edge location to subpixel values in digital imagery a new method for locating edges in digital data to subpixel values and which is invariant to additive and multiplicative changes in the data is presented for one dimensional edge patterns an ideal edge is fit to the data by matching moments it is shown that the edge location is related to the so called christoffel numbers also presented is the study of the effect of additive noise on edge location the method is extended to include two dimensional edge patterns where a line equation is derived to locate an edge this in turn is compared with the standard hueckel edge operator an application of the new edge operator as an edge detector is also provided and is compared with sobel and hueckel edge detectors in presence and absence of noise

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

stochastic stability of systems with semi markovian switching this paper examines stochastic stability of switched dynamics in continuous time the time evolution of the so called continuous state is at all times determined by the dynamics indexed by the switching process or discrete state the main contribution of this paper appears as stochastic stability results for switched dynamics with semi markovian switching the notion of moment stability in the wide sense msws is applied as a generalization of moment stability a sufficient criterion for msws is presented for the above class of systems where each subsystem is assumed to be characterized by a lyapunov function candidate together with an associated growth rate equation for the set of lyapunov functions a compatibility criterion is assumed to be fulfilled bounding the ratio between pairs of lyapunov functions

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

two dimensional polar harmonic transforms for invariant image representation this paper introduces a set of 2d transforms based on a set of orthogonal projection bases to generate a set of features which are invariant to rotation we call these transforms polar harmonic transforms phts unlike the well known zernike and pseudo zernike moments the kernel computation of phts is extremely simple and has no numerical stability issue whatsoever this implies that phts encompass the orthogonality and invariance advantages of zernike and pseudo zernike moments but are free from their inherent limitations this also means that phts are well suited for application where maximal discriminant information is needed furthermore phts make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application

brief paper h estimation for discrete time piecewise homogeneous markov jump linear systems this paper concerns the problem of h estimation for a class of markov jump linear systems mjls with time varying transition probabilities tps in discrete time domain the time varying character of tps is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types arbitrary variation and stochastic variation respectively the latter means that the variation is subject to a higher level transition probability matrix the mode dependent and variation dependent h filter is designed such that the resulting closed loop systems are stochastically stable and have a guaranteed h filtering error performance index using the idea in the recent studies of partially unknown tps for the traditional mjls with homogeneous tps a generalized framework covering the two kinds of variations is proposed a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

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

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

precision edge contrast and orientation estimation the contrast and orientation estimation accuracy of several edge operators that have been proposed in the literature is examined both for the noiseless case and in the presence of additive gaussian noise the test image is an ideal step edge that has been sampled with a square aperture grid the effects of subpixel translations and rotations of the edge on the performance of the operators are studied it is shown that the effect of subpixel translations of an edge can generate more error than moderate noise levels methods with improved results are presented for sobel angle estimates and the nevatia babu operator and theoretical noise performance evaluations are also provided an edge operator based on two dimensional spatial moments is presented all methods are compared according to worst case and rms error in an ideal noiseless situation and rms error under various noise levels

almost sure stabilization of uncertain continuous time markov jump linear systems this work deals with the robust almost sure as stabilization problem for continuous time markov jump linear systems mjls norm bounded uncertainties affecting the system state and input matrices are considered a deterministically testable sufficient condition for robust as stability is provided which relies on a bound on the 2 norm of the system transition matrix such a condition can be profitably employed also to design a robust feedback stabilization strategy such feedback design is based on a formulation of the sufficient condition for robust as stability in terms of an equivalent lmi problem

subpixel measurements using a moment based edge operator recent results in precision measurements using computer vision are presented an edge operator based on two dimensional spatial moments is given the operator can be implemented for virtually any size of window and has been shown to locate edges in digitized images to a twentieth of a pixel this accuracy is unaffected by additive or multiplicative changes to the data values the precision is achieved by correcting for many of the deterministic errors caused by nonideal edge profiles using a lookup table to correct the original estimates of edge orientation and location this table is generated using a synthesized edge which is located at various subpixel locations and various orientations the operator is extended to accommodate nonideal edge profiles and rectangularly sampled pixels the technique is applied to the measurement of imaged machined metal parts theoretical and experimental noise analyses show that the operator has relatively small bias in the presence of noise

finding edges in noisy scenes edge detection in the presence of noise is a well known problem this paper examines an applications motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets roc curves are used to compare this method with other well known edge detection operators with favorable results a theoretical argument is presented that favors lmmse filtering over median filtering in extremely noisy scenes simulated results of the research are presented

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

galois theory for braided tensor categories and the modular closure abstract given a braided tensor category c with conjugate dual objects and irreducible unit together with a full symmetric subcategory s we define a crossed product c s this construction yields a tensor category with conjugates and an irreducible unit a category is a category enriched over vect c with positive operation a galois correspondence is established between intermediate categories sitting between c and c s and closed subgroups of the galois group gal c s c aut c c s of c the latter being isomorphic to the compact group associated with s by the duality theorem of doplicher and roberts denoting by d c the full subcategory of degenerate objects i e objects which have trivial monodromy with all objects of c the braiding of c extends to a braiding of c s iff s d under this condition c s has no non trivial degenerate objects iff s d if the original category c is rational i e has only finitely many isomorphism classes of irreducible objects then the same holds for the new one the category c c d is called the modular closure of c since in the rational case it is modular i e gives rise to a unitary representation of the modular group sl 2 z if all simple objects of s have dimension one the structure of the category c s can be clarified quite explicitly in terms of group cohomology

duality and modular invariance in rational conformal field theories we investigate the polynomial equations which should be satisfied by the duality data for a rational conformal field theory we show that by these duality data we can construct some vector spaces which are isomorphic to the spaces of conformal blocks one can construct explicitly the inner product for the former if one deals with a unitary theory these vector spaces endowed with an inner product are the algebraic reminiscences of the hilbert spaces in a chern simons theory as by products we show that the polynomial equations involving the modular transformations for the one point blocks on the torus are not independent we discuss the solution of structure constants for a physical theory making some assumption we obtain a neat solution and this solution in turn implies that the quantum groups of the left sector and of the right sector must be the same although the chiral algebras need not be the same some examples are given finally we discuss the reconstruction of the quantum group in a rational conformal theory

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

stochastic stability of markovianly switched systems this technical note examines the stochastic stability of noisy dynamics in discrete and continuous time the notion of moment stability in the wide sense msws is presented as a generalization of moment stability msws is intentionally not based on stochastic convergence properties since in most practically appearing systems convergence to any equilibrium is not present a sufficient criterion for both msws and ergodicity is presented for a class of systems comprising a finite set of noisy dynamical systems among which switching is governed by a markov chain stability instability properties for each separate subsystem are assumed to be quantified by a lyapunov function candidate together with an associated growth rate equation for the set of lyapunov functions a compatibility criterion is assumed to be fulfilled bounding the ratio between pairs of lyapunov functions

adaptive pseudo dilation for gestalt edge grouping and contour detection we consider the problem of detecting object contours in natural images in many cases local luminance changes turn out to be stronger in textured areas than on object contours therefore local edge features which only look at a small neighborhood of each pixel cannot be reliable indicators of the presence of a contour and some global analysis is needed we introduce a new morphological operator called adaptive pseudo dilation apd which uses context dependent structuring elements in order to identify long curvilinear structure in the edge map we show that grouping edge pixels as the connected components of the output of apd results in a good agreement with the gestalt law of good continuation the novelty of this operator is that dilation is limited to the voronoi cell of each edge pixel an efficient implementation of apd is presented the grouping algorithm is then embedded in a multithreshold contour detector at each threshold level small groups of edges are removed and contours are completed by means of a generalized reconstruction from markers the use of different thresholds makes the algorithm much less sensitive to the values of the input parameters both qualitative and quantitative comparison with existing approaches prove the superiority of the proposed contour detector in terms of larger amount of suppressed texture and more effective detection of low contrast contours

orbifold construction in subfactors we use the lattice models to determine the obstructions to the flatness of the orbifold connections in some finite depth subsfactors

generalized goodman harpe jones construction of subfactors ii we build some exceptional representations of birman wenzl algebras from the data of certain conformal embeddings as a result we construct new finite depth subfactors whose principal graphs are completely determined

detection of composite edges the paper presents a new parametric model based approach to high precision composite edge detection using orthogonal zernike moment based operators it deals with two types of composite edges a generalized step and b pulse staircase edges a 2 d generalized step edge is modeled in terms of five parameters two gradients on two sides of the edge the distance from the center of the candidate pixel the orientation of the edge and the step size at the location of the edge a 2 d pulse staircase edge is modeled in terms of two steps located at two positions within the mask and the edge orientation a pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity two complex and two real zernike moment based masks are designed to determine parameters of both the 2 d edge models for a given edge model estimated parameter values at a point are used to detect the presence or absence of that type of edge extensive noise analysis is performed to demonstrate the robustness of the proposed operators experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment based step edge detection technique and canny s 1986 edge detector