numerical methods for approximating digitized curves by piecewise circular arcs abstract two dimensional digitized curves are often approximated by some piecewise linear or high order curves the approximation usually results in a compact and effective representation for further applications in this paper we propose new algorithms to approximate digitized curves by piecewise circular arcs with geometric continuity g 0 or g 1 first iterative methods are proposed to solve the best single arc and biarc approximation problems of a digitized curve with respect to the maximum norm the basic notion of our methods is to show that the error functions of two approximations are unimodal functions so techniques developed in optimization theory can be used to search for the best approximation then the piecewise arcs approximation problems can be solved by applying these approximation algorithms to construct an arcwise curve such that each join point between two arcs is g 0 or g 1 continuity and its maximum approximation error is no more than a given tolerance e 0 some experimental results are given to demonstrate the quality and the performance of the proposed algorithms

stabilization and robustness analysis for a chain of exponential integrators using strict lyapunov functions we provide a new method for building strict lyapunov functions for two dimensional chains of exponential integrators using nested exponential functions one challenge is that the right sides of the systems saturate so they are not completely controllable the strictness of the lyapunov functions is key to proving input to state stability or iss properties with respect to additive uncertainty on the controls we show how a large class of tracking problems for nonlinear systems with positivity constraints on the states can be solved using our theory

wold slocinski decompositions for commuting isometric triples abstract extending two remarkable results by von neumann halmos wold for isometric operators and slocinski for pairs of commuting isometries we discuss the possibility to decompose a given commuting triple v v 1 v 2 v 3 of isometric operators acting on a hilbert space h into the direct sum between commuting triples consisting of unitary operators and or unilateral shifts we prove that such a decomposition exists if and only if the pairs v 1 v 2 v 3 v 2 v 3 v 1 and v 1 v 3 v 2 have decompositions of wold slocinski type if only two of these pairs are supposed to have such a decomposition then the wold slocinski decomposition associated to v has seven summands several structure results of geometric type for these summands are also presented examples and counterexamples are used for illustrative purposes certain results are presented in full generality i e for commuting isometric n tuples

backstepping with bounded feedbacks for time varying systems a family of time varying nonlinear systems is globally uniformly asymptotically stabilized by bounded feedbacks constructed through a new extension of the backstepping approach explicit expressions of control laws and lyapunov functions are given

on the commuting isometries abstract the paper summarizes clarifies and supplements results on decompositions and a model for pairs of commuting isometries the geometrical model is given whenever it is possible the remaining problem of describing the model for completely non compatible pairs of isometries is reduced to completely non compatible pairs of unilateral shifts moreover subspaces generating incompatibility are determined

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

an efficient evolutionary algorithm for accurate polygonal approximation an optimization problem for polygonal approximation of 2 d shapes is investigated in this paper the optimization problem for a digital contour of n points with the approximating polygon of k vertices has a search space of c n k instances i e the number of ways of choosing k vertices out of n points a genetic algorithm based method has been proposed for determining the optimal polygons of digital curves and its performance is better than that of several existing methods for the polygonal approximation problems this paper proposes an efficient evolutionary algorithm eea with a novel orthogonal array crossover for obtaining the optimal solution to the polygonal approximation problem it is shown empirically that the proposed eea outperforms the existing genetic algorithm based method under the same cost conditions in terms of the quality of the best solution average solution variance of solutions and the convergence speed especially in solving large polygonal approximation problems

polygonal approximation of closed discrete curves optimal polygonal approximation of closed curves differs from the case of open curve in the sense that the location of the starting point must also be determined straightforward exhaustive search would take n times more time than the corresponding optimal algorithm for an open curve because there are n possible points to be considered as the starting point faster sub optimal solution can be found by iterating the search and heuristically selecting different starting point at each iteration in this paper we propose to find the optimal approximation of a cyclically extended closed curve of double size and to select the best possible starting point by search in the extended search space for the curve the proposed approach provides solution very close to the optimal one using at most twice as much time as required by the optimal algorithm for the corresponding open curve

new control design for bounded backstepping under input delays we provide a new backstepping result for time varying systems with input delays the novelty of our work is in the bounds on the controls and the facts that i one does not need to compute any lie derivatives to apply our controls ii the controls have no distributed terms and iii we do not require any differentiability conditions on the available controls for the subsystems

further results on strict lyapunov functions for rapidly time varying nonlinear systems we explicitly construct global strict lyapunov functions for rapidly time varying nonlinear control systems the lyapunov functions we construct are expressed in terms of oftentimes more readily available lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable this leads to new sufficient conditions for uniform global exponential uniform global asymptotic and input to state stability of fast time varying dynamics we also construct strict lyapunov functions for our systems using a strictification approach we illustrate our results using several examples

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

nonparametric segmentation of curves into various representations this paper describes and demonstrates the operation and performance of an algorithm for segmenting connected points into a combination of representations such as lines circular elliptical and superelliptical arcs and polynomials the algorithm has a number of interesting properties including being scale invariant nonparametric general purpose and efficient

backstepping for nonlinear systems with delay in the input revisited in this paper a new solution to the problem of globally asymptotically stabilizing a nonlinear system in feedback form with a known pointwise delay in the input is proposed the result covers a family of systems wider than those studied in the literature and endows with control laws with a single delay in contrast to those given in previous works which include two distinct pointwise delays or distributed delays the strategy of design is based on the construction of an appropriate lyapunov krasovskii functional an illustrative example ends the paper

piecewise linear approximation of plane curves by perimeter optimization abstract a method for the piecewise linear approximation of a plane curve is described an approximate curve is obtained by choosing a certain number of points from a set of sampled points of the original curve a point choice function that represents the relation between the original points and the chosen points is formulated the approximation is performed by the dynamic programming principle searching for the optimal point choice function that attains the minimal error about arc length of the curve evaluation of the global approximate error provides efficient curve approximations irrespective of shape complexity number of sampled points and irregularity of sampling interval

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

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

algebraic description of curve structure the authors propose a compact and concise method of describing curves in terms of the quasi topological features and the structure of each singular point the quasi topological features are the convexity loop and connectivity the quasi topological structure is analyzed in a hierarchical way and algebraic structure is presented explicitly for each representation level the lower level representations are integrated into the higher level one in a systematic way when a curve has singular points branch points the curve is decomposed into components where each is a simple arc or a simple closed curve by decomposing each singular point the description scheme is applied to character recognition

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

new polygonal approximation schemes for object shape representation abstract object shape representation is an important issue in pattern recognition and computer vision applications a set of new polygonal approximation schemes namely the internal maximum area polygonal approximation imapa the external minimum area polygonal approximation emapa and the minimum area deviation polygonal approximation madpa are proposed for object shape representation the area deviation between the initial object shape and its approximation polygon is defined as the cost function instead of outputting a unique approximation polygon each proposed scheme outputs a sequence of approximation polygons with different numbers of line segments and different area deviations for various application situations for a given area deviation bound and an initial object shape each proposed scheme can give a corresponding optimal approximation polygon with a minimum number of line segments a performance comparison among the proposed schemes is included the proposed schemes are compared with two other existing schemes some experimental results show the feasibility of the proposed approaches

automated design of linear tree classifiers abstract an automated method is presented for the design of linear tree classifiers i e tree classifiers in which a decision based on a linear sum of features is carried out at each node the method exploits the discriminability of tomek links joining opposed pairs of data points in multidimensional feature space to produce a hierarchically structured piecewise linear decision function the corresponding decision surface is optimized by a gradient descent that maximizes the number of tomek links cut by each linear segment of the decision surface followed by training each node s linear decision segment on the data associated with that node experiments on real data obtained from ship images and character images suggest that the accuracy of the tree classifier designed by this scheme is comparable to that of the k nn classifier while providing much greater decision speeds and that the trade off between the speed and the accuracy in pattern classification can be controlled by bounding the number of features to be used at each node of the tree further experiments comparing the classification errors of our tree classifier with the tree classifier produced by the mui fu technique indicate that our tree classifier is no less accurate and often much faster than the mui fu classifier

relaxed lyapunov criteria for robust global stabilisation of non linear systems the notion of the restricted robust control lyapunov function rclf is introduced and is exploited for the design of robust feedback stabilisers for non linear systems particularly it is shown for systems with input constraints that restricted rclfs can be easily obtained while rclfs are not available moreover it is shown that the use of restricted rclfs usually results in different feedback designs from the ones obtained by the use of the standard rclf methodology using the restricted rclfs feedback design methodology a simple controller that guarantees robust global stabilisation of a perturbed chemostat model is provided

ant colony search algorithms for optimal polygonal approximation of plane curves this paper presents a new polygonal approximation method using ant colony search algorithm the problem is represented by a directed graph such that the objective of the original problem becomes to find the shortest closed circuit on the graph under the problem specific constraints a number of artificial ants are distributed on the graph and communicate with one another through the pheromone trails which are a form of the long term memory guiding the future exploration of the graph the important properties of the proposed method are thoroughly investigated the performance of the proposed method as compared to those of the genetic based and the tabu search based approaches is very promising

wold decomposition for doubly commuting isometries abstract in this paper we obtain a complete description of the class of n tuples n 2 of doubly commuting isometries in particular we present a several variables analogue of the wold decomposition for isometries on hilbert spaces our main result is a generalization of m slocinski s wold type decomposition of a pair of doubly commuting isometries

curve description based on directional features and quasi convexity concavity abstract qualitative and global features are appropriate for describing the shape of a complex and deformed object rather than quantitative and local features in particular quantized directional features and quasi convexity concavity are powerful and flexible for describing the shape of handwritten characters in this paper we present a method for structural analysis and description of simple open arcs or closed curves based on 2 m directional features m 1 2 3 and quasi convexity concavity we show some examples of shape description of handwritten characters and experimental results for selecting the optimal quantization of direction in handwritten character recognition

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 using a competitive hopfield neural network abstract polygonal approximation plays an important role in pattern recognition and computer vision in this paper a parallel method using a competitive hopfield neural network chnn is proposed for polygonal approximation based on the chnn the polygonal approximation is regarded as a minimization of a criterion function which is defined as the arc to chord deviation between the curve and the polygon the chnn differs from the original hopfield network in that a competitive winner take all mechanism is imposed the winner take all mechanism adeptly precludes the necessity of determining the values for the weighting factors in the energy function in maintaining a feasible result the proposed method is compared to several existing methods by the approximation error norms l2 and l with the result that promising approximation polygons are obtained

unsupervised segmentation and approximation of digital curves with rate distortion curve modeling this paper considers the problem of unsupervised segmentation and approximation of digital curves and trajectories with a set of geometrical primitives model functions an algorithm is proposed based on a parameterized model of the rate distortion curve the multiplicative cost function is then derived from the model by analyzing the minimum of the cost function a solution is defined that produces the best possible balance between the number of segments and the approximation error the proposed algorithm was tested for polygonal approximation and multi model approximation circular arcs and line segments for digital curves and polynomials for trajectory the algorithm demonstrated its efficiency in comparisons with known methods with a heuristic cost function the proposed method can additionally be used for segmentation and approximation of signals and time series a new algorithm for unsupervised segmentation of digital curves is introduced this method gives solutions with the best balance between error and description length a multiplicative criterion for evaluation of solutions is introduced

the role of algebraic structure in the invariant subspace theory abstract following a recent work of authors 1 we establish the algebraic analogs of three major decomposition theorems of nagy foias langer halmos wallen and fishel in baer rings this approach not only provides purely algebraic and shorter proofs of these decomposition theorems but also suggests the possibility of eliminating the role of analytic structure in results related to the invariant subspace theory

determination of optimal polygon from digital curve using l1 norm abstract a technique to determine optimal polygons of digital curves is proposed it determines the longest possible line segments with the minimum possible error the l 1 norm is used to measure the closeness of a polygon to a digital curve the algorithm runs in linear time the procedure is applied to several digital curves and promising results are obtained

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

a shimorin type analytic model on an annulus for left invertible operators and applications abstract a new analytic model for left invertible operators which extends both shimorin s analytic model for left invertible and analytic operators and gellar s model for bilateral weighted shift is introduced and investigated we show that a left invertible operator t which satisfies certain conditions can be modeled as a multiplication operator m z on a reproducing kernel hilbert space of vector valued analytic functions on an annulus or a disc a similar result for composition operators in l 2 spaces is established

space filling approach for fast window query on compressed images based on the space filling approach this paper presents a fast algorithm for window query on compressed images given a query window of size n sub 1 spl times n sub 2 the proposed algorithm takes o n sub 1 logt p time to perform the window query where n sub 1 max n sub 1 n sub 2 and t spl times t is the image size p is the number of outputted codes the proposed algorithm improves the naive algorithm which needs o n sub 1 n sub 2 log t p time significantly some experimentations are carried out to demonstrate the computational advantage of the proposed algorithm from the experimental results it is observed that the proposed algorithm has about 72 98 time improvement when compared to the naive algorithm

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

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

data reduction of large vector graphics fast algorithm for joint near optimal approximation of multiple polygonal curves is proposed it is based on iterative reduced search dynamic programming introduced earlier for the min eproblem of a single polygonal curve the proposed algorithm jointly optimizes the number of line segments allocated to the different individual curves and the approximation of the curves by the given number of segments trade off between time and optimality is controlled by the breadth of the search and by the numbers of iterations applied

open curve segmentation via a two phase scheme abstract a two phase scheme is proposed for the segmentation of open curves in the first phase the curvature of each point of the curve is calculated based on the coordinates of five skipped points and the assumption that these five points form a b spline curve the points with significant curvatures are collected as candidate corners during the second phase the candidate corners are verified for deviations in the global trend of the curve those with small deviations are considered excessive and are removed application of the proposed method in the segmentation of a typical pcb printed circuit board curve an aerial image of medioni and yasumoto comput vision graphics image process 39 267 278 1987 and a multi scale four semicircle curve of teh and chin ieee trans pattern analysis mach intell pami 11 859 872 1989 show that it is both minimal and accurate

using simple decomposition for smoothing and feature point detection of noisy digital curves this correspondence presents an algorithm for smoothed polygonal approximation of noisy digital planar curves and feature point detection the resulting smoothed polygonal representation preserves the signs of the curvature function of the curve the algorithm is based on a simple decomposition of noisy digital curves into a minimal number of convex and concave sections the location of each separation point is optimized yielding the minimal possible distance between the smoothed approximation and the original curve curve points within a convex concave section are discarded if their angle signs do not agree with the section sign and if the resulted deviations from the curve are less than a threshold spl epsi which is derived automatically inflection points are curve points between pairs of convex concave sections and cusps are curve points between pairs of convex convex or concave concave sections corners and points of local minimal curvature are detected by applying the algorithm to respective total curvature graphs the detection of the feature points is based on properties of pairs of sections that are determined in an adaptive manner rather than on properties of single points that are based on a fixed size neighborhood the detection is therefore reliable and robust complexity analysis and experimental results are presented

the structure of doubly non commuting isometries abstract suppose that n 1 and that for all i and j with 1 i j n and i j z i j t are given such that z j i z i j for all i j if v 1 v n are isometries on a hilbert space such that v i v j z i j v j v i for all i j then v 1 v n is called an n tuple of doubly non commuting isometries the generators of non commutative tori are well known examples in this paper we establish a simultaneous wold decomposition for v 1 v n this decomposition enables us to classify such n tuples up to unitary equivalence we show that the joint listing of a unitary equivalence class of a representation of each of the 2 n non commutative tori that are naturally associated with the structure constants is a classifying invariant a dilation theorem is also established showing that an n tuple of doubly non commuting isometries can be extended to an n tuple of doubly non commuting unitary operators on an enveloping hilbert space

shape recognition with a neural classifier based on a fast polygon approximation technique abstract a method is presented for the fast recognition of two dimensional 2d binary shapes with complicated form like islands on a map or medical images the proposed method is based on a new polygon approximation technique which extracts suitable feature vectors with specified dimension which characterizes a given shape these feature vectors are used as inputs in an efficient neural based classifier for the fast recognition of the shape the proposed technique is characterized by high speed performance which is desired for real time applications

optimal polygonal approximation of digitized curves using the sum of square deviations criterion abstract we address the problem of finding an optimal polygonal approximation of digitized curves several optimal algorithms have already been proposed to determine the minimum number of points that define a polygonal approximation of the curve with respect to a criterion error we present a new algorithm with reasonable complexity to determine the optimal polygonal approximation using the mean square error norm the idea is to estimate the remaining number of segments and to integrate the cost in the a algorithm the solution is optimal in the minimum number of segments

a comparison of neural net classifiers and linear tree classifiers their similarities and differences abstract both neural net classifiers utilizing multilayer perceptron and linear tree classifiers composed of hierarchically structured linear discriminant functions can form arbitrarily complex decision boundaries in the feature space and have similar decision making processes the structure of the linear tree classifier can be easily mapped to that of the neural nets having two hidden layers by using the hyperplanes produced by the linear tree classifier a new method for mapping the linear tree classifier to the neural nets having one hidden layer is presented with theoretical basis of mapping the convex decision regions produced by the linear tree classifier to the neurons in the neural nets this mapping may be useful for choosing appropriately sized neural nets having one or two hidden layers as well as for initializing the connection weights to speed up the learning rate and avoid the local trapping of the backpropagation algorithm also the internal operations of the hidden layer neurons in the three layer feedforward nets could be well described by this mapping experimental results on both synthetic and real data suggest that this mapping is effective and that there exists no significant difference in the classification accuracy of the neural net classifiers having one and two hidden layers substantial advantages of the neural net classifiers over the linear tree classifier were not found in the experiment while the latter is much faster in both training and classifying stages

moment preserving piecewise linear approximations of signals and images approximation techniques are an important aspect of digital signal and image processing many lossy signal compression procedures such as the fourier transform and discrete cosine transform are based on the idea that a signal can be represented by a small number of transformed coefficients which are an approximation of the original existing approximation techniques approach this problem in either a time spatial domain or transform domain but not both this paper briefly reviews various existing approximation techniques subsequently we present a new strategy to obtain an approximation f spl circ x of f x in such a way that it is reasonably close to the original function in the domain of the variable x and exactly preserves some properties of the transformed domain in this particular case the properties of the transformed values that are preserved are geometric moments of the original function the proposed technique has been applied to single variable functions two dimensional planar curves and two dimensional images and the results obtained are demonstrative

on piecewise linear approximation of planar jordan curves abstract the existence and uniqueness of a shortest polygonal path in a compact planar set bounded by two polygonal planar jordan curves is proved further the convergence of a sequence of planar polygonal curves to a rectifiable planar jordan curve and an application to piecewise linear approximation of boundaries of planar compact sets by a gridding technique is described

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

recognition of handwritten digits based on contour information abstract in this paper a new character recognition method based on topological properties positions of starting point statistical analysis and shape recognition is proposed for recognition of unconstrained handwritten digits based on various contour information first input digits are classified into three groups according to their topological properties in group 1 the features of normalized length of the digit contour the normalized area of the digit and fourier descriptors of the outer contour of a digit are used for recognition of digits in group 2 the relative position of outer and interior contour centroids the position of interior contour centroid the mean and the variance of the outer contour distance function and fourier descriptors of the outer contour of a digit are used for the recognition of digits in group 3 usually there is only one digit 8 but because of the complexity of writing styles some other digits are still classified into this group the final recognition is based on shape comparison of the input digit with models in the recognition process some special models are established and used for recognition of broken digits and digits whose topological properties are destroyed in our experiment 1000 digits from the nist database are used for training and 5278 unseen digits are used for testing the recognition rate has reached 98 5 with a reliability rate of 99 09 a substitution rate of 0 91 and a rejection rate of 0 59

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

efficient algorithms for 3 d polygonal approximation based on lise criterion abstract given a polygonal curve p in three dimensional 3 d space the polygonal approximation pa problem in this research is to find a polygon p to approximate p either with the minimal polygonal segments under a given error or conversely with the minimal error under a specified number of segments allowable the former pa problem is called the pa problem the latter pa problem is called the pa e problem given a 3 d p with n nodes under the local integral square error criterion this paper first presents an o n2 time algorithm for solving the pa problem using o n space then we present an o n 2 log n time algorithm for solving the pa e using o n2 space finally a sampling technique is employed to reduce the memory requirement from o n2 to o n some experiments are carried out to confirm the theoretical analysis

wold type decompositions in baer rings abstract a fundamental theorem due to wold asserts that an isometry t on a hilbert space h is the orthogonal direct sum of a unitary operator and a unilateral shift our main goal is to prove algebraic analogs of this result and its generalizations for commuting pairs of isometries in the context of baer rings our results not only extend wold type decomposition theorems from b h to arbitrary baer rings but also provide purely algebraic proofs of these known decomposition theorems which unlike their classic analogs are independent of the underlying hilbert space

equilateral polygon approximation of closed contours numerous algorithms have been suggested for computing polygonal approximations of closed contours we present an algorithm which as a unique feature creates polygons which are equilateral that is whose edges are all of the same length this allows one dimensional shape descriptions to be derived using the interior polygon angles conceptually the algorithm is an optimization framework for finding the minimum energy configuration of a mechanical system of particles and springs that represent the contour points the polygon vertices and their interaction in practice the dominant points are detected on the gaussian smoothed contour and used to seed an initial polygon nonlinear programming is then used to minimize the system energy subject to the constraint that adjacent vertices must be equidistant the objective function is the sum of a curvature weighted distance between each vertex and a set of contour points associated therewith experimental results are given for closed contours obtained from grey scale images

piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming based solution methods various optimization problems result from the introduction of nonlinear terms into combinatorial optimization problems in the context of energy optimization for example energy sources can have very different characteristics in terms of power range and energy demand cost function also known as efficiency function or energy conversion function introducing these energy sources characteristics in combinatorial optimization problems such as energy resource allocation problems or energy consuming activity scheduling problems may result into mixed integer nonlinear problems neither convex nor concave approximations via piecewise linear functions have been proposed in the literature non convex optimization models and heuristics exist to compute optimal breakpoint positions under a bounded absolute error tolerance we present an alternative solution method based on the upper and lower bounding of nonlinear terms using non necessarily continuous piecewise linear functions with a relative epsilon tolerance conditions under which such approach yields a pair of mixed integer linear programs with a performance guarantee are analyzed models and algorithms to compute the non necessarily continuous piecewise linear functions with absolute and relative tolerances are also presented computational evaluations performed on energy optimization problems for hybrid electric vehicles show the efficiency of the method with regards to the state of the art

the viterbi optimal runlength constrained approximation nonlinear filter simple nonlinear filters are often used to enforce hard syntactic constraints while remaining close to the observation data e g in the binary case it is common practice to employ iterations of a suitable median or a one pass recursive median openclose or closeopen filter to impose a minimum symbol runlength constraint while remaining faithful to the observation unfortunately these filters are in general suboptimal motivated by this observation we pose the following optimization given a finite alphabet sequence of finite extent y y n sub n 0 sup n 1 find a sequence x x n sub n 0 sup n 1 that minimizes d x y spl sigma sub n 0 sup n 1 d sub n y n x n subject to the following x is piecewise constant of plateau run length spl ges m we show how a suitable reformulation of the problem naturally leads to a simple and efficient viterbi type optimal algorithmic solution we call the resulting nonlinear input output operator the viterbi optimal runlength constrained approximation vorca filter the method can be easily generalized to handle a variety of local syntactic constraints the vorca is optimal computationally efficient and possesses several desirable properties e g idempotence we therefore propose it as an attractive alternative to standard median stack and morphological filtering we also discuss some applications

moment based methods for polygonal approximation of digitized curves object shape representation plays an important role in the area of image processing pattern recognition and computer vision in the past two decades many algorithms have been suggested for creating approximated polygons in this study two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of legendre polynomials are proposed the difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function each algorithm provides various polygonal approximation results with different number of line segments for different application situations for a given error bound we can determine the optimal polygon with a minimum number of line segments the procedures are applied to some digital curves and better results are obtained in comparison with some known methods

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

dynamic two strip algorithm in curve fitting abstract in this paper a new dynamic strip algorithm for fitting a curve with lines is presented the algorithm first finds the best fitted left hand side and right hand side strips at each point on the curve a figure of merit is computed based on the fitting results then a local maximum detection process is applied to pick out points of high curvature the approximated curve is one with the high curvature points connected by straight lines the global structure of a shape which is insensitive to a scale and orientation changes is obtained by merging the results from several runs of the algorithm with different minimum strip widths

a method for representing shape based on an equivalence relation on polygons abstract it is proved that there is a correspondence between deformations of polygons and a grammar this gives rise to an o n lo g n algorithm to match regions whose connectivity has been changed based on boundary contours this has application to problems in handwriting recognition it is then shown that deformations of polygons can be decomposed into canonical types this gives rise to new types of features to measure symmetry handedness rigidity bending and stretching

wold type decompositions and wandering subspaces for operators close to isometries for operators t satisfying certain inequalities we obtain a weak analog of the classical wold kolmogorov decomposition theorem representing t as a direct sum of a unitary operator and a shift operator acting in some hilbert space of analytic functions the concept of a dual operator is introduced which reflects relationships between shift operators acting in two hilbert spaces of analytic functions dual to each other with respect to the cauchy pairing among different aspects of this duality we consider relationships between hereditary inequalities and properties of reproducing kernels

determining the 3 d pose of a flexible object by stereo matching of curvature representations a 3 d pose determining method for flexible objects is developed by which the stereo matching problem of images is transformed into the matching of two curvature representations a heuristic chain coding method is presented for the chain coding of self overlapped skeletonized images and a wrapping method to cope with abrupt changes in curvature representations is described two curvature based stereo matching methods are proposed to determine the 3 d poses of flexible objects experimental results with real flexible objects are presented

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

a curve bend function based method to characterize contour shapes in this paper a new curve bend function cbf based method is presented to extract main features of a contour it utilizes two quantities one called a curve bend angle cba and the other known as a type coefficient of curve segment defined on a contour the cba measures the bending degree at each point on the contour while the type coefficient characterizes the properties convexity and concavity of simple curve segments the cbf combines the advantages of the two quantities and provides an overall description of a contour a local maximum or minimum of the cbf corresponds to a critical point of the contour and the peak value is the cosine of the cba hence the problem of locating critical points of a contour is reduced to the problem of finding peak points of the cbf the sign of a peak value indicates the related cba being an inner or outer angle our experimental results and comparisons between the cbf method and rosenfeld johnston s method show that our method is effective and accurate in generating the description of a contour

invariant subspaces of h2 t2 and l2 t2 preserving compatibility abstract operators of multiplication by independent variables on the space of square summable functions over the torus and its hardy subspace are considered invariant subspaces where the operators are compatible are described

structure theorems for star commuting power partial isometries abstract we give a new formulation and proof of a theorem of halmos and wallen on the structure of power partial isometries on hilbert space we then use this theorem to give a structure theorem for a finite set of partial isometries which star commute each operator commutes with the others and with their adjoints