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

interpolation by vector valued analytic functions with applications to controllability in this paper norm estimates are obtained for the problem of minimal norm tangential interpolation by vector valued analytic functions expressed in terms of the carleson constants of related scalar measures applications are given to the controllability properties of linear semigroup systems with a riesz basis of eigenvectors

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

optimization models for shape matching of nonconvex polygons abstract the shape matching problem is concerned with fitting an input shape represented by a set of discrete boundary data to a defect free reference shape two aspects of the problem must be considered 1 shape modeling and 2 matching algorithm in this paper two shape modeling schemes are proposed to represent the reference shape by a set of primitives in which the object geometric configuration is encoded the primitives uniquely define the pose and dimension of a given polygonal object based on these models optimization matching procedures that use the least squares criterion to find the best fitting between the set of scene data and the reference shape are developed the complexity analysis and computational results show our shape matching approaches to be extremely fast

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

on zero preserving linear transformations for an arbitrary subset i of r and for a function f defined on i the number of zeros of f on i will be denoted byzi f in this paper we attempt to characterize all linear transformations t taking a linear subspace w of c i into functions defined on j i j r such thatzi f zj tf for all f w

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

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

a general necessary condition for exact observability suppose a generates an exponentially stable strongly continuous semigroup on the hilbert space x y is another hilbert space and c d a rightarrow y is an admissible observation operator for this semigroup this means that to any initial state in x we can associate an output function in l 2 0 infty y this paper gives a necessary condition for the exact observability of the system defined by a and c this condition called bf e is related to the hautus lemma from finite dimensional systems theory it is an estimate in terms of the operators a and c alone in particular it makes no reference to the semigroup this paper shows that bf e implies approximate observability and if a is bounded it implies exact observability this paper conjectures that bf e is in fact equivalent to exact observability the paper also shows that for diagonal semigroups bf e takes on a very simple form and applies the results to sequences of complex exponential functions

ordered structural shape matching with primitive extraction by mathematical morphology abstract structural shape matching procedures begin by decomposing the shapes to be matched into primitive parts and extracting the properties of and relationships among these primitives the resultant structural descriptions are matched to structural models usually via a tree search whose time is exponential in the number of primitives in this paper we introduce a new fast method of structural shape matching called ordered structural matching which has polynomial time complexity instead of exponential the approach presented also uses mathematical morphology to rapidly decompose the shapes into primitives to be used in the matching the primitives so produced are pieces of the original shape but not necessarily those pieces that a human would select the method has been tested on the toy task of determining which plastic shapes match the shapes of the holes in a child s six sided toy box it is also directly applicable to the inspection and manipulation of certain airplane parts

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

pac learning with generalized samples and an applicaiton to stochastic geometry an extension of the standard probably approximately correct pac learning model that allows the use of generalized samples is introduced a generalized sample is viewed as a pair consisting of a functional on the concept class together with the value obtained by the functional operating on the unknown concept it appears that this model can be applied to a number of problems in signal processing and geometric reconstruction to provide sample size bounds under a pac criterion a specific application of the generalized model to a problem of curve reconstruction is considered and some connections with a result from stochastic geometry are discussed

the signature of a plane curve the signature of a plane curve gamma associated with every point p of gamma the length of gamma to the left of or on the line tangent to gamma at p the signature has properties that make it a useful tool for pattern recognition it discards the location orientation and scale and slant in special cases but preserves symmetries its integral is a measure of convexity this paper explores the theoretical properties of this concept it is shown that in the special case of closed rectilinear curves the signature retains enough information to permit exact reconstruction of the curve computing the signature and reconstructing curves from their signatures are interesting computational problems time complexity bounds on these problems are presented several challenging open questions are posed

necessary conditions for exact controllability with a finite dimensional input space we derive necessary conditions for exact controllability of infinite dimensional systems described by x ax bu where the generator a has a riesz basis of eigenvectors and the input space is finite dimensional these conditions are in terms of the eigenvalues of a and the degree of unboundedness of b but no further information about b is needed our results easily imply lack of exact controllability for a wide range of distributed parameter systems it is known from partial differential equation pde examples that the addition of damping into an exactly controllable second order system can destroy exact controllability we discuss the effect of damping on such systems using our general conditions we also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension

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

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

contour sequence moments for the classification of closed planar shapes abstract a technique for classifying closed planar shapes is described in which a shape is characterized by a one dimensional sequence that represents the euclidean distance between the centroid and all contour pixels of the shape contour sequences obtained from shapes belonging to the same class are similar and are considered to be different realizations of a stochastic process statistical moment functions derived from contour sequences are used to characterize the process and hence the shapes it is shown that these moment functions are invariant to shape translation rotation and scale transformations examples are presented to illustrate the performance of these moment functions in the classification of noisy shapes

total curvature and intersection tomography abstract we show how to reconstruct certain one dimensional generalized sets in the plane which we callk sets from their projections a projection onto a linegat the pointpcounts with multiplicities the number of points in the set which lie on the line which is perpendicular togand passes throughp we also prove a formula analogous to crofton s formula relating the total absolute curvature of such a set to the average total variation of its projections the formulation of the class ofk sets captures a notion of finite total absolute curvature that is independent of parametrizations we define the total absolute curvature of ak set to be the minimal total absolute curvature of a collection of curves which represent the set

segmentation of two dimensional boundaries using the chain code abstract we divide the boundary of a two dimensional object into segments each of which is either straight or a circular arc associated with the segment end points are angle measures that can be used to match an object with a transformed rotated scaled version of itself the chain code easily extracted from the boundary pixels is the basis of this division the approach avoids problems common to many of the existing methods for identification of curvature extrema sensitivity to noise and dependence on parameters that are chosen empirically to each section of the boundary we assign a code that represents the change in slope between it and the previous section this set of codes is integrated and thus provides a measure of the total directional change relative to the first section for a closed object the sequence of these sums is periodic and one cycle can be plotted as a function of arc length s such a plot can be shown to contain only straight lines those that are not parallel to the s axis representing circular arcs on the original boundary of the object and those that are representing straight sections on the boundary this paper describes a recursive procedure for dividing the digital version of the curve described above into its linear segments each segment represents an arc that is the best fit to a portion of the original boundary the angle which is defined by the arc is identical to the angle change of the edge in the same section and the length of the arc is identical to that of the edge the recursive procedure measures the error for each value of arc length between a proposed fitting line and the actual value of cumulative angle where the error is maximum and above a threshold the line is segmented the procedure is repeated until the error is sufficiently small the breakpoints thus indicate the location and value of points of greatest curvature change a formal definition of the procedure is given and it is shown to perform well for rotated scaled and noisy objects

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

on line segmentation of freehand sketches by knowledge based nonlinear thresholding operations this paper describes an on line procedure for segmenting freehand sketches into 2d primitives and smooth curves by knowledge based nonlinear thresholding operations drawing position direction speed and acceleration information is used for establishing fuzzy knowledge and inferring user s intention the procedure can be divided into three stages 1 obtaining corner points based on the fuzzy knowledge and adaptive thresholds which includes detecting obtuse and acute corner points 2 finding smooth join points during which stage we use both curve linearity and curvature and 3 classifying the sketches into the corresponding curves according to curve linearity and changes of curve convexity the method is illustrated and tested with a number of sketches

on controllability of diagonal systems with one dimensional input space abstract this paper deals with diagonal systems on a hilbert state space with a one dimensional input space and a possibly unbounded control operator a priori it is not assumed that the input operator is admissible necessary and sufficient conditions for different notions of controllability such as null controllability exact controllability and approximate controllability are presented these conditions which are given in terms of the eigenvalues of the diagonal operator and in terms of the control operator are linked with the theory of interpolation in hardy spaces

a method for shift rotation and scale invariant pattern recognition using the form and arrangement of pattern specific features abstract a new computer based method for visual pattern recognition is described the process extracts shape features from binary edge images represented in either real valued or discrete coordinates both separate and overlapping features are extracted maximizing their completeness and continuity without using templates or mathematical feature descriptions these features and their arrangement are encoded in a shift rotation and scale invariant manner and used to recognize incoming patterns from a set of previously encoded patterns stored in memory new patterns may be automatically classified and stored in memory allowing the system to learn and generalize without operator intervention testing shows the system to be completely shift rotation and scale invariant and insensitive to local image distortion

weighted interpolation in paley wiener spaces and finite time controllability this paper considers the solution of weighted interpolation problems in model subspaces of the hardy space h 2 that are canonically isometric to paley wiener spaces of analytic functions a new necessary and sufficient condition is given on the set of interpolation points which guarantees that a solution in h 2 can be transferred to a solution in a model space the techniques used rely on the reproducing kernel thesis for hankel operators which is given here with an explicit constant one of the applications of this work is to the finite time controllability of diagonal systems specified by a c 0 semigroup c 2010 elsevier inc all rights reserved

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

applications of laplace carleson embeddings to admissibility and controllability it is shown how results on carleson embeddings induced by the laplace transform can be used to derive new and more general results concerning the weighted infinite time admissibility of control and observation operators for linear semigroup systems with q riesz bases of eigenvectors as an example the heat equation is considered next a new carleson embedding result is proved which gives further results on weighted admissibility for analytic semigroups finally controllability by smoother inputs is characterized by means of a new result about weighted interpolation