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

comparison results for parallel multisplitting methods with applications to aor methods abstract in this paper we present some comparison theorems between two general parallel multisplittings these comparison theorems can be applied to many classical splittings such as jacobi gauss seidel and aor splittings some significant improvements and generalizations of the existing comparison results are obtained

nonnegative splittings for rectangular matrices the extension of the nonnegative splitting for rectangular matrices called proper nonnegative splitting is proposed first different convergence and comparison theorems for the proper nonnegative splittings are established the notion of double nonnegative splitting is then generalized to rectangular matrices finally different convergence and comparison results are presented for this decomposition the case for singular square matrices is also studied

comparisons of nonnegative splittings of matrices abstract the comparison of the asymptotic rates of convergence of two iteration matrices induced by two splitting of the same matrix has arisen in the work of many authors in this article some new comparison theorems for two nonnegative splittings a splitting a m n is nonnegative if m 1 exist and m 1 n is nonnegative are derived they extend the known results in the literature in addition we also point out three incorrect conditions in a paper by beauwens furthermore we give some reasonable conditions ensuring the strict inequality between the asymptotic convergence rates this also answers the open question which additional and appropriate conditions should be imposed on miller neumann splittings to obtain strict inequality finally some applications to a class of generalized aor sor and jor iterative methods whose special cases imply block also point aor sor and jor iterative methods for solving linear systems are discussed

weighted max norms splittings and overlapping additive schwarz iterations summary weighted max norm bounds are obtained for algebraic additive schwarz iterations with overlapping blocks for the solution of ax b when the coefficient matrix a is an m matrix the case of inexact local solvers is also covered these bounds are analogous to those that exist using a norms when the matrix a is symmetric positive definite a new theorem concerningp regular splittings is presented which provides a useful tool for the a norm bounds furthermore a theory of splittings is developed to represent algebraic additive schwarz iterations this representation makes a connection with multisplitting methods with this representation and using a comparison theorem it is shown that a coarse grid correction improves the convergence of additive schwarz iterations when measured in weighted max norm

new parallel sor method by domain partitioning in this paper we propose and analyze a new parallel sor method the psor method formulated by using domain partitioning and interprocessor data communication techniques we prove that the psor method has the same asymptotic rate of convergence as the red black r b sor method for the five point stencil on both strip and block partitions and as the four color r b g o sor method for the nine point stencil on strip partitions we also demonstrate the parallel performance of the psor method on four different mimd multiprocessors a ksr1 an intel delta a paragon and an ibm sp2 finally we compare the parallel performance of psor r b sor and r b g o sor numerical results on the paragon indicate that psor is more efficient than r b sor and r b g o sor in both computation and interprocessor data communication

some comparison theorems for nonnegative splittings of matrices in a recent paper the author has proposed some theorems on the comparison of the asymptotic rates of convergence of two nonnegative splittings they extended the corresponding result of miller and neumann and implied the earlier theorems of varga beauwens csordas and varga an open question by miller and neumann which additional and appropriate conditions should be imposed to obtain strict inequality was also answered this article continues to investigate the comparison theorems for nonnegative splittings the new results extend and imply the known theorems by the author miller and neumann

convergence of parallel multisplitting iterative methods for m matrices abstract despite the major recent activity in parallel processing few effective new algorithms designed exclusively for multiprocessors have been put forth one such is the multisplitting iterative algorithm suggested by o leary and white although they have given some sufficient conditions for convergence a general convergence theory has not been developed even for the classical situation where the coefficient matrix a is an m matrix or is symmetric positive definite in this paper we study the m matrix case in detail the multisplitting process for a rn n is recast as an ordinary iterative process for a certain block matrix a r kn kn where k is the number of processors and standard convergence results are used to develop a convergence theory for multisplitting iterative methods where a is an m matrix comparison results between multisplitting methods are established in terms of monotonic norms and for the case where a is irreducible in terms of the asymptotic convergence rate a key observation here is that in certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of a and is independent of the manner in which the work is distributed among the processors thus in general one can distribute the work for load balancing purposes without affecting the convergence rate

bd splittings of matrices abstract a new matrix decomposition of real square singular matrices called b d splitting is proposed by extending the notion of b splitting 16 for nonsingular matrices then different convergence and comparison theorems for these splittings are discussed another convergence theorem using a generalized regular splitting is also proved as a result a new characterization of monotone matrices using regular splitting is obtained as a corollary

positive cones and convergence conditions for iterative methods based on splittings the study of convergence conditions to solve large and sparse linear systems ax b by iterative methods has been discussed by many authors in this paper by using the partial order induced by positivity cone of matrices and conditions on the matrices and splittings we obtain the convergence of the iterative method the usual partial orders of nonnegative matrices and nonnegative definite matrices satisfy the conditions presented for this new order and hence we unify the theory moreover we also show that the new conditions apply to other partial orders as well thus extending the usual convergence theory to a new situation

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

on the perron frobenius theory for complex matrices abstract we extend here the perron frobenius theory of nonnegative matrices to certain complex matrices following the generalization of the perron frobenius theory to matrices that have some negative entries given by noutsos 14 we introduce here two types of extensions of the perron frobenius theory to complex matrices we present and prove here some sufficient conditions and some necessary and sufficient conditions for a complex matrix to have a perron frobenius eigenpair we apply this theory by introducing perron frobenius splittings as well as complex perron frobenius splittings for the solution of complex linear systems a x b by classical iterative methods perron frobenius splittings constitute an extension of the well known regular splittings weak regular splittings and nonnegative splittings convergence and comparison properties are also given and proved

the effect of the number of processors on the convergence of the parallel block jacobi method abstract we investigate the effect on the rate of convergence of a model of the asychronized parallel iteration method of allowing the number of processors to differ from the number of splittings under certain regularization assumptions we prove that decreasing the number of processors increases the convergence rate our interpretation of this result for the model is as follows increasing the number of processors means that each processor updates the global approximation in the host node with a local iteration which is computed from older global data hence the convergence rate is reduced to prove our results we develop theorems for comparison of the spectral radii for certain nonnegative matrices which are of interest in their own right we provide numerical examples to illustrate our results

minimization of norms and the spectral radius of a sum of nonnegative matrices under diagonal equivalence abstract we generalize in various directions a result of friedland and karlin on a lower bound for the spectral radius of a matrix that is positively diagonally equivalent to a doubly stochastic matrix the original result characterizes the equality case for two special zero patterns of the doubly stochastic matrix here we characterize the equality cases for doubly stochastic matrices of general zero pattern we further generalize the results to sums of matrices that are diagonally equivalent to doubly stochastic matrices our claims follow from inequalities we prove on norms of matrices finally we prove the corresponding inequalities and equalities for nonnegative matrices that are not sums of matrices diagonally equivalent to doubly stochastic matrices

effective equidistribution for closed orbits of semisimple groups on homogeneous spaces we prove effective equidistribution with polynomial rate for large closed orbits of semisimple groups on homogeneous spaces under certain technical restrictions notably the acting group should have finite centralizer in the ambient group the proofs make extensive use of spectral gaps and also of a closing lemma for such actions

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

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

comparison theorems for splittings of matrices this paper investigates the comparisons of asymptotic rates of convergence of two iteration matrices on the basis of nonnegative matrix theory comparisons between two nonnegative splittings and between two parallel multisplitting methods are derived when the coefficient matrix a is hermitian positive semi definite comparison theorems about two p regular splittings and two parallel multisplitting methods are proved

a note on comparison theorems for splittings and multisplittings of hermitian positive definite matrices abstract we discuss iterative methods for the solution of the linear system ax b which are based on a single splitting or a multisplitting of a in order to compare different methods it is common to compare the spectral radius of the iterative matrix for m matrices a and weak regular splittings there exist well known comparison theorems here we give a comparison theorem for splittings of hermitian positive definite matrices furthermore we establish a comparison theorem for multisplittings of a hermitian positive definite matrix

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

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

comparisons of regular splittings of matrices in this article new comparison theorems for regular splittings of matrices are derived in so doing the initial results of varga in 1960 on regular splittings of matrices and the subsequent unpublished results of wo nicki in 1973 on regular splittings of matrices will be seen to be special cases of these new comparison theorems

parallel multisplitting methods for a class of systems of weakly nonlinear equations without isotone mapping a parallel matrix multisplitting iterative method is set up for a class of systems of weakly nonlinear equations without isotone mapping the two sided monotone convergence is shown a sufficient condition is given to ensure the monotone convergence of the new method to the unique solution of the system in some sector the influences of different multisplittings on the convergence rate are investigated in the sense of monotonicity a numerical example is given ams classification 65f10 65h20

comparison theorems using general cones for norms of iteration matrices we prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms subject to mild additional hypotheses we show that these comparison theorems can hold only for such norms within the class of cone absolute norms finally in a banach algebra setting we prove a comparison theorem for spectral radii without appealing to perron frobenius theory

existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods given a nonsingular matrix a and a matrix t of the same order under certain very mild conditions there is a unique splitting a b c such that t b 1 c moreover all properties of the splitting are derived directly from the iteration matrix t these results do not hold when the matrix a is singular in this case given a matrix t and a splitting a b c such that t b 1 c there are infinitely many other splittings corresponding to the same matrices a and t and different splittings can have different properties for instance when t is nonnegative some of these splittings can be regular splittings while others can be only weak splittings analogous results hold in the symmetric positive semidefinite case given a singular matrix a not for all iteration matrices t there is a splitting corresponding to them necessary and sufficient conditions for the existence of such splittings are examined as an illustration of the theory developed the convergence of certain alternating iterations is analyzed different cases where the matrix is monotone singular and positive semi definite are studied

uniformly distributed orbits of certain flows on homogeneous spaces is non compact for a co compact lattice this result was strengthened by f irstenberg 1 lj proving that every orbit is uniformly distributed with respect to a g invariant measure for non uniform lattices in sl 2 r using a classification of invariant measures obtained by dani in 21 dani and smillie 31 proved that every non periodic orbit is uniformly distributed there are also various results obtained on orbit closures and invariant measures etc of larger subgroups consisting of unipotent elements especially the horospherical subgroups recently there was a spurt in the area initiated by margulis proof cf 151 see also 7 of oppenheim conjecture on values of quadratic forms at integral points using the study of unipotent flows the reader is referred to the survey articles by dani 41 and margulis 14j for various related developments we now note some conjectures expected to hold for orbits of a unipotent flow namely the u action on

on raghunathan s measure conjecture this paper represents the last in our three part series on raghunathan s measure conjecture see r1 r2 for parts i and ii more specifically let g be a real lie group all groups in this paper are assumed to be second countable with the lie algebra r a discrete subgroup of g and ir g r g the projection lwg rg the group g acts by right translations on r g x x g x e r g g e g let gt be a borel probability measure on r g define

algebraic theory of multiplicative schwarz methods the convergence of multiplicative schwarz type methods for solving linear systems when the coefficient matrix is either a nonsingular m matrix or a symmetric positive definite matrix is studied using classical and new results from the theory of splittings the effect on convergence of algorithmic parameters such as the number of subdomains the amount of overlap the result of inexact local solves and of coarse grid corrections global coarse solves is analyzed in an algebraic setting results on algebraic additive schwarz are also included

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

on algebraic multi level methods for non symmetric systems comparison results abstract we establish theoretical comparison results for algebraic multi level methods applied to non singular non symmetric m matrices we consider two types of multi level approximate block factorizations or amg methods the amli and the mamli method we compare the spectral radii of the iteration matrices of these methods this comparison shows that the spectral radius of the mamli method is less than or equal to the spectral radius of the amli method moreover we establish how the quality of the approximations in the block factorization effects the spectral radii of the iteration matrices we prove comparisons results for different approximations of the fine grid block as well as for the used schur complement we also establish a theoretical comparison between the amg methods and the classical block jacobi and block gauss seidel methods

tridiagonal splittings in the conditioning and parallel solution of banded linear systems abstract we study the conditioning and the parallel solution of banded linear systems of algebraic equations we propose an iterative method for solving the linear system au b based on a tridiagonal splitting of the real coefficient matrix a which permits the study of the conditioning and the parallel solution of banded linear systems using the theoretical results known for tridiagonal systems sufficient conditions for the convergence of this method are studied and the definition of tridiagonal dominant matrices is introduced observing that for this class of matrices the iterative method converges when the iterative method converges the conditioning of a may be studied using that of its tridagonal part finally we consider a parallel version of this iterative method and show some parallel numerical tests

exact convergence and divergence domains for the symmetric successive overrelaxation iterative ssor method applied to h matrices abstract in this paper exact convergence and divergence domains for the ssor iterative method as applied to the class of h matrices are obtained the theory of regular splittings and the recent results of varga niethammer and cai are used as tools in establishing these convergence and divergence domains

comparison theorems for iterative methods based on strong splittings by means of strong splittings of an n times n interval m matrix mathcal a one can construct iterative methods to enclose the solution set x x ax b a in a b in mathfrak b where mathfrak b is an interval vector and x in mathbb r n we derive comparison theorems for an upper bound of the asymptotic convergence factor and for the fixpoints resulting from those methods

prehomogeneous vector spaces and field extensions letk be an infinite field of characteristic not equal to 2 3 5 in this paper we construct a natural map from the set of orbits of certain prehomogeneous vector spaces to the set of isomorphism classes of galois extensions ofk which are splitting fields of equations of certain degrees and prove that the inverse image of this map corresponds bijectively with conjugacy classes of galois homomorphisms

the angle of sight signature for two dimensional shape analysis of manufactured objects abstract a new two dimensional 2d shape encoding scheme is introduced which is based on the idea of the angle of sight aos using this scheme a shape can be efficiently transformed into a one dimensional 1d signature by recording the aos vs distance of each boundary point with respect to a shape specific chord of sight cos the cos is selected by using an extension of the notion of shape boundary to the idea of shape specific points and the characteristic ellipse ce the aos signature has many important properties including it is information preserving and thus unique it does not require boundary smoothing it has its own selectable smoothing property it can provide a set of multi scale representations by means of a simple operation it is transformation invariant it is defined at all points it preserves symmetries as well for matching purposes a two level matching process is proposed using a global measure the eccentricity of the ce of a shape and a dissimilarity measure based on the aos signature the encoding and matching techniques developed have been tested with 35 manufactured objects the results obtained show that the aos signature and the two level matching technique are quite effective and reliable for the recognition of 2d shapes of typical manufactured objects

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

conditions for strict inequality in comparisons of spectral radii of splittings of different matrices we present new comparison theorems for the spectral radii of matrices arising from splittings of different matrices under nonnegativity assumptions our focus is on establishing strict inequalities of the spectral radii without imposing strict inequalities of the matrices but we also obtain new results for nonstrict inequalities of the spectral radii we emphasize two different approaches one combinatorial and the other analytic and discuss their merits in the light of the results obtained we try to get fairly general results and indicate by counter examples that some of our hypotheses cannot be relaxed in certain directions

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

on domains of superior convergence of the ssor method to that of the sor method let v denote the spectral radius of jab the block jacobi iteration matrix for the classes of 1 nonsingular m matrices and 2 p cyclic p 3 consistently ordered matrices we study domains in the v plane when v 1 where the block ssor iteration method has at least as favorable an asymptotic rate of convergence as the block sor method let la and sa denote respectively the block sor and ssor iteration matrices for the class of nonsingular m matrices a we determine conditions when the spectral radii satisfy sa la 0 21 v and 0 v 1 under these conditions we also show that the optimal sor iteration parameter is b 1 for the class of p cyclic p 3 consistently ordered matrices a we determine for which s and v s sa 1 la our investigations make use of the equality case in wielandt s inequality between the spectral radii of a complex matrix and its nonnegative and irreducible majorizers and of rouche s theorem for the location of zeros of complex functions

sequential and parallel synchronous alternating iterative methods the so called parallel multisplitting nonstationary iterative model a was introduced by bru elsner and neumann linear algebra and its applications 103 175 192 1988 for solving a nonsingular linear system ax b using a weak nonnegative multisplitting of the first type in this paper new results are introduced when a is a monotone matrix using a weak nonnegative multisplitting of the second type and when a is a symmetric positive definite matrix using a p regular multisplitting also nonstationary alternating iterative methods are studied finally combining model a and alternating iterative methods two new models of parallel multisplitting nonstationary iterations are introduced when matrix a is monotone and the multisplittings are weak nonnegative of the first or of the second type both models lead to convergent schemes also when matrix a is symmetric positive definite and the multisplittings are p regular the schemes are also convergent

some comparison theorems for weak nonnegative splittings of bounded operators abstract the comparison of the asymptotic rates of convergence of two iteration matrices induced by two splittings of the same matrix has arisen in the works of many authors in this paper we derive new comparison theorems for weak nonnegative splittings and weak splittings of bounded operators in a general banach space and rather general cones and in a hilbert space which extend some of the results obtained by wo nicki japan j indust appl math 11 1994 289 342 and marek and szyld numer math 44 1984 23 35 furthermore we present new theorems also for bounded operator which extend some results by csordas and varga numer math 44 1984 23 35 for weak nonnegative splittings of matrices

a note on the perturbation of positive matrices by normal and unitary matrices abstract in a recent paper neumann and sze considered for an n n nonnegative matrix a the minimization and maximization of a s the spectral radius of a s as s ranges over all the doubly stochastic matrices they showed that both extremal values are always attained at an n n permutation matrix as a permutation matrix is a particular case of a normal matrix whose spectral radius is 1 we consider here for positive matrices a such that a n is a nonnegative matrix for all normal matrices n whose spectral radius is 1 the minimization and maximization problems of a n as n ranges over all such matrices we show that the extremal values always occur at an n n real unitary matrix we compare our results with a less recent work of han neumann and tastsomeros in which the maximum value of a x over all n n real matrices x of frobenius norm n was sought

on perron frobenius property of matrices having some negative entries we extend the theory of nonnegative matrices to the matrices that have some negative entries we present and prove some properties which give us information when a matrix possesses a perron frobenius eigenpair we apply also this theory by proposing the perron frobenius splitting for the solution of the linear system ax b by classical iterative methods perron frobenius splittings constitute an extension of the well known regular splittings weak regular splittings and nonnegative splittings convergence and comparison properties are given and proved

a geometrical approach to polygonal dissimilarity and shape matching two geometrical measures have been proposed to quantify the dissimilarity between two irregular polygons these measures capture the intuitive notion of the dissimilarity between shapes and are related to the minimum value of the intersecting area of the polygons on superposing one on the other in various configurations a more easily computable measure of dissimilarity referred to as the minimum integral square error between the polygons has also been proposed and using the latter measure pattern classification has been performed experimental results involving the classification of the noisy boundaries of the four great lakes erie huron michigan and superior using this measure have been presented

a note on comparison theorems for nonnegative matrices in a recent paper 4 csordas and varga have unified and extended earlier theorems of varga in 10 and wo nicki in 11 on the comparison of the asymptotic rates of convergence of two iteration matrices induced by two regular splittings the main purpose of this note is to show a connection between the csordas varga paper and a paper by beauwens 1 in which a comparison theorem is developed for the asymptotic rate of convergence of two nonnegative iteration matrices induced by two splittings which are not necessarily regular monotonic norms already used in 1 play an important role in our work here

comparisons of weak regular splittings and multisplitting methods comparison results for weak regular splittings of monotone matrices are derived as an application we get upper and lower bounds for the convergence rate of iterative procedures based on multisplittings this yields a very simple proof of results of neumann plemmons on upper bounds and establishes lower bounds which has in special cases been conjectured by these authors

optimization of the spectral radius of a product for nonnegative matrices abstract let a be an n n irreducible nonnegative matrix we show that over the set n of all n n doubly stochastic matrices s the multiplicative spectral radius sa attains a minimum and a maximum at a permutation matrix for the case when a is a symmetric nonnegative matrix a by product of our technique of proof yields a result allowing us to show that s 1 a s 2 a when s 1 and s 2 are two symmetric matrices such that both s 1 a and s 2 a are nonnegative matrices and s 1 s 2 is a positive semidefinite matrix this result has several corollaries one corollary is that s 1 a s 2 a when s 1 1 n j and s 2 1 n 1 j i where j is the matrix of all 1 s a second corollary is a comparison theorem for weak regular splittings of two monotone matrices

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

comparison theorems for weak splittings in respect to a proper cone of nonsingular matrices the asymptotic rates of convergence of two iteration matrices induced by two splittings of the same nonsingular matrix have been compared in the works of many authors in this paper new comparison theorems which extend song s results y song numer math 65 1993 245 252 for weak splittings of the same or different types are presented these new comparison theorems are derived by using nonnegativity in respect to a proper cone k n ew converses which partially solve an open question asked by v a miller m neumann numer math 47 1985 427 434 are also presented 1999 elsevier science inc all rights reserved

comparison theorems for the convergence factor of iterative methods for singular matrices abstract iterative methods for the solution of consistent singular systems of linear equations are governed by the convergence factor of the iteration matrix t i e by the quantity t max t 1 where t is the spectrum of t theorems are presented comparing the convergence factor of two iterative methods the comparison is based on the relationship between the matrices of the splittings a cone other than the usual nonnegative hyperoctant is used to define the order used in this comparison although this cone is based on the unknown projection onto the null space of a matrix the characterization provided in the paper allows in specific instances the cone to be readily computable

the monotone convergence of a class of parallel nonlinear relaxation methods for nonlinear complementarity problems abstract we set up a class of parallel nonlinear multisplitting aor methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems the different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems the two sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown and sufficient conditions guaranteeing the methods to converge globally are discussed finally a lot of numerical results show that our new methods are feasible and efficient

theorems on m splittings of a singular m matrix which depend on graph structure abstract let a m ne r n n be a splitting we investigate the spectral properties of the iteration matrix m 1n by considering the relationships of the graphs of a m n and m 1n we call a splitting an m splitting if m is a nonsingular m matrix and n 0 for an m splitting of an irreducible z matrix a we prove that the circuit index of m 1n is the greatest common divisor of certain sets of integers associated with the circuits of a for m splittings of a reducible singular m matrix we show that the spectral radius of the iteration matrix is 1 and that its multiplicity and index are independent of the splitting these results hold under somewhat weaker assumptions

comparison theorems for weak splittings of bounded operators comparison theorems for weak splittings of bounded operators are presented these theorems extend the classical comparison theorem for regular splittings of matrices by varga the less known result by wo nicki and the recent results for regular and weak regular splittings of matrices by neumann and plemmons elsner and lanzkron rose and szyld the hypotheses of the theorems presented here are weaker and the theorems hold for general banach spaces and rather general cones hypotheses are given which provide strict inequalities for the comparisons it is also shown that the comparison theorem by alefeld and volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators

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

some applications of spectral theory of nonnegative matrices to input output models abstract we show the necessary and sufficient condition that a nonnegative matrix has a unique positive eigenvector where the analytic expression displaying the linear relations between each remnant component and a basic characteristic subvector of the unique eigenvector is discovered when the nonnegative matrix is reducible as a result we infer the exact necessary and sufficient condition that the iteration matrix m 1 n as a special nonnegative matrix has a unique positive eigenvector when m n is an m splitting which is applied to the condition for the existence and uniqueness of a balanced growth solution for the leontief dynamic input output model previous work in the field did not clearly involve the uniqueness of the balanced growth solution in this paper we develop the prior results that is we find the necessary and sufficient condition that the leontief dynamic input output model has a unique bal anced growth solution finally we obtain the necessary and sufficient condition for theexistence and uniqueness of both the balanced growth solution and the production prices system

maximizing the spectral radius of fixed trace diagonal perturbations of nonnegative matrices abstract let a be an n by n irreducible entrywise nonnegative matrix for a given t 0 we consider the problem of maximizing the perron root of a nonnegative diagonal trace t perturbation of a because of the convexity of the perron root as a function of diagonal entries the maximum occurs for some teii such an index i which is called a winner may depend on t we show how to determine the nonempty set of indices i that are winners for all sufficiently small t and the possibly different nonempty set of indices that are winners for all sufficiently large t we also show how to determine if there are indices that are winners for all t

a note on weak splittings of matrices in this note an open question proposed by marek and szyld is solved i marek d b szyld comparison theorems for weak splittings of bounded operators numer math 58 1990 387 397 at the same time some new comparison theorems are presented

new convergence results for alternating methods abstract the alternating methods for solving the large system of linear equations ax b are investigated the convergence and the monotone convergence theories for the alternating method are formulated when the coefficient matrix is an h matrix or a monotone matrix sufficient conditions are established for the induced splitting by the alternating method to be a regular splitting furthermore new comparison theorems which improve previous comparison theorems are proved and several concrete applications are given

on stein rosenberg type theorems for nonnegative and perron frobenius splittings abstract the stein rosenberg theorem is extended and generalized to the class of nonnegative splittings a m 1 n 1 m 2 n 2 as well as to the most generalized class of perron frobenius splittings two types of the stein rosenberg theorem are stated and proved for both classes these theorems allow us to obtain comparison results for the rate of convergence of the associated iterative methods specific assumptions are given under which the inequalities of the spectral radii become equalities or strict inequalities the theoretical results are confirmed by numerical examples

uniform resampling of digitized contours this paper addresses the problem of the nonuniform intersample distance of digital curves obtained as a result of quantization of continuous contours on a square lattice a resampling algorithm based on variable factor interpolation and decimation is presented and its performance is evaluated analytically and by computer simulations assuming the grid intersect quantization it is shown that the output of the resampling algorithm outperforms the original digital curve in terms of the average and maximum error in the measurement of length by 50 and 73 percent respectively the resampling algorithm can be used as a preprocessing stage in shape analysis systems to enhance their performance by increasing the accuracy and consistency of both local and global features such as curvature and the fourier shape descriptors

convergence and comparison theorems for a generalized alternating iterative method using as a principal tool the convergence results of standard iterative process for the solution of linear systems alternating iterative methods are studied we extend the convergence theorem for the stationary alternating iterative method of benzi and szyld numererische mathematik 76 1997 309 for weak nonnegative splittings of the first type of a monotone matrix to weak nonnegative splitting of the second type on the other hand we introduce a more general method the nonstationary alternating iterative method establishing convergence results for weak nonnegative splittings of a monotone matrix and for p regular splittings of a symmetric positive definite matrix

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area