generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

efficient parallel algorithms for string editing and related problems the string editing problem for input strings x and y consists of transforming x into y by performing a series of weighted edit operations on x of overall minimum cost an edit operation on x can be the deletion of a symbol from x the insertion of a symbol in x or the substitution of a symbol of x with another symbol this problem has a well known o x y time sequential solution efficient pram parallel algorithms for the string editing problem are given if m min x y and n max x y then the crew bound is o log m log n time with o mn log m processors the crow bound is o log n log log m 2 time with o mn log log m processors in all algorithms space is o mn

optimal correspondence of string subsequences the definition of optimal correspondent subsequence ocs which extends the finite alphabet editing error minimization matching to infinite alphabet penalty minimization matching is given the authors prove that the string distance derived from ocs is a metric an algorithm to compute the string to string ocs is given the computational complexity of ocs is analyzed ocs is more efficient than relaxation and elastic matching for 1d problems an algorithm combining syntactic information in template matching is given to show the ease of integrating regular grammar into the ocs technique since in different applications different penalty functions may be required two of them are discussed one pointwise and the other piecewise the pointwise application consists of a stereo epipolar line matching problem solved by using string to string ocs the feasibility of applying ocs to upc bar code recognition is investigated showing the elegance of string to regular expression ocs compared to the relaxation and elastic matching techniques

spherical and hyperbolic embeddings of data many computer vision and pattern recognition problems may be posed as the analysis of a set of dissimilarities between objects for many types of data these dissimilarities are not euclidean i e they do not represent the distances between points in a euclidean space and therefore cannot be isometrically embedded in a euclidean space examples include shape dissimilarities graph distances and mesh geodesic distances in this paper we provide a means of embedding such non euclidean data onto surfaces of constant curvature we aim to embed the data on a space whose radius of curvature is determined by the dissimilarity data the space can be either of positive curvature spherical or of negative curvature hyperbolic we give an efficient method for solving the spherical and hyperbolic embedding problems on symmetric dissimilarity data our approach gives the radius of curvature and a method for approximating the objects as points on a hyperspherical manifold without optimisation for objects which do not reside exactly on the manifold we develop a optimisation based procedure for approximate embedding on a hyperspherical manifold we use the exponential map between the manifold and its local tangent space to solve the optimisation problem locally in the euclidean tangent space this process is efficient enough to allow us to embed data sets of several thousand objects we apply our method to a variety of data including time warping functions shape similarities graph similarity and gesture similarity data in each case the embedding maintains the local structure of the data while placing the points in a metric space

differential algebraic systems as differential equations on manifolds based on the theory of differential equations on manifolds existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications both the autonomous and nonautonomous case are considered moreover a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower dimensional manifolds this class includes systems for which the application of ode solvers is known to lead to difficulties finally some solution approach based on continuation techniques is outlined

dynamic programming alignment of sequences representing cyclic patterns string alignment by dynamic programming is generalized to include cyclic shift and corresponding optimal alignment cost for strings representing cyclic patterns a guided search algorithm uses bounds on alignment costs to find all optimal cyclic shifts the bounds are derived from submatrices of an initial dynamic programming matrix algorithmic complexity is analyzed for major stages in the search the applicability of the method is illustrated with satellite dna sequences and circularly permuted protein sequences

algorithms for approximate string matching the edit distance between strings a 1 a m and b 1 b n is the minimum cost s of a sequence of editing steps insertions deletions changes that convert one string into the other a well known tabulating method computes s as well as the corresponding editing sequence in time and in space o mn in space o min m n if the editing sequence is not required starting from this method we develop an improved algorithm that works in time and in space o s min m n another improvement with time o s min m n and space o s min s m n is given for the special case where all editing steps have the same cost independently of the characters involved if the editing sequence that gives cost s is not required our algorithms can be implemented in space o min s m n since s o max m n the new methods are always asymptotically as good as the original tabulating method as a by product algorithms are obtained that given a threshold value t test in time o t min m n and in space o min t m n whether s t finally different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets including for example transposition of adjacent characters

monge properties of sequence alignment alignment is an important sequence comparison measure algorithms that compute alignments have a wide range of applications namely in bioinformatic tools alignments can be computed as maximum scoring paths in alignment dags in this paper we study the properties of matrices that contain alignment scores between a string and all the sub strings of another string we focus on the fact that these matrices have the monge property and are sparse in some sense related studies were recently presented for hsm and dist matrices leading to o nlogn procedure for multiplying those matrices where o n bounds the sizes of the strings our results strictly generalize previous solutions we measure the sparseness of the matrices with variable d and present an algorithm for matrix multiplication in o email protected log 3 email protected time which we improve to o email protected log 2 email protected within the same space we discuss applications of this algorithm namely fully incremental alignment and alignment update we study experimentally the performance of the methods we propose

on a computational method for the second fundamental tensor and its application to bifurcation problems an algorithm is presented for the computation of the second fundamental tensorv of a riemannian submanifoldm ofr n fromv the riemann curvature tensor ofm is easily obtained moreover v has a close relation to the second derivative of certain functionals onm which in turn provides a powerful new tool for the computational determination of multiple bifurcation directions frequently in applications thed dimensional manifoldm is defined implicitly as the zero set of a submersionf onr n in this case the principal cost of the algorithm for computingv p at a given pointp m involves only the decomposition of the jacobiandf p off atp and the projection ofd d 1 neighboring points ontom by means of a local iterative process usingdf p several numerical examples are given which show the efficiency and dependability of the method

solving algebraically explicit daes with the manpak manifold algorithms abstract recently the author introduced a package of algorithms called manpak for effective computations on implicitly defined submanifolds of r n here algebraically explicit differential algebraic equations daes are considered that is daes in which either the algebraic equations and or the algebraic variables are explicitly specified existence proofs for several types of such daes of index one two and three are given which directly suggest computational approaches this is used in the development of solution algorithms for these daes all of them intrinsically based on the manpak routines some numerical examples for the methods are included

fast object recognition using dynamic programming from combination of salient line groups this paper presents a new method of grouping and matching line segments to recognize objects we propose a dynamic programming based formulation extracting salient line patterns by defining a robust and stable geometric representation that is based on perceptual organizations as the endpoint proximity we detect several junctions from image lines we then search for junction groups by using the collinear constraint between the junctions junction groups similar to the model are searched in the scene based on a local comparison a dp based search algorithm reduces the time complexity for the search of the model lines in the scene the system is able to find reasonable line groups in a short time

longest common subsequence problem for unoriented and cyclic strings given a finite set of strings x the longest common subsequence problem lcs consists in finding a subsequence common to all strings in x that is of maximal length lcs is a central problem in stringology and finds broad applications in text compression conception of error detecting codes or biological sequence comparison however in numerous contexts words represent cyclic or unoriented sequences of symbols and lcs must be generalized to consider both orientations and or all cyclic shifts of the strings involved this occurs especially in computational biology when genetic material is sequenced from circular dna or rna molecules in this work we define three variants of lcs when the input words are unoriented and or cyclic we show that these problems are np hard and w 1 hard if parameterized in the number of input strings these results still hold even if the three lcs variants are restricted to input languages over a binary alphabet we also settle the parameterized complexity of our problems for most relevant parameters moreover we study the approximability of these problems we discuss the existence of approximation bounds depending on the cardinality of the alphabet on the length of the shortest sequence and on the number of input sequences for this we prove that maximum independent set in r uniform hypergraphs is w 1 hard if parameterized in the cardinality of the sought independent set and at least as hard to approximate as maximum independent set in graphs

manpak a set of algorithms for computations on implicitly defined manifolds abstract mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations the resulting computational tasks differ considerably from those arising for manifolds defined in parametric form here a collection of algorithms is presented for performing a range of essential tasks on general implicitly specified submanifolds of a finite dimensional space this includes algorithms for determining local parametrizations and their derivatives and for evaluating quantities related to the curvature with sensitivity measures the methods have been implemented as a fortran 77 package called manpak

polygonal shape recognition using string matching techniques in this paper we study several aspects of the use of string matching techniques as an approach to the problem of recognizing and classifying polygons several authors have already proposed methods for polygon recognition that are based on string matching in many cases however linear strings are used to represent polygons which makes it difficult to handle different orientations of an object efficiently we can however easily extend the linear string matching techniques to cyclic strings at some small computational cost we will propose a method to represent polygons as cyclic strings and we will show how cyclic string matching techniques can be used for rotation translation and scale independent polygonal shape recognition we will however also point out the limitations of such an approach

an improved algorithm for solving the banded cyclic string to string correction problem the banded cyclic string to string correction bcssc problem is a generalized version of the cyclic string to string correction cssc problem and has some applications in stereo matching and speech recognition this note presents an improved algorithm for solving the bcssc problem and the time complexity required ranges from o nm to o nm log b where n and m are the lengths of the two strings and b is the allowable bandwidth the result of this paper generalizes the result of gregor and thomason 1996 for solving the cssc problem since the special version of the bcssc problem can be transformed into the cssc problem when setting b m

on the sensitivity of solutions of parameterized equations the sensitivity of a solution of a parameterized equation f z lambda 0 with respect to the parameter vector lambda is usually defined as the change of the state z in dependence of lambda in other words for any solution expressible in the form z lambda lambda with some smooth function z z lambda the sensitivity is the derivative dz lambda typically the solutions form a manifold m in the product of 1the state space and the parameter space and this sensitivity is available only at those points of m where the parameters can be used to define a local coordinate system this paper introduces a general sensitivity concept which applies at all solutions on m and which includes the earlier definition some general geometric interpretations of the new measure are presented and it is shown that the sensitivity analysis can be easily integrated into the solution process the theory also suggests the introduction of a readily computable second order sensitivity measure reflectin

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

efficient dynamic programming alignment of cyclic strings by shift elimination abstract optimal alignment of two strings of length m and n is computed in time o mn by dynamic programming when the strings represent cyclic patterns the alignment computation must consider all possible shifts and the computation complexity increases accordingly we present an algorithm for efficient dynamic programming alignment of cyclic strings which uses a previously established channeling technique to reduce the complexity of each alignment and a new shift elimination technique to reduce the number of alignments carried out the result is a data dependent time complexity that varies between o 2 mn and o mn log 2 n an experimental evaluation is provided using randomly generated sequences

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

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

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

applications of approximate string matching to 2d shape recognition abstract a new method for the recognition of arbitrary two dimensional 2d shapes is described it is based on string edit distance computation the recognition method is invariant under translation rotation scaling and partial occlusion a set of experiments are described demonstrating the robustness and reliability of the proposed approach

the computation of simplicial approximations of implicitly defined p dimensional manifolds abstract a method is presented for the computation of a simplicial approximation covering a subset m 0 of a p dimensional manifold m in r n defined implicitly as the solution set of a nonlinear system f x 0 of n p equations in n unknowns n p 2 the subset m 0 is either the intersection of m with some polyhedral domain in r n and is assumed to be bounded and nonempty or it is an entire manifold component which has no boundary such as a sphere the method represents a generalization of a simplicial approximation process for the case p 2 developed earlier by the author and w rheinboldt

edit distance based kernel functions for structural pattern classification a common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance based nearest neighbor classifier in this paper we introduce an alternative method for classification using kernel functions based on edit distance the proposed approach is applicable to both string and graph representations of patterns by means of the kernel functions introduced in this paper string and graph classification can be performed in an implicit vector space using powerful statistical algorithms the validity of the kernel method cannot be established for edit distance in general however by evaluating theoretical criteria we show that the kernel functions are nevertheless suitable for classification and experiments on various string and graph datasets clearly demonstrate that nearest neighbor classifiers can be outperformed by support vector machines using the proposed kernel functions