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

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

optimal polygonal approximation of digital curves abstract an algorithm for optimal polygonal approximation is presented given a value for the maximal allowed distance between the approximation and the curve the algorithm finds an approximation with the minimal number of vertices the city block metric is used to measure the distance between the approximation and the curve the algorithm worst case complexity is o n 2 where n is the number of points in the curve an efficient and optimal solution for the case of closed curves where no initial point is given is also presented

on automatic threshold selection for polygonal approximations of digital curves polygonal approximation is a very common representation of digital curves a polygonal approximation depends on a parameter e which is the error value in this paper we present a method for an automatic selection of the error value e let e be a polygonal approximation of the original curve with an error value e we define a set of function ns e s s s such that for a given value of s ns e is the number of edges that contain at least s vertices in e the time complexity for computing the set of functions ns e s ss s is almost linear in n the number of vertices in in this paper we analyse the ns graph and show that for adequate values of s a wide plateau is expected to appear at the top of the graph this plateau corresponds to a stable state in the multi scale representation of e we show that the functions ns s s are a statistical representation of some kind of scale space image

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

reduced length checking sequences here the method proposed by ural wu and zhang 1997 for constructing minimal length checking sequences based on distinguishing sequences is improved the improvement is based on optimizations of the state recognition sequences and their use in constructing test segments it is shown that the proposed improvement further reduces the length of checking sequences produced from minimal completely specified and deterministic finite state machines

the rate of total entropy generation for riemann problems abstract under fairly broad conditions we establish a lower bound for the rate of total entropy generation associated with a similarity solution of a riemann problem for a hyperbolic system of conservation laws for weak riemann problems under more restrictive assumptions we show that dafermos entropy condition is equivalent to the classical condition

a piecewise linear approximation based on a statistical model a statistical model is introduced and then based on it a piecewise linear approximation algorithm of linear computational complexity is presented the advantages of the algorithm are proved experimentally in small sample cases and theoretically in the large sample case the paper is closed with a discussion on some possible extensions

on minimizing the lengths of checking sequences a general model for constructing minimal length checking sequences employing a distinguishing sequence is proposed the model is based on characteristics of checking sequences and a set of state recognition sequences some existing methods are shown to be special cases of the proposed model and are proven to construct checking sequences the minimality of the resulting checking sequences is discussed and a heuristic algorithm for the construction of minimal length checking sequences is given

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

computing the shortest network under a fixed topology we show that in any given uniform orientation metric plane the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations when the given topology is restricted to a steiner topology our result implies that the steiner minimum tree under a given steiner topology can be computed in polynomial time in any given uniform orientation metric with spl lambda legal orientations for any fixed integer spl lambda spl ges 2 this settles an open problem posed by brazil thomas and weng 2000

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

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

observability of finite labeled transition systems finite labeled transition systems are nondeterministic and nontotal systems with finitely many inputs states and outputs this paper provides algorithms for verifying the observability of finite labeled transition systems in the so called multiple experiment case the simple experiment case and the arbitrary experiment case respectively where these algorithms run in exponential time exponential time and quartic polynomial time respectively and are more effective than the existing algorithms in the literature

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

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

existence in the large for riemann problems for systems of conservation laws on obtient un theoreme d existence pour le probleme de riemann pour des systemes non lineaires de lois de conservation on utilise l inegalite d entropie pour obtenir une estimation a priori des forces des chocs et des ondes de refraction formant une solution il s ensuit l existence d une telle solution par une application de la theorie du degre de dimension finie

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

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

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

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

uniqueness failure for entropy solutions of hyperbolic systems of conservation laws we consider a nonlinear system of conservation laws which is strictly hyperbolic genuinely nonlinear in the large equipped with a convex entropy function and global riemann invariants nevertheless for such a system for dimension five it is shown that uniqueness of the similarity solution of a riemann problem satisfying the entropy condition can fail

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

testing finite state machines state identification and verification we study the complexity of two fundamental problems in the testing of finite state machines 1 distinguishing sequences state identification we show that it is pspace complete to determine whether a finite state machine has a preset distinguishing sequence there are machines that have distinguishing sequences but only of exponential length we give a polynomial time algorithm that determines whether a finite state machine has an adaptive distinguishing sequence the previous classical algorithms take exponential time furthermore if there is an adaptive distinguishing sequence then we give an efficient algorithm that constructs such a sequence of length at most n n spl minus 1 2 which is the best possible where n is the number of states 2 unique input output sequences state verification it is pspace complete to determine whether a state of a machine has a unique input output sequence there are machines whose states have unique input output sequences but only of exponential length

verification of initial state opacity in security applications of discrete event systems in this paper we formulate and analyze methodologies for verifying the notion of initial state opacity in discrete event systems that are modeled as non deterministic finite automata with partial observation on their transitions a system is initial state opaque if the membership of its true initial state to a set of secret states remains opaque i e uncertain to an intruder who observes system activity through some projection map initial state opacity can be used to characterize security requirements in a variety of applications including tracking problems in sensor networks in order to model and analyze the intruder capabilities regarding initial state opacity we first address the initial state estimation problem in a non deterministic finite automaton via the construction of an initial state estimator we analyze the properties and complexity of the initial state estimator and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant we also establish that the verification of initial state opacity is a pspace complete problem