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

symmetry detection by generalized complex gc moments a close form solution this paper presents a unified method for detecting both reflection symmetry and rotation symmetry of 2d images based on an identical set of features i e the first three nonzero generalized complex gc moments this method is theoretically guaranteed to detect all the axes of symmetries of every 2d image if more nonzero gc moments are used in the feature set furthermore we establish the relationship between reflectional symmetry and rotational symmetry in an image which can be used to check the correctness of symmetry detection this method has been demonstrated experimentally using more than 200 images

generalized affine invariant image normalization we provide a generalized image normalization technique which basically solves all problems in image normalization the orientation of any image can be uniquely defined by at most three non zero generalized complex moments the correctness of our method is demonstrated theoretically as well as in practice by applying them to a number of degenerate images which have failed other previously reported techniques for image normalization

fast computation of tchebichef moments for binary and grayscale images discrete orthogonal moments have been recently introduced in the field of image analysis it was shown that they have better image representation capability than the continuous orthogonal moments one problem concerning the use of moments as feature descriptors is the high computational cost which may limit their application to the problems where the online computation is required in this paper we present a new approach for fast computation of the 2 d tchebichef moments by deriving some properties of tchebichef polynomials and using the image block representation for binary images and intensity slice representation for grayscale images a fast algorithm is proposed for computing the moments of binary and grayscale images the theoretical analysis shows that the computational complexity of the proposed method depends upon the number of blocks of the image thus it can speed up the computational efficiency as far as the number of blocks is smaller than the image size

normalization of rotationally symmetric shapes for pattern recognition abstract image normalization is useful for image recognition by the matching method recently a normalization algorithm was developed to normalize images under the distortion of translation rotation scaling and skew however the method fails when the image is rotationally symmetric a method is introduced called the modified fourier descriptor to normalize rotationally symmetric shapes this method is simple and fast and can be combined with the preceding normalization algorithm to make it more general and realizable

conserved quantities of some hamiltonian wave equations after full discretization hamiltonian pdes have some invariant quantities which would be good to conserve with the numerical integration in this paper we concentrate on the nonlinear wave and schrodinger equations under hypotheses of regularity and periodicity we study how a symmetric space discretization makes that the space discretized system also has some invariants or nearly invariants which well approximate the continuous ones we conjecture some facts which would explain the good numerical approximation of them after time integration when using symplectic runge kutta methods or symmetric linear multistep methods for second order systems

error propagation in numerical approximations near relative equilibria we study the propagation of errors in the numerical integration of perturbations of relative equilibrium solutions of hamiltonian differential equations with symmetries first it is shown that taking an initial perturbation of a relative equilibrium the corresponding solution is related in a first approximation to another relative equilibrium with the parameters perturbed from the original then this is used to prove that for stable relative equilibria error growth with respect to the perturbed solution is in general quadratic but only linear for schemes that preserve the invariant quantities of the problem in this sense the conclusion is similar to the one obtained when integrating unperturbed relative equilibria numerical experiments illustrate the results

frequency domain classification of cyclic and dihedral symmetries of finite 2 d patterns this paper presents a very simple and effective algorithm for classifying cyclic and dihedral symmetries from images of finite two dimensional patterns it consists in an extension of a frequency domain algorithm proposed by the author for estimating two dimensional rotation of rigid objects within this framework the estimation of rotation is conveniently turned into the problem of detecting two orthogonal lines within the locus of the zero crossings of a certain function represented in orthogonal cartesian coordinates the main contribution of this paper is the use and interpretation of the ambiguities that arise in such a locus in the form of additional pairs of orthogonal lines when applied to symmetric patterns and the development of other algorithmic steps which allow a simple and fast discrimination between cyclic and dihedral symmetries unlike any other available method this algorithm does not require any conversion from cartesian to polar image representations besides classification reliability and consistency observed through several dozen testing experiments the nice features of this new method also include robustness to noise and ease of implementation with fast fourier transform algorithms which makes it amenable to almost real time pattern classifications applications several examples representative of the performance of the algorithm through extensive testing are reported and discussed in the paper

asymptotic stability of solitary waves we show that the family of solitary waves 1 solitons of the korteweg de vries equation partial t u u partial x u partial x 3 u 0 is asymptotically stable our methods also apply for the solitary waves of a class of generalized korteweg de vries equations partial t u partial x f u partial x 3 u 0 in particular we study the case wheref u up 1 p 1 p 1 2 3 and 3 0 withf c4 the same asymptotic stability result for kdv is also proved for the casep 2 the modified korteweg de vries equation we also prove asymptotic stability for the family of solitary waves for all but a finite number of values ofp between 3 and 4 the solitary waves are known to undergo a transition from stability to instability as the parameterp increases beyond the critical valuep 4 the solution is decomposed into a modulating solitary wave with time varying speedc t and phase t bound state part and an infinite dimensional perturbation radiating part the perturbation is shown to decay exponentially in time in a local sense relative to a frame moving with the solitary wave asp 4 the local decay or radiation rate decreases due to the presence of aresonance pole associated with the linearized evolution equation for solitary wave perturbations

automatic symmetry determination and normalization for rotationally symmetric 2d shapes and 3d solid objects abstract determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision application however the usual normalization methods are inapplicable when the shape is n fold rotationally symmetric n 3 in this paper an efficient and reliable new method using modified fourier transform is introduced to normalize such a 2d rotationally symmetric shape furthermore we extend this new method to the normalization of a n fold axial rotationally symmetric 3d object there are two obvious advantages when using this new method 1 it prevents the high computation load and the difficulty in normalizing the shape s orientation which occurred in the old methods using full matching or correlation functions and 2 the weakness introduced by the old methods using data reduction from 2d data to 1d data is remedied experiments will show the validity of our method

a technique to construct symmetric variable stepsize linear multistep methods for second order systems some previous works show that symmetric fixed and variable stepsize linear multistep methods for second order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems in this paper we give a technique to construct variable stepsize symmetric methods from their fixed stepsize counterparts in such a way that the former have the same order as the latter the order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed stepsize integrators as this technique looks for efficiency we concentrate on explicit linear multistep methods which just make one function evaluation per step and we offer some numerical comparisons with other one step adaptive methods which also show a good long term behaviour

k types for the tempered components of a p adic general linear group with an appendix by p schneider u stuhler the definition of the tempered category

a technique for finding the symmetry axes of implicit polynomial curves under perspective projection this paper presents an algebraic technique for detecting the symmetry axes of a perspectively projected plane curve the procedure applies to implicit polynomials which has been fitted to 2d image data acquired by means of a photo camera or a tv set the effectiveness of the proposed method has been demonstrated experimentally by using both synthetic and real images

an explicit matching theorem for level zero discrete series of unit groups of p adic simple algebras for a f a central simple algebra over a p adic local field the group of units a glm dd is a general linear group over a central division algebra dd f of index d the product n dm being fixed the abstract matching theorem amt implies the existence of bijective maps jl between the sets of discrete series representations of the groups a such that a character relation is preserved in this paper we construct maximal level zero extended type components for every level zero discrete series representation of a its maximal level zero extended type determines the discrete series representation uniquely without any twist ambiguities as for the usual types and conversely every level zero discrete series representation contains a maximal level zero extended type component which is unique up to conjugacy in order to determine how jl matches the extended types we find certain regular elliptic elements where the characters of and are the same and we compute the character values at these elements by using a version of shintani descent which we develop in appendix b surprisingly we find that amt also implies explicit shintani descent for irreducible characters of finite general linear groups which have cuspidal descent named author let f be a locally compact p adic field let dd be a central division algebra of index d over f and let a mm dd the algebra of all m m matrices with entries in dd then a is a central simple f algebra of reduced degree n dm and the group of units a of a is the group of f points of a connected reductive algebraic group defined over f the group a is separable totally disconnected and unimodular and the harmonic analysis of a as is well known is linked to numerous problems in arithmetic it is interesting and perhaps may be regarded as a version of the abstract matching theorem amt see 0 2 that the representation theory of a depends upon the parameters d m associated to a but not more specifically on the isomorphism class of a we follow the convention of writing dd for any central f division algebra of index d we also write dn for any one of the n isomorphism class representatives of central f division algebras of index n 1991 mathematics subject classification 22e50 1the work reported in this paper grew out of a research in pairs sojourn at the mathematisches institut oberwolfach the authors wish to express their appreciation to the institut for its support of their research as well as for an enjoyable stay at the institut

a unifying approach to moment based shape orientation and symmetry classification in this paper the problem of moment based shape orientation and symmetry classification is jointly considered a generalization and modification of current state of the art geometric moment based functions is introduced the properties of these functions are investigated thoroughly using fourier series analysis and several observations and closed form solutions are derived we demonstrate the connection between the results presented in this work and symmetry detection principles suggested from previous complex moment based formulations the proposed analysis offers a unifying framework for shape orientation symmetry detection in the context of symmetry classification and matching the second part of this work presents a frequency domain method aiming at computing a robust moment based feature set based on a true polar fourier representation of image complex gradients and a novel periodicity detection scheme using subspace analysis the proposed approach removes the requirement for accurate shape centroid estimation which is the main limitation of moment based methods operating in the image spatial domain the proposed framework demonstrated improved performance compared to state of the art methods

explicit shintani base change and the macdonald correspondence for characters of gln k let kd d1 denote the set of unramified extensions of a local field k and kd d1 the respective residual field extensions the authors recall macdonald s parameterization i g macdonald zeta functions attached to finite general linear groups math ann 249 1980 1 15 of the irreducible characters of gln kd in terms of i equivalence classes of tame n dimensional representations of the weil deligne group w kd using zelevinsky s psh hopf algebra theory a zelevinsky representations of finite classi

unitary integrators and applications to continuous orthonormalization techniques in this paper the issue of integrating matrix differential systems whose solutions are unitary matrices is addressed such systems have skew hermitian coefficient matrices in the linear case and a

a moment based approach for deskewing rotationally symmetric shapes the covariance matrix of a pattern is composed by its second order central moments for a rotationally symmetric shape its covariance matrix is a scalar identity matrix in this work we apply this property to restore the skewed shape of rotational symmetry the relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived by computing the covariance matrix of the skewed shape and letting the covariance matrix of the original shape be a scalar identity matrix the skew transformation matrix can be solved then the rotationally symmetric shape can be recovered by multiplying the inverse transformation matrix with the skewed shape the method does not rely on continuous contours and is robust to noise because only the second order moments of the input shape are required experimental results are also presented

detection of generalized principal axes is rotationally symmetric shapes abstract automatic detection of the principal axes of given shapes with known symmetry properties is studied in this paper the inapplicability of a well known equation which is used to compute the direction of the principal axis of a given shape using moment functions to a class of so called degenerate shapes is first pointed out rotationally symmetric shapes often encountered in real applications are shown to belong to this class this problem is solved by extending the notion of principal axis to higher order ones in terms of higher order moment functions analytic equations for computing the direction of high order principal axes are derived they include the well known equation for computing the direction of the second order principal axis as a special case some experimental results are included finally to show the effectiveness of the derived analytic equations

affine permutation invariance of 2 d shapes shapes provide a rich set of clues on the identity and topological properties of an object in many imaging environments however the same object appears to have different shapes due to distortions such as translation rotation reflection scaling or skewing further the order by which the object s feature points are scanned changes i e the order of the pixels may be permuted relating two dimensional shapes of the same object distorted by different affine and permutation transformations is a challenge we introduce a shape invariant that we refer to as the intrinsic shape of an object and describe an algorithm blaiser to recover it the intrinsic shape is invariant to affine permutation distortions it is a uniquely defined representative of the equivalence class of all affine permutation distortions of the same object blaiser computes the intrinsic shape from any arbitrarily affine permutation distorted image of the object without prior knowledge regarding the distortions or the undistorted shape of the object the critical step of blaiser is the determination of the shape orientation and we provide a detailed discussion on this topic the operations of blaiser are based on low order moments of the input shape and thus robust to error and noise examples illustrate the performance of the algorithm

analysis of variable stepsize linear multistep methods with special emphasis on symmetric ones in this paper we deal with several issues concerning variable stepsize linear multistep methods first we prove their stability when their fixed stepsize counterparts are stable and under mild conditions on the stepsizes and the variable coefficients then we prove asymptotic expansions on the considered tolerance for the global error committed using them we study the growth of error with time when integrating periodic orbits we consider strongly and weakly stable linear multistep methods for the integration of first order differential systems as well as those designed to integrate special second order ones we place special emphasis on the latter which are also symmetric because of their suitability when integrating moderately eccentric orbits of reversible systems for these types of methods we give a characterization for symmetry of the coefficients which allows their construction and provide some numerical results for them

automatic rotational symmetry determination for shape analysis abstract the determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision applications in this paper a simple but effective algorithm to analyse the rotational symmetry of a given closed curve shape s is proposed a circle c with the centroid of s as the circle center and the average radius of s as the circle radius is superimposed on s resulting in the intersection of c and s at a set of points by theoretical analysis the relationship between the order n s of the rotational symmetry of s and the number of intersection points between c and s is established all the possible values for n s are determined and finally n s is determined by evaluating the similarity between s and its rotated versions in the proposed algorithm only simple pixel operations and second order moment function computation are involved several problems caused by the use of discrete image coordinates are analysed and solved for correct decision making in the algorithm good experimental results are also included

symmetric multistep methods over long times for computations of planetary motions with special linear multistep methods an excellent long time behaviour is reported in the literature without a theoretical explanation neither the total energy nor the angular momentum exhibit secular error terms in this paper we completely explain this behaviour by studying the modified equation of these methods and by analyzing the remarkably stable propagation of parasitic solution components