derivation of optimal filters for the detection of coronary arteries optimal filters for the detection of coronary arteries with a diameter range of 0 5 6 0 mm in digital x ray images are derived using a computational approach this approach is based on the two requirements for optimal detection first the filter should maximize the number of detected true edges and minimize the number of detected false edges second if an edge has been detected its position should be as close as possible to the true edge position in the image since the grey value profile in a digital x ray image associated with an arterial vessel is asymmetric the theory on edge detection derived by canny has been expanded with two additional boundary constraints to make it suitable for the derivation of filters for asymmetric edges it is demonstrated that it is possible to derive optimal filters for coronary segments the localization error defined by the square root of the sum of the squared systematic and random errors in the assessment of the arterial diameter depends on the size of the coronary artery and the amount of noise in the image here an evaluation study is described to assess the relationship between localization error and the amount of noise upon the vessel profile for that purpose an analytical description of the vessel profile in an angiographic image was derived for the larger arteries the relation between noise and localization error was found to be linear and no systematic over or underestimations were observed even if the noise level was very high however it can be shown that the smallest diameter that can be measured depends on the amount of noise present in the data even for images that contain only a low amount of noise arterial diameters below 0 7 mm cannot be measured accurately if the noise in the image increases the lowest measurable arterial diameter value also increases also the random error increases rapidly for vessel diameters below 1 2 mm but with a limited amount of noise and a diameter value above 0 7 mm the random error is still acceptable 0 15 mm 21 for 0 7 mm vessels 0 06 mm 6 for 1 mm vessels

a luminance and contrast invariant edge similarity measure a novel similarity measure for edge detection that is robust to varying luminance and contrast is presented it incorporates a regularization term and employs directional fir edge filters with hyperbolic tangent profiles to ensure improved noise performance and edge localization compared to classical methods

robust frequency selective filtering using weighted myriad filters admitting real valued weights weighted myriad smoothers have been proposed as a class of nonlinear filters for robust non gaussian signal processing in impulsive noise environments however weighted myriad smoothers are severely limited since their weights are restricted to be non negative this constraint makes them unusable in bandpass or highpass filtering applications that require negative filter weights further they are incapable of amplifying selected frequency components of an input signal in this paper we generalize the weighted myriad smoother to a richer structure a weighted myriad filter admitting real valued weights this involves assigning a pair of filter weights one positive and the other negative to each of the input samples equivalently the filter can be described as a weighted myriad smoother applied to a transformed set of samples that includes the original input samples as well as their negatives the weighted myriad filter is analogous to a normalized linear fir filter with real valued weights whose absolute values sum to unity by suitably scaling the output of the weighted myriad filter we extend it to yield the so called scaled weighted myriad filter which includes but is more powerful than the traditional unconstrained linear fir filter finally we derive stochastic gradient based nonlinear adaptive algorithms for the optimization of these novel myriad filters under the mean square error criterion

a new zero crossing based discontinuity detector general zero crossing based discontinuity detectors in two dimensions which include marr hildreth 1980 residual difference of gaussians and other detectors as special cases are discussed mathematical justification for this class of detectors is presented an optimal detector that maximizes the signal to noise ratio is derived preliminary experimental results for real images are reported

adaptive weighted myriad filter algorithms for robust signal processing in spl alpha stable noise environments stochastic gradient based adaptive algorithms are developed for the optimization of weighted myriad filters wmyfs wmyfs form a class of nonlinear filters motivated by the properties of spl alpha stable distributions that have been proposed for robust non gaussian signal processing in impulsive noise environments the weighted myriad for an n long data window is described by a set of nonnegative weights w sub i sub i l sup n and the so called linearity parameter k 0 in the limit as k spl rarr spl infin the filter reduces to the familiar weighted mean filter which is a constrained linear fir filter necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion an implicit formulation of the filter output is used to find an expression for the gradient of the cost function using instantaneous gradient estimates an adaptive steepest descent algorithm is then derived to optimize the weights this algorithm involves a very simple update term that is computationally comparable to the update in the classical lms algorithm the robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one dimensional chirp type signal in impulsive noise

myriad type polynomial filtering linear combinations of polynomial terms yield poor performance in environments characterized by heavy tailed distributions weighted myriad wmy filters however are well known for their outlier suppression and detail preservation properties it is shown here that the wmy methodology is naturally extended to the polynomial sample case yielding filter structures that exploit the higher order statistics of the observed samples while simultaneously being robust to outliers for heavy tailed distributions environments moreover the introduced power weighted myriad pwmy filter class is well motivated by analysis of cross and square term statistics of heavy tailed distributions the effectiveness of the proposed filter is evaluated through simulations

using focus of attention with the hough transform for accurate line parameter estimation abstract in this paper we describe a hough transform algorithm for finding lines in an image that can have an order of magnitude denser sampling in both parameters of the parameter space without significant increase in required memory or overhead in cpu time by increasing the sampling density we determine the line parameters for each line segment much more accurately the method circumvents the problems of requiring large amounts of memory to store the accumulator array and is not significantly slower than other hough algorithms by using a focus of attention approach we illustrate the benefits that can be obtained on a wide variety of images and quantify the improvements in line parameter estimation by performing statistical tests we also discuss the benefits that can be obtained by algorithms attempting to locate higher level features in the image and determining the 3d model of the image scene

hybrid polynomial filters for gaussian and non gaussian noise environments traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by gaussian and heavy tailed distributions weighted median and weighted myriad filters in contrast are well known for their outlier suppression and detail preservation properties it is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case yielding hybrid filter structures that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers for both gaussian and heavy tailed distributions environments moreover the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of gaussian and heavy tailed distributions a presented asymptotic tail mass analysis shows that polynomial terms both under gaussian and heavy tailed noise statistics have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms for the gaussian noise case and weighted median and weighted myriad processing of cross and square terms respectively for the heavy tailed noise case are justified from a maximum likelihood perspective filters parameter optimization procedures are also presented finally the effectiveness of hybrid filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

generalized feature extraction using expansion matching a novel generalized feature extraction method based on the expansion matching exm method and on the karhunen loeve transform klt is presented the method provides an efficient way to locate complex features of interest like corners and junctions with reduced number of filtering operations the exm method is used to design optimal detectors for a set of model elementary features the kl representation of these model exm detectors is used to filter the image and detect candidate interest points from the energy peaks of the eigen coefficients the kl coefficients at these candidate points are then used to efficiently reconstruct the response and differentiate real junctions and corners from arbitrary features in the image the method is robust to additive noise and is able to successfully extract classify and find the myriad compositions of corner and junction features formed by combinations of two or more edges or lines this method differs from previous works in several aspects first it treats the features not as distinct entities but as combinations of elementary features second it employs an optimal set of elementary feature detectors based on the em approach third the method incorporates a significant reduction in computational complexity by representing a large set of exm filters by a relatively small number of eigen filters derived by the kl transform of the basic exm filter set this is a novel application of the kl transform which is usually employed to represent signals and not impulse responses as in our present work

hypothesis testing a framework for analyzing and optimizing hough transform performance in this paper a formal quantitative approach to designing optimum hough transform ht algorithms is proposed this approach takes the view that a ht is a hypothesis testing method each sample in the ht array implements a test to determine whether a curve with the given parameters fits the edge point data this view allows the performance of ht algorithms to be quantified the power function which gives the probability of rejection as a function of the underlying parametric distribution of data points is shown to be the fundamentally important characteristic of ht behaviour attempting to make the power function narrow is a formal approach to optimizing ht performance to illustrate how this framework is useful the particular problem of line detection is discussed in detail it is shown that the hypothesis testing framework leads to a redefinition of the ht in which the values are a measure of the distribution of points around a curve rather than the number of points on a curve this change dramatically improves the sensitivity of the method to small structures the solution to many ht design problems can be posed within the framework including optimal quantizations and optimum sampling of the parameter space in this paper the authors consider the design of optimum i d filters which can be used to sharpen the peak structure in parameter space results on several real images illustrate the improvements obtained

robust extrema features for time series data analysis the extraction of robust features for comparing and analyzing time series is a fundamentally important problem research efforts in this area encompass dimensionality reduction using popular signal analysis tools such as the discrete fourier and wavelet transforms various distance metrics and the extraction of interest points from time series recently extrema features for analysis of time series data have assumed increasing significance because of their natural robustness under a variety of practical distortions their economy of representation and their computational benefits invariably the process of encoding extrema features is preceded by filtering of the time series with an intuitively motivated filter e g for smoothing and subsequent thresholding to identify robust extrema we define the properties of robustness uniqueness and cardinality as a means to identify the design choices available in each step of the feature generation process unlike existing methods which utilize filters x201c inspired x201d from either domain knowledge or intuition we explicitly optimize the filter based on training time series to optimize robustness of the extracted extrema features we demonstrate further that the underlying filter optimization problem reduces to an eigenvalue problem and has a tractable solution an encoding technique that enhances control over cardinality and uniqueness is also presented experimental results obtained for the problem of time series subsequence matching establish the merits of the proposed algorithm

optimal edge detectors for ramp edges it is argued that the best way to model an edge is by assuming all ideal mathematical function passed through a low pass filter and and immersed in noise using techniques similar to those developed by j canny 1983 1986 and l a spacek 1986 optimal filters are derived for ramp edges of various slopes the optimal nonrecursive filter for ideal step edges is then derived as a limiting case of the filters for ramp edges because there are no step edges in images edge detection is improved when the ramp filter is used instead of the filters developed for step edges for practical purposes some convolution masks are given which can be used directly for edge detection without the need to go into the details of the subject

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

the bayesian operating point of the canny edge detector we have investigated the operating point of the canny edge detector which minimizes the bayes risk of misclassification by considering each of the sequential stages which constitute the canny algorithm we conclude that the linear filtering stage of canny without postprocessing performs very poorly by any standard in pattern recognition and achieves error rates which are almost indistinguishable from a priori classification we demonstrate that the edge detection performance of the canny detector is due almost entirely to the postprocessing stages of nonmaximal suppression and hysteresis thresholding

sub optimum receiver architecture for awgn channel with symmetric alpha stable interference in many scenarios the undesirable disturbance at a communication receiver has to be modeled as the sum of gaussian noise and impulsive interference for which closed form probability density function pdf generally does not exist this makes optimum receiver implementation difficult in this paper motivated by the heavy tail nature of the resultant pdf an alternate parametric solution is proposed after estimation of the appropriate parameters the alternate solution may then be written in closed form leading to a relatively simple architecture simulation results show that the proposed receiver performance in terms of bit error rate ber is almost indistinguishable from the optimum receiver while outperforming other sub optimum receivers noise parameter estimation using empirical characteristic functions is also discussed

multi edge detection by isotropical 2 d isef cascade most research in edge detection has been based on the classical mono edge model in the present paper we propose an optimal edge detector for complicated noisy multi edge images and the isotropical 2 d realization of the optimal filter we introduce at first the complicated multi edge model and show that the optimal filter as a preparation for multi edge detection is a cascade of infinite size symmetrical exponential filters isef we then propose a fast realization of the isotropical 2 d optimal filter experimental results are also presented

directional filtering in edge detection two dimensional 2 d edge detection can be performed by applying a suitably selected optimal edge half filter in n directions computationally such a two dimensional n directional filter can be represented by a pair of real masks that is by one complex number matrix regardless of the number of filtering directions n specific calculations of the edge strength were conducted using a 2 d tridirectional filter based on a petrou kittler 1991 one dimensional 1 d detector optimized for the ramp edges which are characteristic of posterior eye capsule images that were used here as a test set in applications to image segmentation tridirectional filtering results in co occurrence arrays of low dimensionality

first passage method for the study of the efficiency of a two channel reaction on a lattice we study the efficiency of a two channel reaction between two walkers on a finite one dimensional periodic lattice the walkers perform a combination of synchronous and asynchronous jumps on the lattice and react instantaneously when they meet at the same site first channel or upon position exchange second channel we develop a method based on a conditional first passage problem to obtain exact results for the mean number of time steps needed for the reaction to take place as well as for higher order moments previous results obtained in the framework of a difference equation approach are fully confirmed including the existence of a parity effect for even lattices the maximum efficiency corresponds to a mixture of synchronous events and a small amount of asynchronous events while for odd lattices the reaction time is minimized by a purely synchronous process we provide an intuitive explanation for this behavior in addition we give explicit expressions for the variance of the reaction time the latter displays a similar even odd behavior suggesting that the parity effect extends to higher order moments 2005 the american physical society

fast adaptation and performance characteristics of fir wos hybrid filters fast adaptive algorithms are developed for training weighted order statistic wos filters and fir wos hybrid fwh filters under the mean absolute error mae criterion these algorithms are based on the threshold decomposition of real valued signals introduced in this paper with this method an n length wos filter can be implemented by thresholding the input signals at most n times independent of the accuracy used beside saving in computations the proposed algorithms can be applied to process arbitrary real valued signals directly performance characteristics of fwh filters in 1 d and 2 d signal restoration are investigated through computer simulations we show that both in restoration of signals containing edges and in the case of heavy tailed nongaussian noise considerable improvement in performance can be achieved with fwh filters over wos filters ll filters and adaptive linear filters two new fwh filter design strategies are found for removal of impulsive noise and for restoration of a square wave respectively

gabor filter based edge detection abstract it is common practice to utilize evidence from biological and psychological vision experiments to develop computational models for low level feature extraction the receptive profiles of simple cells in mammalian visual systems have been found to closely resemble gabor filters daugman proved that gabor filters achieve joint minimal joint uncertainty these results led researchers to develop computational models based on gabor filters for several low level vision applications such as edge detection texture classification optical flow estimation and data compression in this paper the performance of a gabor odd filter based edge detector is investigated using the measures proposed by canny based on this performance analysis a design criterion for one dimensional 1d gabor filter based edge detector is derived it is shown that this design criterion also holds good for a two dimensional 2d gabor filter based edge detector experimental results are presented to demonstrate the performance of the gabor filter based edge detector

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

close form solution and parameter selection for convex minimization based edge preserving smoothing this work presents a new approach for the analysis of convex minimization based edge preserving image smoothing and the parameter selection therein the global solution that is the response of a convex smoothing model to the ideal step edge is derived in close form by analyzing the close form solution insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution based on this a scheme is proposed for selecting parameters to achieve desirable responses at edges the theoretic results are substantiated by experiments

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

a nonlinear derivative scheme applied to edge detection this paper presents a nonlinear derivative approach to addressing the problem of discrete edge detection this edge detection scheme is based on the nonlinear combination of two polarized derivatives its main property is a favorable signal to noise ratio snr at a very low computation cost and without any regularization a 2d extension of the method is presented and the benefits of the 2d localization are discussed the performance of the localization and snr are compared to that obtained using classical edge detection schemes tests of the regularized versions and a theoretical estimation of the snr improvement complete this work

inverted regions induced by geometric constraints on a classical encounter controlled binary reaction abstract the efficiency of an encounter controlled reaction between two independently mobile reactants on a lattice is characterized by the mean number n of steps to reaction the two reactants are distinguished by their mass with the light walker performing a jump to a nearest neighbor site in each time step while the heavy walker hops only with a probability p we associate p with the temperature of the system to account for geometric exclusion effects in the reactive event two reaction channels are specified for the walkers irreversible reaction occurs either in a nearest neighbor collision or when the two reactants attempt to occupy the same site lattices subject to periodic and to confining boundary conditions are considered for periodic lattices depending on the initial state the reaction time either falls off monotonically with p or displays a local minimum with respect to p occurrence of the latter signals a regime where the efficiency of the reaction effectively decreases with increasing temperature such behavior can also occur when one averages over all initial conditions but it disappears if the jump probability of the light walker falls below a characteristic threshold value even more robust behavior can occur on lattices subject to confining boundary conditions depending on the initial conditions the reaction time as a function of p may increase monotonically decrease monotonically display a single maximum or even a maximum and minimum in the latter case one can identify distinct regimes where the above noted inversion in reaction efficiency can occur we document both numerically and theoretically that these inversion regions are a consequence of a strictly classical interplay between excluded volume effects implicit in the specification of the two reaction channels and the system s dimensionality and spatial extent our results highlight situations where the description of an encounter controlled reactive event cannot be described by a single effective diffusion coefficient we also distinguish between the inversion region identified here and the marcus inverted region which arises in electron transfer reactions

zero order statistics a mathematical framework for the processing and characterization of very impulsive signals impulsive or heavy tailed processes with infinite variance appear naturally in a variety of practical problems that include wireless communications teletraffic hydrology geology and economics most signal processing and statistical methods available in the literature have been designed under the assumption that the processes possess finite variance and they usually break down in the presence of infinite variance although methods based on fractional lower order statistics flos have proven successful in dealing with infinite variance processes they fail in general when the noise distribution has very heavy algebraic tails in this paper we introduce a new approach to statistical moment characterization which is well defined over all processes with algebraic or lighter tails unlike flos these zero order statistics zos as we will call them provide a common ground for the analysis of basically any distribution of practical use known today three new parameters namely the geometric power the zero order location and the zero order dispersion constitute the foundation of zos they play roles similar to those played by the power the expected value and the standard deviation in the theory of second order processes we analyze the properties of the new parameters and derive a zos framework for location estimation that gives rise to a novel mode type estimator with important optimality properties under very impulsive noise several simulations are presented to illustrate the potential of zos methods

an edge detection technique using the facet model and parameterized relaxation labeling we present a method for detecting and labeling the edge structures in digital gray scale images in two distinct stages first a variant of the cubic facet model is applied to detect the location orientation and curvature of the putative edge points next a relaxation labeling network is used to reinforce meaningful edge structures and suppress noisy edges each node label of this network is a 3d vector parameterizing the orientation and curvature information of the corresponding edge point a hysteresis step in the relaxation process maximizes connected contours for certain types of images prefiltering by adaptive smoothing improves robustness against noise and spatial blurring

comparison of the convergence of two algorithms for adaptive fir digital filters the convergence properties of two different algorithms for the updating of the coefficients of an adaptive fir digital filter are investigated and compared with one another these algorithms are the stochastic iteration algorithm and the sign algorithm in this latter algorithm a one bit gradient estimation is used which makes its implementation very simple the convergence is characterized by the residual echo variance after convergence and a parameter that indicates the speed of the convergence it is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained

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

edge and line feature extraction based on covariance models image segmentation based on contour extraction usually involves three stages of image operations feature extraction edge detection and edge linking this paper is devoted to the first stage a method to design feature extractors used to detect edges from noisy and or blurred images the method relies on a model that describes the existence of image discontinuities e g edges in terms of covariance functions the feature extractor transforms the input image into a log likelihood ratio image such an image is a good starting point of the edge detection stage since it represents a balanced trade off between signal to noise ratio and the ability to resolve detailed structures for 1 d signals the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called average risk measure the results are compared with the performances of 1 d edge detectors known from literature generalizations to 2 d operators are given applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors finally it is shown that the covariance model can be coupled to a mrf model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

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

fast algorithms for weighted myriad computation by fixed point search this paper develops fast algorithms to compute the output of the weighted myriad filter myriad filters form a large and important class of nonlinear filters for robust non gaussian signal processing and communications in impulsive noise environments just as the weighted mean and the weighted median are optimized for the gaussian and laplacian distributions respectively the weighted myriad is based on the class of spl alpha stable distributions which can accurately model impulsive processes the weighted myriad is an m estimator that is defined in an implicit manner no closed form expression exists for it and its direct computation is a nontrivial and prohibitively expensive task in this paper the weighted myriad is formulated as one of the fixed points of a certain mapping an iterative algorithm is proposed to compute these fixed points and its convergence is proved rigorously using these fixed point iterations fast algorithms are developed for the weighted myriad numerical simulations demonstrate that these algorithms compute the weighted myriad with a high degree of accuracy at a relatively low computational cost

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

scale invariant filtering design and analysis for edge detection existing edge detection filters work well on straight edges but make significant errors near sharp corners by producing rounded corners this is due to the fact that the edge maps produced by these filters are scale variant we enhance canny s optimality criteria to incorporate detection performance near corners as an explicit design objective the resulting optimal filter termed bessel integral filter can be derived analytically and exhibits superior performance over recent alternatives both in terms of numerical accuracy and experimental fidelity a noise free localization index is also derived here to account for the detection accuracy of discontinuities forming sharp corners in the absence of noise we prove here that edges detected by the filters which are not optimal with respect to this noise free localization index are scale variant however the bessel integral filter proposed here is optimal with respect to the noise free localization index and therefore it is a scale invariant filter

optimal ramp edge detection using expansion matching in practical images ideal step edges are actually transformed into ramp edges due to the general low pass filtering nature of imaging systems this paper discusses the application of the expansion matching exm method for optimal ramp edge detection exm optimizes a novel matching criterion called discriminative signal to noise ratio dsnr and has been shown to robustly recognize templates under conditions of noise severe occlusion and superposition we show that our ramp edge detector performs better than the ramp detector obtained from canny s criteria in terms of dsnr and is relatively easier to derive for various noise levels and slopes

effects of confinement on the statistics of encounter times exact analytical results for random walks in a partitioned lattice we study the effects of temporarily and permanently confining domains on the statistics of first passage times in finite lattices in one and two dimensions we present exact results for the mean and variance of the first passage time between arbitrary sites in the following 1 a finite one dimensional lattice partitioned into temporarily confining domains and 2 a finite two dimensional lattice with reflecting boundaries for a single random walker and an immobile target in the one dimensional case we also present the full first passage time distribution via numerical inversion of laplace transforms

optimal edge detection using expansion matching and restoration discusses the application of a newly developed expansion matching method for edge detection expansion matching optimizes a novel matching criterion called the discriminative signal to noise ratio dsnr and has been shown to robustly recognize templates under conditions of noise severe occlusion and superposition the dsnr criterion is better suited to evaluate matching in practical conditions than the traditional snr since it considers as noise even the off center response of the filter to the template itself we introduce a family of optimal dsnr edge detectors based on the expansion filter for several edge models for step edges the optimal dsnr step expansion filter sef is compared with the widely used canny edge detector ced experimental comparisons show that our edge detector yields better performance than the ced in terms of dsnr even under very adverse noise conditions as for boundary detection the sef consistently yields higher figures of merit than the ced on a synthetic binary image over a wide range of noise levels results also show that the design parameters of size or width of the sef are less critical than the ced variance this means that a single scale of the sef spans a larger range of input noise than a single scale of the ced experiments on a noisy image reveal that the sef yields less noisy edge elements and preserves structural details more accurately on the other hand the ced output has better suppression of multiple responses than the corresponding sef output

jump surface estimation edge detection and image restoration surface estimation is important in many applications when conventional smoothing procedures e g running averages local polynomial kernel smoothing procedures smoothing spline procedures are used for estimating jump surfaces from noisy data jumps are blurred at the same time when noise is removed in recent years new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved we provide a review of these methodologies because a monochrome image can be considered a jump surface of the image intensity function with jumps at the outlines of objects edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics we also review major methodologies on edge detection and image restoration and discuss connections and differences among these methods and related methods in the statistical literature

first passage properties of mortal random walks ballistic behavior effective reduction of dimensionality and scaling functions for hierarchical graphs we consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites the configuration comprising the graph the starting point of the walk and the locations of the trap sites is taken to be exactly self similar as one goes from one generation of the family to the next under these circumstances the total probability that the walker hits a trap is determined exactly as a function of the single step survival probability q of the mortal walker on the nth generation graph of the family this probability is shown to be given by the nth iterate of a certain scaling function or map q f q the properties of the map then determine in each case the behavior of the trapping probability the mean time to trapping the temporal scaling factor governing the random walk dimension on the graph and other related properties the formalism is illustrated for the cases of a linear hierarchical lattice and the sierpinski graphs in two and three euclidean dimensions we find an effective reduction of the random walk dimensionality due to the ballistic behavior of the surviving particles induced by the mortality constraint the relevance of this finding for experiments involving travel times of particles in diffusion decay systems is discussed

uncertainty propagation and the matching of junctions as feature groupings the interpretation of the 3d world from image sequences requires the identification and correspondences of key features in the scene we describe a robust algorithm for matching groupings of features related to the objects in the scene we consider the propagation of uncertainty from the feature detection stage through the grouping stage to provide a measure of uncertainty at the matching stage we focus upon indoor scenes and match junctions which are groupings of line segments that meet at a single point a model of the uncertainty in junction detection is described and the junction uncertainty under the epipolar constraint is determined junction correspondence is achieved through matching of each line segment associated with the junction a match likelihood is then derived based upon the detection uncertainties and then combined with information on junction topology to create a similarity measure a robust matching algorithm is proposed and used to match junctions between pairs of images the presented experimental results on real images show that the matching algorithm produces sufficiently reliable results for applications such as structure from motion