proposed fitting line and the actual value of cumulative angle where the error is maximum and above a threshold the line is segmented the procedure is repeated until the error is sufficiently small the breakpoints thus indicate the location and value of points of greatest curvature change a formal definition of the procedure is given and it is shown to perform well for rotated scaled and noisy objects

noncausal minimax linear state estimation for systems with uncertain second order statistics this note considers the problem of minimax state estimation of the states of a linear time invariant system which is driven by and observed in the presence of noise processes with uncertain second order statistics when the process noise and observations are scalars the problem is shown to be equivalent to a scalar minimax estimation problem the existence of a minimax solution is thereby established and the minimax filter is shown to be a linear transformation of the minimax filter for the scalar problem

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

on line segmentation of freehand sketches by knowledge based nonlinear thresholding operations this paper describes an on line procedure for segmenting freehand sketches into 2d primitives and smooth curves by knowledge based nonlinear thresholding operations drawing position direction speed and acceleration information is used for establishing fuzzy knowledge and inferring user s intention the procedure can be divided into three stages 1 obtaining corner points based on the fuzzy knowledge and adaptive thresholds which includes detecting obtuse and acute corner points 2 finding smooth join points during which stage we use both curve linearity and curvature and 3 classifying the sketches into the corresponding curves according to curve linearity and changes of curve convexity the method is illustrated and tested with a number of sketches

a relationship between sensitivity and stability of multivariable feedback systems both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design although the two bodies of work have developed about a decade apart the basic philosophies are similar both attempt to maintain a system property sensitivity reduction versus stability in the presence of plant modeling errors this paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations

intrinsically optimal bayesian robust filtering when designing optimal filters it is often unrealistic to assume that the statistical model is known perfectly the issue is then to design a robust filter that is optimal relative to an uncertainty class of processes robust filter design has been treated from minimax best worst case performance and bayesian best average performance perspectives heretofore the bayesian approach has involved finding a model specific optimal filter one that is optimal for some model in the uncertainty class lifting this constraint we optimize over the full class from which the original optimal filters were obtained for instance over all linear filters by extending the original characteristics determining the filter such as the power spectral density to effective characteristics that apply across the uncertainty class we demonstrate for both linear and morphological filtering that an intrinsically optimal bayesian robust filter can be represented in the same form as the standard solution to the optimal filter except via the effective characteristics solutions for intrinsic bayesian robust filters are more transparent and intuitive than solutions for model specific filters and also less tedious because effective characteristics push through the spectral theory into the bayesian setting whereas solutions in the model specific case depend on grinding out the optimization

an estimator for uncertain output matrix systems a linear time invariant optimal estimator for uncertain output matrix systems is considered uncertainty of the output matrix is represented by a set of multiple parameters and the optimal estimator is introduced by minimizing the expected cost function of the estimation error when the number of measured variables is small the order of the optimal estimator does not depend on the number of models and meeting the computational demand becomes quite feasible

minimax robust discrete time matched filters the problem of designing finite length discrete time matched filters is considered for situations in which exact knowledge of the input signal and or noise characteristics is not available such situations arise in many applications due to channel distortion incoherencies nonlinear effects and other modeling uncertainties in such cases it is often of interest to design a minimax robust matched filter i e a nonadaptive filter with an optimum level of worst case performance for the expected uncertainty class this problem is investigated here for three types of uncertainty models for the input signal namely the mean absolute mean square and maximum absolute distortion classes and for a wide generality of norm deviation models for the noise covariance matrix some numerical examples illustrate the robustness properties of the proposed designs

minimax robust deconvolution filters under stochastic parametric and noise uncertainties the author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties it is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second order statistics of stochastic parameters and initial conditions three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems their approach is based on saddle point theory and the sensitivity analysis of kalman filters the design algorithms give the recursive realization of the minimax deconvolution filters for the time varying uncertain systems under fairly general conditions for the time invariant uncertain case the existence and solutions of steady state deconvolution filters are further developed finally the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach