corner detection on digital curves based on local symmetry of the shape abstract the detection of corners on digital curves is a problem of important in shape analysis this paper describes a new method for detecting corners based on local symmetry of the shape the proposed method consists of two steps the first is the computation of symmetry measure for symmetry relative to a line at every point on a digital curve the second is the location of reasonable local maxima of the symmetry measure as corners the effectiveness of the new method is illustrated with the results of experiments for a number of different types of digital curves

a nonlinear parallel algorithm with application to the stefan problem the algebraic problem b gamma e a beta e eta which may evolve from elliptic or parabolic partial differential equations is studied conditions are given so that a parallel algorithm of a nonlinear gauss seidel type converges to the unique solution an application is given to the solidification of a channel in which the continuum problem is discretized by the finite element method these computations show a significant decrease in computing times as compared to serial algorithms

wavelet based corner detection abstract a non parametric algorithm for detecting and locating corners of planar curves is proposed the algorithm is based on the multiscale wavelet transform of the orientation of the curve which can effectively utilize both the information of local extrema positions and magnitudes of the transform results the corner candidates can then be selected easily based on this information according to the angle preserving concept intrinsic ratios of several corner models have been derived and used to evaluate the corner candidates the corner angles can also be obtained during these processes to make the evaluation process robust a masking algorithm is proposed experiments depict that our detector is more effective than the single scale corner detectors while is more efficient than the multiscale corner detector by rattarangsi and chin proc int conf pattern recognition pp 923 930 1990

convergence of the ssor method for nonlinear systems of simultaneous equations in der vorliegenden arbeit wird fur die konvergenz des symmetrischen relaxationsverfahrens ssor verfahren bei anwendung auf eine klassenichtlinearer gleichungssysteme die globale konvergenz bewiesen diese gleichungssysteme treten z b bei der diskretisierung nichtlinearer partieller differentialgleichungen auf

fuzzy tree automata and syntactic pattern recognition an approach of representing patterns by trees and processing these trees by fuzzy tree automata is described fuzzy tree automata are defined and investigated the results include that the class of fuzzy root to frontier recognizable trees is closed under intersection union and complementation thus the class of fuzzy root to frontier recognizable trees forms a boolean algebra fuzzy tree automata are applied to processing fuzzy tree representation of patterns based on syntactic pattern recognition the grade of acceptance is defined and investigated quantitative measures of approximate isosceles triangle approximate elongated isosceles triangle approximate rectangle and approximate cross are defined and used in the illustrative examples of this approach by using these quantitative measures a house a house with high roof and a church are also presented as illustrative examples in addition three fuzzy tree automata are constructed which have the capability of processing the fuzzy tree representations of fuzzy houses houses with high roofs and fuzzy churches respectively the results may have useful applications in pattern recognition image processing artificial intelligence pattern database design and processing image science and pictorial information systems

bounds on the information rate of intertransition time restricted binary signaling over an awgn channel upper and lower bounds on the capacity of a continuous time additive white gaussian noise awgn channel with bilevel spl plusmn spl radic p input signals subjected to a minimum inter transition time t sub min constraint are derived the channel model and input constraints reflect basic features of certain magnetic recording systems the upper bounds are based on duncan s relation between the average mutual information in an awgn regime and the mean square error mse of an optimal causal estimator evaluation or upper bounding the mse of suboptimal causal estimators yields the desired upper bounds the lower bound is found by invoking the extended mrs gerber s lemma and asymptotic properties of the entropy of max entropic bipolar d k codes asymptotic results indicate that at low snr pt sub min n sub 0 with n sub 0 designating the noise one sided power spectral density the capacity tends to p n sub 0 nats per second nats s i e it equals the capacity in the simplest average power limited case at high snr the capacity in the simplest average power limited case at high snr the capacity behaves asymptotically as t sub min sup 1 ln snr ln snr nats s demonstrating the degradation relatively to t sub avg sup 1 lnsnr which is the asymptotic known behavior of the capacity with a bilevel average intertransition time t sub avg restricted channel input additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation the effect of mild channel filtering on the lower bounds on capacity is also addressed and novel techniques to lower bound the capacity in this case are introduced

necessary and sufficient conditions for the two point phase probability function of two phase random media constructing realizations of random media with a specified two point phase probability function s2 has attracted considerable attention in the recent literature however little is known about cond

information rates for magnetic recording channels with peak and slope limited magnetization a model for magnetic recording is proposed which uses two parameters to describe the limitations on the remanent magnetization in the medium the dimensionless peak value a sub m and the steepest slope b s sup 1 a low pass bandwidth restriction w s sup 1 due to read circuits is also included lower and upper bounds on the achievable transmission rates are derived in terms of the signal to noise ratio for the case of ideal low pass restriction with b

on the capacity penalty due to input bandwidth restrictions with an application to rate limited binary signaling it is well known that in cases of unlimited channel bandwidth and unconstrained signal spectrum a constant envelope constraint on the signal does not reduce the capacity of an additive gaussian channel as compared to its capacity with the optimum signals of similar average power for band limited channels of bandwidth b however the constant envelope constraints does reduce the capacity even if the signals themselves are allowed arbitrarily rapid alternations transitions here using a recently introduced technique it is shown that the capacity is further drastically reduced if in addition to the channel limitation the constant envelope signal is itself restricted to a small fractional out of band power epsilon ideal lowpass and bandpass channel filters are considered and upper bounds on the capacity are derived the out of band power restrictions can be met for example by restricting the average rate of transitions rho of the binary input signal it is shown that in this case epsilon

optimized polygonal approximation by dominant point deletion an algorithm for polygonal approximation based on dominant point dp deletion is presented in this paper the algorithm selects an initial set of dps and starts eliminating them one by one depending upon the error associated with each dp the associated error value is based on global measure a local optimization of few neighboring points is performed after each deletion although the algorithm does not guarantee an optimal solution the combination of local and global optimization is expected to produce optimal results the algorithm is extensively tested on various shapes with varying number of dps and error threshold in general optimal results were observed for about 96 of the times a good comparative study is also presented in this paper

non parametric dominant point detection abstract a new method for detecting dominant points is presented it does not require any input parameter and the dominant points obtained by this method remain relatively the same even when the object curve is scaled or rotated in this method for each boundary point a support region is assigned to the point based on its local properties each point is then smoothed by a gaussian filter with a width proportional to its determined support region a significance measure for each point is then computed dominant points are finally obtained through nonmaximum suppression unlike other dominant point detection algorithms which are sensitive to scaling and rotation of the object curve the new method will overcome this difficulty furthermore it is robust in the presence of noise the proposed new method is compared to the teh chin algorithm see c teh and r t chin ieee trans pattern anal mach intell 11 859 872 1989 in terms of the computational complexity the approximation errors and the number of detected dominant points of an object curve

fuzzy sets in pattern recognition methodology and methods abstract an objective of the paper is to discuss a state of the art of methodology and algorithms of fuzzy sets in the field of pattern recognition in real world recognition and classification problems we are faced with fuzziness that is connected with diverse facets of cognitive activity of the human being an origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification procedures an evident difference between a way of information processing by means of probability and fuzzy set theory and a way of interpretation of results is explained in detail in sequel methods of pattern recognition are studied in two main streams namely supervised and unsupervised learning different approaches to designing of classification schemes as e g relation calculus decision making approach etc are put into account a method of feature selection with the aid of fuzzy measure and fuzzy integral is introduced in clustering techniques methods relying on minimization of objective function are analyzed in detail also a problem of cluster validity expressed in terms of clustering indices is addressed numerical examples are also provided

a class of iteration methods based on the hss for toeplitz systems of weakly nonlinear equations for toeplitz systems of weakly nonlinear equations combining the separability and strong dominance between the linear and the nonlinear terms with the hermitian and skew hermitian splitting hss iteration technique we establish two nonlinear composite iteration schemes called picard csss and nonlinear csss like iteration methods which are based on a special case of the hss where the symmetric part h 1 2 a a t is a centrosymmetric matrix and the skew symmetric part h 1 2 a a t is a skew centrosymmetric matrix the advantages of these methods are that they can transfer the linear sub systems involved in inner iteration to two linear systems of half an order besides fast methods are available for computing the two half steps involved in the inner iteration numerical results are provided to further show that both picard csss and nonlinear csss like iteration methods are feasible and effective

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

on a fuzzy theory based computer aided particle shape description abstract a central problem of particle shape analysis consists in the characterization of the shape of any natural of produced particle by a small number of parameters which are to be evaluated from a two dimensional picture of the particle e g from its projection we suggest using the grey tone picture obtained by a camera to compute a sympathy function with respect to a suitable family of planar shapes the computation is performed by means of the image processing equipment robotron a 6471 the sympathy function defines a fuzzy set on the parameter space the procedure is applied to a quartz particle

models of parallel chaotic iteration methods abstract we consider two models of parallel multisplitting chaotic iterations for solving large nonsingular systems of equations ax b in the first model each processor can carry out an arbitrary number of local iterations before the next global approximation to the solution is formed in the second model any processor can update the global approximation which resides in the central processor at any time this model is a generalization of a sequential iterative scheme due to ostrowski called the free steering group jacobi iterative scheme and a chaotic relaxation point iterative scheme due to chazan and miranker we show that when a is a monotone matrix and all the splittings are weak regular both models lead to convergent schemes

convergence of partially asynchronous block quasi newton methods for nonlinear systems of equations in this paper a partially asynchronous block broyden method is presented for solving nonlinear systems of equations of the form f x 0 sucient conditions that guarantee its local convergence are given in particular local convergence is shown when the jacobian f 0 x i s anh matrix where x is the zero point of f the results are extended to schubert s method a connection with discrete schwarz alternating procedure is also shown c 1999 elsevier science b v all rights reserved

scale based detection of corners of planar curves a technique for detecting and localizing corners of planar curves is proposed the technique is based on gaussian scale space which consists of the maxima of absolute curvature of the boundary function presented at all scales the scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners the analysis shows that the resulting scale space contains line patterns that either persist terminate or merge with a neighboring line next the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales finally a multiple scale corner detection scheme is developed using a coarse to fine tree parsing technique the parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales experiments were performed to show that the scale space corner detector is reliable for objects with multiple size features and noisy boundaries and compares favorably with other corner detectors tested

on filtered binary processes the problem of calculating the probability density function of the output of an rc filter driven by a binary random process with intervals generated by an equilibrium renewal process is studied new integral equations closely related to mcfadden s original integral equations are derived and solved by a matrix approximation method and by iteration transformations of the integral equations into differential equations are investigated and a new closed form solution is obtained in one special case some numerical results that compare the matrix and iteration solutions with both exact solutions and approximate solutions based upon the fokker planck equation are presented

a fuzzy region growing approach for segmentation of color images segmentation is one of the most important preprocessing steps towards pattern recognition and image understanding and a significant step towards image compression and coding with detecting edges most of the large segments can be found and separated from others by edge pixels it is however the pixels on edge locations or those in high detailed areas whose association to adjacent segments must be found a pixel can be a part of the closest segment or in association with the neighboring pixels from a new smaller segment in this paper two segmentation algorithms are presented one is used for fine segmentation towards compression and coding of images and the other for coarse segmentation towards other applications like object recognition and image understanding edge detection and region growing approaches are combined to find large and crisp segments for coarse segmentation segments can grow or expand based on two fuzzy criteria the fuzzy region growing and expanding approaches presented here use histogram tables for fine segmentation the procedures introduced here can be used in any order or combination to yield the best result for any particular application or image type

regular splittings and monotone iteration functions in this paper we introduce the set of so called monotone iteration functions mi functions belonging to a given function we prove necessary and sufficient conditions in order that a given mi function is in a precisely defined sense at least as fast as a second one regular splittings of a function which were initially introduced for linear functions by r s varga in 1960 are generating mi functions in a natural manner for linear functions every mi function is generated by a regular splitting for nonlinear functions however this is generally not the case

two dimensional shape decomposition using fuzzy subset theory applied to automated chromosome analysis abstract this paper describes a technique to transform a two dimensional shape into a generalized fuzzy binary relation whose clusters represent the meaningful simple parts of the shape the fuzzy binary relation is defined on the set of convex and concave boundary points implying a piecewise linear approximation of the boundary and describes the dissemblance of two vertices to a common cluster next some fuzzy subsets are defined over the points which determine the connection between the clusters the decomposition method first determines nearly convex regions which are subgraphs of the total graph and then selects the greatest nearly convex region which satisfies best the defined fuzzy subsets and relations using this procedure on touching chromosomes defining the simple parts to be the separated chromosomes the decomposition often corresponds well to the decomposition that a human might make

color image segmentation advances and prospects abstract image segmentation is very essential and critical to image processing and pattern recognition this survey provides a summary of color image segmentation techniques available now basically color segmentation approaches are based on monochrome segmentation approaches operating in different color spaces therefore we first discuss the major segmentation approaches for segmenting monochrome images histogram thresholding characteristic feature clustering edge detection region based methods fuzzy techniques neural networks etc then review some major color representation methods and their advantages disadvantages finally summarize the color image segmentation techniques using different color representations the usage of color models for image segmentation is also discussed some novel approaches such as fuzzy method and physics based method are investigated as well

polygonal approximation of digital curves based on the principles of perceptual organization abstract a new approach to the problem of polygonal approximation of digital shapes is presented in this paper in this approach the approximation process is divided into three stages based on the principles of perceptual organization and three algorithms are developed accordingly the linking merging algorithm is firstly proposed for low level processing the smoothing algorithm is then followed for further approximation the high level rule based algorithm is finally applied to preserve the visual feature points while reducing the number of segments in the approximated polygon as much as possible the effectiveness of the proposed algorithm is demonstrated by testing both synthetic shapes and scanned in shapes

polygonal approximation of digital planar curves through break point suppression this paper presents a new algorithm that detects a set of dominant points on the boundary of an eight connected shape to obtain a polygonal approximation of the shape itself the set of dominant points is obtained from the original break points of the initial boundary where the integral square is zero for this goal most of the original break points are deleted by suppressing those whose perpendicular distance to an approximating straight line is lower than a variable threshold value the proposed algorithm iteratively deletes redundant break points until the required approximation which relies on a decrease in the length of the contour and the highest error is achieved a comparative experiment with another commonly used algorithm showed that the proposed method produced efficient and effective polygonal approximations for digital planar curves with features of several sizes

representation of uncertainty in computer vision using fuzzy sets uncertainty in computer vision can arise at various levels it can occur in the low level in the raw sensor input and extends all the way through intermediate and higher levels ideally at any level where decisions are being made on the basis of previous processing steps a computer vision system must have sufficient flexibility for representation of uncertainty in any of these levels

bounds on the symmetric binary cutoff rate for dispersive gaussian channels bounds on the symmetric binary cutoff rate for a pulse amplitude modulated pam signaling over dispersive gaussian channels are evaluated and discussed these easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary two level pam schemes operating through a prefiltered additive white gaussian channel the memory of which is long enough to make the exact evaluation of the cutoff rate formidable the core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix commonly applied in large deviation problems these bounds are calculated for some examples and their respective tightness is considered further potential applications of the proposed bounding technique are pointed out

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

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

parallel nonlinear multisplitting methods linear multisplitting methods are known as parallel iterative methods for solving a linear systemax b we extend the idea of multisplittings to the problem of solving a nonlinear system of equationsf x 0 our nonlinear multisplittings are based on several nonlinear splittings of the functionf in a parallel computing environment each processor would have to calculate the exact solution of an individual nonlinear system belonging to his nonlinear multisplitting and these solutions are combined to yield the next iterate although the individual systems are usually much less involved than the original system the exact solutions will in general not be available therefore we consider important variants where the exact solutions of the individual systems are approximated by some standard method such as newton s method several methods proposed in literature may be regarded as special nonlinear multisplitting methods as an application of our systematic approach we present a local convergence analysis of the nonlinear multisplitting methods and their variants one result is that the local convergence of these methods is determined by an induced linear multisplitting of the jacobian off

a unified curvature definition for regular polygonal and digital planar curves in this paper we propose a new definition of curvature called visual curvature it is based on statistics of the extreme points of the height functions computed over all directions by gradually ignoring relatively small heights a multi scale curvature is obtained the theoretical properties and the experiments presented demonstrate that multi scale visual curvature is stable even in the presence of significant noise to our best knowledge the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves moreover it yields stable curvature estimates of curves in digital images even under sever distortions we also show a relation between multi scale visual curvature and convexity of simple closed curves

achievable rates for a constrained gaussian channel the authors obtained lower bounds to the capacity of the continuous time filtered additive gaussian noise channel with two valued inputs essentially the problem reduces to the continuous time peak limited case which remains an unsolved problem of primary importance in communication theory

deb definite error bounded tangent estimator for digital curves we propose a simple and fast method for tangent estimation of digital curves this geometric based method uses a small local region for tangent estimation and has a definite upper bound error for continuous as well as digital conics i e circles ellipses parabolas and hyperbolas explicit expressions of the upper bounds for continuous and digitized curves are derived which can also be applied to nonconic curves our approach is benchmarked against 72 contemporary tangent estimation methods and demonstrates good performance for conic nonconic and noisy curves in addition we demonstrate a good multigrid and isotropic performance and low computational complexity of o 1 and better performance than most methods in terms of maximum and average errors in tangent computation for a large variety of digital curves

on the convergence of parallel chaotic nonlinear multisplitting newton type methods abstract a class of parallel chaotic nonlinear multisplitting newton type methods for solving the nonlinear system of equations f x 0 f d r n r n is established and its local convergence theory is presented

a fast algorithm to solve systems of nonlinear equations abstract a new hss based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved spectral properties of the new method are investigated performance profile for the new scheme is computed and compared with hss algorithm besides by a numerical example in which a two dimensional nonlinear convection diffusion equation is solved we compare the new method and the newton hss method numerical results show that the new scheme solves the problem faster than the newton hss scheme in terms of cpu time and number of iterations moreover the application of the new method is found to be fast reliable flexible accurate and has small cpu time

using dominant points and variants for profile extraction from chromosomes abstract the most accurate methods for automatic analysis of chromosomes under a light microscope today extract numerical features from band pattern profiles along their longitudinal axes the construction of a reliable axis is a crucial step in this process we propose a new way based on the dominant points of the contour and cubic splines the dominant points serve as candidates for the tips of the chromosome ambiguities are dissolved by the recently developed method of variants for object identification a voronoi diagram decomposes the chromosome in slices for profile extraction the method improves the currently best classification results significantly yielding a test set error rate of 0 61

reliable polygonal approximations of imaged real objects through dominant point detection abstract the problem of dominant point detection is posed taking into account what usually happens in practice the algorithms found in the literature often prove their performance with laboratory contours but the shapes in real images present noise quantization and high inter and intra shape variability these effects are analyzed and solutions to them are proposed we will also focus on the conditions for an efficient few points and precise low error dominant point extraction that preserves the original shape a measurement of the committed error optimization error e 0 that takes into account both aspects is defined for studying this feature

a shape recognition scheme based on relative distances of feature points from the centroid abstract in this paper a simple but efficient scheme to recognize shapes is proposed in our scheme all of the boundary points are used to calculate the centroid of an object then the distance between each feature point and the centroid is computed we have shown that the time complexity of our shape matching algorithm is o m where m is the number of feature points the most important advantage of our method is its independence to translation rotation and scaling of objects

polygonal representation of digital planar curves through dominant point detection a nonparametric algorithm we describe a new algorithm that detects a set of feature points on the boundary of an 8 connected shape that constitute the vertices of a polygonal approximation of the shape itself the set of feature points nodes is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape nodes are ranked based on their strength in terms of their importance to other boundary points length of support region and distance from the centroid the polygon obtained by linking the detected nodes approximates the contour in an intuitive way the proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes

curvature and tangential deflection of discrete arcs a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data this paper introduces a new theory for the tangential deflection and curvature of plane discrete curves our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats its rationale is drawn from the statistical and geometric properties associated with the eigenvalue eigenvector structure of sample covariance matrices specifically we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces and further we show that this entry is in certain limiting cases also proportional to the analytical curvature of the plane curve from which the discrete data are drawn these results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection and moreover they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts as a concrete example we develop the commutator vertex detection cvd algorithm which identifies the location of vertices in shape data based on excessive cummulative tangential deflection and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding approximate curvature extrema

a class of iteration methods based on the generalized preconditioned hermitian and skew hermitian splitting for weakly nonlinear systems abstract for large sparse systems of weakly nonlinear equations based on the separable property and strong dominance between the linear and the nonlinear terms bai and yang studied two nonlinear composite iteration schemes called picard hss and nonlinear hss like methods see z z bai x yang on hss based iteration methods for weakly nonlinear systems appl numer math 59 12 2009 2923 2936 in this paper we generalize these methods and propose a class of generalized nonlinear composite splitting iteration schemes called picard gphss and nonlinear gphss like iteration methods to solve the large sparse systems of weakly nonlinear equations we derive conditions for guaranteeing the local convergence of these iterative methods and derive some special case of iterative methods by choosing different parameters and preconditioned matrices numerical experiments are used to demonstrate the feasibility and effectiveness and an efficient preconditioner is presented for the new methods in actual implementation the efficiency is effectively testified by some comparisons with numerical results

the detection of dominant points on digital curves by scale space filtering the detection of dominant points is an important preprocessing step for shape recognition an effective method of scale space filtering with a gaussian kernel is introduced to detect dominant points on digital curves the conventional polygonal approximation algorithms are time consuming and need input parameter tuning for gaussian smoothing the noise and quantization error also they are sensitive to scaling and rotation of the object curve the above dit culty can be overcome by finding out the dominant points at each scale by scale space filtering by tracing back the dominant point contours in the scale space image the stable cardinal curvature points can be detected very accurately this new method requires no input parameters and the resultant dominant points do not change under translation rotation and scaling meanwhile a fast convolution algorithm is proposed to detect the dominant points at each scale dominant points scale space gaussian smoothing curvature

upper bounds on capacity for a constrained gaussian channel a low pass and a bandpass additive white gaussian noise channel with a peak power constraint imposed on otherwise arbitrary input signals are considered upper bounds on the capacity of such channels are derived they are strictly less than the capacity of the channel when the peak power constrain is removed and replaced by the average power constraint for which the gaussian inputs are optimum this provides the answer to an often posed question peak power limiting in the case of bandlimited channels does reduce capacity whereas in infinite bandwidth channels it does not as is well known for an ideal low pass filter of bandwidth b the upper bound is blog 0 934p n sub 0 b for p n sub 0 b 1 where p is the peak power of the input signal and n sub 0 2 is the double sided power spectral density of the additive white gaussian noise

generalized nonlinear diagonal dominance and applications to asynchronous iterative methods abstract we introduce a concept of generalized diagonal dominance for nonlinear functions as in the linear case this brings together several apparently different classes of nonlinear functions such as strictly diagonally dominant functions and certain m functions with our concept we easily obtain a quite far reaching result on the global convergence of asynchronous iterative methods for finding zeros of nonlinear functions special cases include some known and several new convergence results for special iterative methods such as the nonlinear jor sor and ssor method

a new algorithm for dominant points detection and polygonization of digital curves a new algorithm for detecting dominant points and polygonal approximation of digitized closed curves is presented it uses an optimal criterion for determining the region of support of each boundary point and a new mechanism for selecting the dominant points the algorithm does not require an input parameter and can handle shapes that contain features of multiple sizes efficiently in addition the approximating polygon preserves the symmetry of the shape

digitized circular arcs characterization and parameter estimation the digitization of a circular arc causes an inherent loss of geometrical information arcs with slightly different local curvature or position may lead to exactly the same digital pattern in this paper the authors give a characterization of all centers and radii of circular arcs yielding the same digitization pattern the radius of the arcs varies over the set however only one curvature or radius estimate can be assigned to the digital pattern the authors derive an optimal estimator and give expressions for the bound on the precision of estimation this bound due to digitization is the deterministic equivalent of the cramer rao bound known from parameter estimation theory consider the estimation of the local curvature and local radius of a smooth object typically such parameters are estimated by moving a window along the digital boundary methods in literature show a poor precision in estimating curvature values relative errors of over 40 are often found from the definition of curvature it follows that locally the curve can be considered a circular arc and hence the method presented in this paper can be applied to the pattern in the window giving estimates with optimal precision and a measure for the remaining error on the practical side the authors present examples of the residual error due to the discrete grid the estimation of the radius or curvature of a circular arc at random position with an estimation window containing 10 points coded with nine freemancodes has a relative deviation exceeding 2 for a full disk the deviation is below 1 when the radius r exceeds four grid units the presented method is particularly useful for problems where some prior knowledge on the distribution of radii is known and where there is a noise free sampling