boosting the margin a new explanation for the effectiveness of voting methods one of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large and often is observed to decrease even after the training error reaches zero in this paper we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label we show that techniques used in the analysis of vapnik s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error we also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples finally we compare our explanation to those based on the bias variance decomposition

a new two dimensional block adaptive fir filtering algorithm and its application to image restoration this paper presents a new two dimensional 2 d optimum block stochastic gradient tdobsg algorithm for 2 d adaptive finite impulse response fir filtering the tdobsg algorithm employs a space varying convergence factor for all the filter coefficients where the convergence factor at each block iteration is optimized in a least squares sense that the squared norm of the a posteriori estimation error vector is minimized it has the same order of computational complexity as another 2 d optimum block adaptive tdoba algorithm computer simulations for image restoration show that the tdobsg algorithm outperforms the tdoba algorithm and other related algorithms in terms of objective and or subjective measures

cohomogeneity one manifolds with positive ricci curvature one of the central problems in riemannian geometry is to determine how large the classes of manifolds with positive nonnegative sectional ricci or scalar curvature are see gr for scalar curvature the situation is fairly well understood by comparison special surgery constructions as in sy wr and bundle constructions as in na have resulted in a large number of interesting manifolds with positive ricci curvature so far the only known obstructions to have positive ricci curvature come from obstructions to have positive scalar curvature see li and rs and from the classical bonnet myers theorem which implies that a closed manifold with positive ricci curvature must have finite fundamental group it is well known that among homogeneous manifolds g h this is also a sufficient condition see e g the proof of corollary 3 5 or br in this paper we prove that this is true as well when the manifold admits an action by a compact lie group g with orbits of codimension one

infinite period bifurcation and global bifurcation branches branches of periodic solutions which exhibit the alternatives of the global hopf bifurcation theorem are calculated for two general systems of differential equations in the first a branch of solu

invariant character recognition with zernike and orthogonal fourier mellin moments abstract in this paper we consider the use of orthogonal moments for invariant classification of alphanumeric characters of different size in addition to the zernike and pseudo zernike moments zms and pzms which have been previously proposed for invariant character recognition a new method of combining orthogonal fourier mellin moments ofmms with centroid bounding circle scaling is introduced which is shown to be useful in characterizing images with large variability through extensive experimentation using zms and ofmms as features different scaling methodologies and classifiers it is shown that ofmms give the best overall performance in terms of both image reconstruction and classification accuracy

codazzi spinors and globally hyperbolic manifolds with special holonomy in this paper we describe the structure of riemannian manifolds with a special kind of codazzi spinors we use them to construct globally hyperbolic lorentzian manifolds with complete cauchy surfaces for any weakly irreducible holonomy representation with parallel spinors t m with a holonomy group g r n 2 so 1 n 1 where g so n 2 is trivial or a product of groups su k sp l g2 or spin 7

holonomy rigidity for ricci flat metrics on a closed connected oriented manifold m we study the space mathcal m vert m of all riemannian metrics which admit a non zero parallel spinor on the universal covering such metrics are ricci flat and all known ricci flat metrics are of this form we show the following the space mathcal m vert m is a smooth submanifold of the space of all metrics and its premoduli space is a smooth finite dimensional manifold the holonomy group is locally constant on mathcal m vert m if m is spin then the dimension of the space of parallel spinors is a locally constant function on mathcal m vert m

real time computation of two dimensional moments on binary images using image block representation this work presents a new approach and an algorithm for binary image representation which is applied for the fast and efficient computation of moments on binary images this binary image representation scheme is called image block representation since it represents the image as a set of nonoverlapping rectangular areas the main purpose of the image block representation process is to provide an efficient binary image representation rather than the compression of the image the block represented binary image is well suited for fast implementation of various processing and analysis algorithms in a digital computing machine the two dimensional 2 d statistical moments of the image may be used for image processing and analysis applications a number of powerful shape analysis methods based on statistical moments have been presented but they suffer from the drawback of high computational cost the real time computation of moments in block represented images is achieved by exploiting the rectangular structure of the blocks

a spinorial energy functional critical points and gradient flow let m be a compact spin manifold on the universal bundle of unit spinors we study a natural energy functional whose critical points if dim m ge 3 are precisely the pairs g varphi consisting of a ricci flat riemannian metric g together with a parallel g spinor varphi we investigate the basic properties of this functional and study its negative gradient flow the so called spinor flow in particular we prove short time existence and uniqueness for this flow

rotation invariants of vector fields from orthogonal moments abstract vector field images are a type of new multidimensional data that appear in many engineering areas although the vector fields can be visualized as images they differ from graylevel and color images in several aspects to analyze them special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area in this paper we propose a method for the description and matching of vector field patterns under an unknown rotation of the field rotation of a vector field is so called total rotation where the action is applied not only on the spatial coordinates but also on the field values invariants of vector fields with respect to total rotation constructed from orthogonal gaussian hermite moments and zernike moments are introduced their numerical stability is shown to be better than that of the invariants published so far we demonstrate their usefulness in a real world template matching application of rotated vector fields

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

the method of normalization to determine invariants the determination of invariant characteristics is an important problem in pattern recognition many invariants are known which have been obtained either by normalization or by other methods this paper shows that the method of normalization is much more general and allows one to derive a lot of sets of invariants from the second list as well to this end the normalization method is generalized and is presented in such a way that it is easy to apply thus unifying and simplifying the determination of invariants furthermore this paper discusses the advantages and disadvantages of the invariants obtained by normalization their main advantage is that the normalization process provides us with a standard position of the object because of the generality of the method also new invariants are obtained such as normalized moments more stable than known ones legendre descriptors and zernike descriptors to affine transformations two dimensional fourier descriptors and affine moment invariants obtained by combining hu s moment invariants and normalized moments

orthogonal moments based on exponent functions exponent fourier moments abstract in this paper we propose a new set of orthogonal moments based on exponent functions named exponent fourier moments efms which are suitable for image analysis and rotation invariant pattern recognition compared with zernike polynomials of the same degree the new radial functions have more zeros and these zeros are evenly distributed this property make efms have strong ability in describing image unlike zernike moments the kernel of computation of efms is extremely simple theoretical and experimental results show that exponent fourier moments perform very well in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions the exponent fourier moments can be thought of as generalized orthogonal complex moments

classification of negatively pinched manifolds with amenable fundamental groups we give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups namely they are precisely the mobius band and the products of r with the total spaces of flat vector bundles over closed infranilmanifolds

determination of blur and affine combined invariants by normalization the determination of invariant characteristics is an important problem in pattern recognition in many situations images to be processed are usually subjected to geometric distortion and or blur degradation in this paper we introduce an approach to derive blur and affine combined invariants bai firstly we normalize the image to a standard form by using blur invariant moments as normalization constraints then we construct the blur and affine combined invariants at the standard form using the method proposed in this paper a set of blur and affine combined invariant features can be obtained easily and effectively several experimental results are presented to illustrate the performance of the invariants for simultaneously affine deformed and blur degraded images

rigidity of group actions on solvable lie groups we establish analogs of the three bieberbach theorems for a lattice gamma in a semidirect product mathsf k rtimes mathsf k where mathsf s is a connected simply connected solvable lie group and mathsf k is a compact subgroup of its automorphism group we first prove that the action of gamma on mathsf s is metrically equivalent to an action of gamma on a supersolvable lie group the latter is shown to be determined by gamma itself up to an affine diffeomorphism then we characterize these lattices algebraically as polycrystallographic groups furthermore we realize any polycrystallographic group gamma as a lattice in a semidirect product mathsf s rtimes mathsf f with mathsf f being a finite group whose order is bounded by a constant only depending on the dimension of mathsf s this generalization of the first bieberbach theorem is used to obtain a partial generalization of the third one as well finally we show for any torsion free closed subgroup upsilon subset mathsf k rtimes mathsf k that the quotient mathsf s upsilon is the total space of a vector bundle over a compact manifold b where b is the quotient of a solvable lie group by a torsion free polycrystallographic group

rotation invariant image recognition using features selected via a systematic method abstract in this paper a new set of rotation invariant features for image recognition is introduced the features are the magnitudes of a set of orthogonal complex moments of the image called zernike moments these features could easily be constructed to an arbitrary high order taking advantage of the orthogonality property a systematic feature selection method for choosing an appropriate number of the zernike features is developed it is based on computing a measure of the information content differences of features of different classes the performance of the method is experimentally tested on a 26 class and a 10 class data set involving differently oriented binary images the first set consists of 624 images of all english characters the second one is an extensive set of numeric handprinted characters involving 16 550 samples using a nearest neighbor classifier 99 and 84 classification accuracies are obtained respectively

a general approach to moment calculation for polygons and line segments abstract the calculation of moments from the boundary of a solid digital area is a quite useful technique used in pattern recognition a straightforward way of doing the calculation that does not have any numerical instabilities is presented all the symmetries available in moment calculations are preserved and it is shown how different moment formulas are related to each other this includes relations between different moments and the relationships among different methods for calculating moments finally a direct relation between the moment expansion of a polygonal area and a stick figure made from one dimensional lines embedded in a two dimensional plane is derived

normalization and shape recognition of three dimensional objects by 3d moments abstract in this paper we are primarily concerned with the recognition of three dimensional 3d objects on the basis of the geometry of their physical surface the 3d moments are defined on the object s surface with two main aims 1 to derive a normalized version irrespective of position size and orientation for each imaged object and 2 to establish global descriptors extracted from normalized shapes in order to make up a representative feature vector to be used in recognition tasks the source data are multiple orthographic views of 3d objects with known viewpoint specifications a volume intersection procedure is used in the recovery of 3d object surface from two dimensional 2d data the problem of normalization to achieve recognition of 3d objects is dealt with and a heuristic solution is proposed to lessen the inherent ambiguity of the principal axes method for object orientation experimental results are described with ten object categories showing excellent percentage classification success rates by using only a small number of normalized moments as elements of the feature vector

image normalization by complex moments the role of moments in image normalization and invariant pattern recognition is addressed the classical idea of the principal axes is analyzed and extended to a more general definition the relationship between moment based normalization moment invariants and circular harmonics is established invariance properties of moments as opposed to their recognition properties are identified using a new class of normalization procedures the application of moment based normalization in pattern recognition is demonstrated by experiment

quaternion polar harmonic fourier moments for color images abstract this paper proposes quaternion polar harmonic fourier moments qphfm for color image processing and analyzes the properties of qphfm after extending chebyshev fourier moments chfm to quaternion chebyshev fourier moments qchfm comparison experiments including image reconstruction and color image object recognition on the performance of qphfm and quaternion zernike moments qzm quaternion pseudo zernike moments qpzm quaternion orthogonal fourier mellin moments qofmm qchfm and quaternion radial harmonic fourier moments qrhfm are carried out experimental results show qphfm can achieve an ideal performance in image reconstruction and invariant object recognition in noise free and noisy conditions in addition this paper discusses the importance of phase information of quaternion orthogonal moments in image reconstruction

two dimensional polar harmonic transforms for invariant image representation this paper introduces a set of 2d transforms based on a set of orthogonal projection bases to generate a set of features which are invariant to rotation we call these transforms polar harmonic transforms phts unlike the well known zernike and pseudo zernike moments the kernel computation of phts is extremely simple and has no numerical stability issue whatsoever this implies that phts encompass the orthogonality and invariance advantages of zernike and pseudo zernike moments but are free from their inherent limitations this also means that phts are well suited for application where maximal discriminant information is needed furthermore phts make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application

recognitive aspects of moment invariants moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance the notion of complex moments is introduced as a simple and straightforward way to derive moment invariants through this relation properties of complex moments are used to characterize moment invariants aspects of information loss suppression and redundancy encountered in moment invariants are investigated and significant results are derived the behavior of moment invariants in the presence of additive noise is also described

on the full holonomy group of lorentzian manifolds the classification of restricted holonomy groups of n dimensional lorentzian manifolds was obtained about ten years ago however up to now not much is known about the structure of the full holonomy group in this paper we study the full holonomy group of lorentzian manifolds with a parallel null line bundle based on the classification of the restricted holonomy groups of such manifolds we prove several structure results about the full holonomy we establish a construction method for manifolds with disconnected holonomy starting from a riemannian manifold and a properly discontinuous group of isometries this leads to a variety of examples most of them being quotients of pp waves with disconnected holonomy including a non flat lorentzian manifold with infinitely generated holonomy group furthermore we classify the full holonomy groups of solvable lorentzian symmetric spaces and of lorentzian manifolds with a parallel null spinor finally we construct examples of globally hyperbolic manifolds with complete spacelike cauchy hypersurfaces disconnected full holonomy and a parallel spinor

completeness of compact lorentzian manifolds with abelian holonomy we address the problem of finding conditions under which a compact lorentzian manifold is geodesically complete a property which always holds for compact riemannian manifolds it is known that a compact lorentzian manifold is geodesically complete if it is homogeneous or has constant curvature or admits a time like conformal vector field we consider certain lorentzian manifolds with abelian holonomy which are locally modelled by the so called pp waves and which in general do not satisfy any of the above conditions we show that compact pp waves are universally covered by a vector space determine the metric on the universal cover and prove that they are geodesically complete using this we show that every ricci flat compact pp wave is a plane wave

quaternion polar complex exponential transform for invariant color image description moments and moment invariants have been widely used as a basic feature descriptors in image analysis pattern recognition and image retrieval however they are mainly used to deal with the binary or gray scale images which lose some significant color information recently quaternion techniques were introduced to conventional image moments including fourier mellin moments zernike pseudo zernike moments and bessel fourier moments etc for describing color images and some quaternion moment and moment invariants were developed but the conventional image moments usually cannot effectively capture the image information especially the edges besides the kernel computation of them involves computation of a number of factorial terms which inevitably cause the numerical stability of these moments based on effective polar complex exponential transform pcet and algebra of quaternions we introduced the quaternion polar complex exponential transform qpcet for describing color images in this paper which can be seen as the generalization of pcet for gray level images it is shown that the qpcets can be obtained from the pcet of each color channel we derived and analyzed the rotation scaling and translation rst invariant property of qpcet we also discussed the problem of color image retrieval using qpcet experimental results are provided to illustrate the efficiency of the proposed color image descriptors

image analysis by generalized chebyshev fourier and generalized pseudo jacobi fourier moments in this paper we present two new sets named the generalized chebyshev fourier radial polynomials and the generalized pseudo jacobi fourier radial polynomials which are orthogonal over the unit circle these generalized radial polynomials are then scaled to define two new types of continuous orthogonal moments which are invariant to rotation the classical chebyshev fourier and pseudo jacobi fourier moments are the particular cases of the proposed moments with parameter 0 the relationships among the proposed two generalized radial polynomials and jacobi polynomials shift jacobi polynomials and the hypergeometric functions are derived in detail and some interesting properties are discussed two recursive methods are developed for computing radial polynomials so that it is possible to improve computation speed and to avoid numerical instability simulation results are provided to validate the proposed moment functions and to compare their performance with previous works highlightspaper presents two generalized radial polynomials that are orthogonal over the unit circle paper constructs two new generalized descriptors using the scaled radial polynomials two recursive strategies for the computation of proposed radial polynomials are presented the proposed polynomials are related to jacobi shift jacobi polynomials and hypergeometric functions the distribution of zeroes of the proposed polynomials can be controlled by free parameter

three dimensional affine crystallographic groups those groups r which act properly discontinuously and aillnely on ii with compact fundamental domain are classified first it is shown that such a group f contains a solvable subgroup of finite index thus establishing a conjecture of auslander in dimension three then unimodular simply transitive altine actions on ir are classified this leads to a classification of attine crystallographic groups acting on ir3 a characterization of which abstract groups admit such an action is given moreover it is proved that every isomorphism between virtually solvable atline crystallographic groups respectively simply transitive afline groups is induced by conjugation by a polynomial automorphism of the affrne space a characterization is given of which closed 3 manifolds can be represented as quotients of ir by groups of afftne transformations a closed 3 manifold m admits a complete atline structure if and only if m has a finite covering homeomorphic or homotopy equivaient to a 2 torus bundle over the circle

methods of holonomy theory for ricci flat riemannian manifolds compact ricci flat riemannian manifolds often arise in physical applications either as a technical device or as models of internal space the idea of extending the holonomy group of such a manifold to a larger gauge group embedding the connection in the gauge group plays a fundamental role in the manifold compactification approach to superstring phenomenology and the work of gepner suggests that this idea may have equally fundamental analogs in other approaches the holonomy theory of simply connected ricci flat manifolds has recently been the subject of much mathematical work but physicists are mainly interested in the case of multiply connected manifolds the purpose of this paper is to present some techniques for understanding the holonomy theory of compact multiply connected ricci flat manifolds these lead to a general classification theorem

revisiting complex moments for 2 d shape representation and image normalization when comparing 2 d shapes a key issue is their normalization translation and scale are easily taken care of by removing the mean and normalizing the energy however defining and computing the orientation of a 2 d shape is not so simple in fact although for elongated shapes the principal axis can be used to define one of two possible orientations there is no such tool for general shapes as we show in the paper previous approaches fail to compute the orientation of even noiseless observations of simple shapes we address this problem and show how to uniquely define the orientation of an arbitrary 2 d shape in terms of what we call its principal moments we start by showing that a small subset of these moments suffices to describe the underlying 2 d shape i e that they form a compact representation which is particularly relevant when dealing with large databases then we propose a new method to efficiently compute the shape orientation principal moment analysis finally we discuss how this method can further be applied to normalize gray level images besides the theoretical proof of correctness we describe experiments demonstrating robustness to noise and illustrating with real images

a comparative analysis of algorithms for fast computation of zernike moments abstract this paper details a comparative analysis on time taken by the present and proposed methods to compute the zernike moments z pq the present method comprises of direct belkasim s prata s kintner s and coefficient methods we propose a new technique denoted as q recursive method specifically for fast computation of zernike moments it uses radial polynomials of fixed order p with a varying index q to compute zernike moments fast computation is achieved because it uses polynomials of higher index q to derive the polynomials of lower index q and it does not use any factorial terms individual order of moments can be calculated independently without employing lower or higher order moments this is especially useful in cases where only selected orders of zernike moments are needed as pattern features the performance of the present and proposed methods are experimentally analyzed by calculating zernike moments of orders 0 to p and specific order p using binary and grayscale images in both the cases the q recursive method takes the shortest time to compute zernike moments

general form for obtaining unit disc based generalized orthogonal moments the rotation invariance of the classical disc based moments such as zernike moments zms pseudo zms pzms and orthogonal fourier mellin moments ofmms makes them attractive as descriptors for the purpose of recognition tasks however less work has been performed for the generalization of these moment functions in this paper four general forms are developed to obtain a class of disc based generalized radial polynomials that are orthogonal over the unit circle these radial polynomials are scaled to ensure numerical stability and some useful properties are discussed for potential applications they could be used in then these scaled radial polynomials are used as kernel functions to construct a series of unit disc based generalized orthogonal moments dgms the variation of parameters in dgms can form various types of orthogonal moments 1 generalized zms 2 generalized pzms and 3 generalized ofmms the classical zms pzms and ofmms correspond to a special case of these three generalized moments for which the free parameter alpha 0 each member of this family will share some excellent properties for image representation and recognition tasks such as orthogonality and rotation invariance in addition we have also developed two algorithms the so called m recursive and n recursive methods for the computation of these proposed radial polynomials to improve the numerical stability experimental results show that the proposed methods are superior to the classical disc based moments in terms of image representation capability and classification accuracy

on the stability of riemannian manifold with parallel spinors inspired by the recent work hhm03 we prove two stability results for compact riemannian manifolds with nonzero parallel spinors our first result says that ricci flat metrics which also admit nonzero parallel spinors are stable in the direction of changes in conformal structures as the critical points of the total scalar curvature functional our second result which is a local version of the first one shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor we also prove a rigidity result for special holonomy metrics in the case of su m holonomy the rigidity result implies that scalar flat deformations of calabi yau metric must be calabi yau finally we explore the connection with a positive mass theorem of d03 which presents another approach to proving these stability and rigidity results

on the accuracy of zernike moments for image analysis we give a detailed analysis of the accuracy of zernike moments in terms of their discretization errors and the reconstruction power it is found that there is an inherent limitation in the precision of computing the zernike moments due to the geometric nature of a circular domain this is explained by relating the accuracy issue to a celebrated problem in analytic number theory of evaluating the lattice points within a circle

invariant representation of orientation fields for fingerprint indexing orientation fields can be used to describe interleaved ridge and valley patterns of fingerprint image providing features useful for fingerprint recognition however for tasks such as fingerprint indexing additional image alignment is often required to avoid confounding effects caused by pose differences in this paper we propose to employ a set of polar complex moments pcms for extraction of rotation invariant fingerprint representation pcms are capable of describing fingerprint ridge flow structures including singular regions and are tolerant to spurious orientations in noisy fingerprints from the orientation fields a set of rotation moment invariants are derived to form a feature vector for comprehensive fingerprint structural description this feature vector gives a compact and rotation invariant representation that is important for pose robust fingerprint indexing a clustering based fingerprint indexing scheme is employed to facilitate efficient and effective retrieval of the most likely candidates from a fingerprint database our experimental results on nist and fvc fingerprint databases indicate that the proposed invariant representation improves the performance of fingerprint indexing as compared to state of the art methods

the geometry of homogeneous submanifolds of hyperbolic space we prove in a purely geometric way that there are no connected irreducible proper subgroups of so n 1 moreover a weakly irreducible subgroup of so n 1 must either act transitively irreducible subgroup of so n 1 must either act transitively on the hyperbolic space or on a horosphere this has obvious consequences for lorentzian holonomy and in particular explains clasification results of marcel berger s list e g the fact that an irreducible lorentzian locally symmetric space has constant curvatures we also prove that a minimal homogeneous submanifold of hyperbolic space must be totally geodesic

structure integral transform versus radon transform a 2d mathematical tool for invariant shape recognition in this paper we present a novel mathematical tool structure integral transform sit for invariant shape description and recognition different from the radon transform rt which integrates the shape image function over a 1d line in the image plane the proposed sit builds upon two orthogonal integrals over a 2d k cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral the proposed sit brings the following advantages over the rt 1 it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition 2 the shape regions are dissected by the k cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery and 3 it is easier to build a completely invariant shape descriptor the experimental results of applying sit to shape recognition demonstrate its superior performance over the well known radon transform and the well known shape contexts and the polar harmonic transforms

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

examples of einstein manifolds with all possible holonomy groups in dimensions less than seven in an earlier work the possible holonomy groups of all compact locally irreducible riemannian manifolds of dimensions up to ten were classified placing particular emphasis on the non simply connected case in this work the problem of finding examples of manifolds with such holonomy groups is discussed it is proven in particular that it is possible to find einsteinian examples of every one of the 23 holonomy types corresponding to manifolds of dimensions less than 7 thus an exact characterization of the groups that can occur as holonomy groups can be given in those dimensions

parallel spinors and holonomy groups in this paper we complete the classification of spin manifolds admitting parallel spinors in terms of the riemannian holonomy groups more precisely we show that on a given n dimensional riemannian manifold spin structures with parallel spinors are in one to one correspondence with lifts to spinn of the riemannian holonomy group with fixed points on the spin representation space in particular we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors

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

on the independence of rotation moment invariants abstract the problem of the independence and completeness of rotation moment invariants is addressed in this paper first a general method for constructing invariants of arbitrary orders by means of complex moments is described as a major contribution of the paper it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated the method how to construct such a basis and how to prove its independence and completeness is presented some practical impacts of the new results are mentioned at the end of the paper

using zernike moments for the illumination and geometry invariant classification of multispectral texture we develop a method for recognizing color texture independent of rotation scale and illumination color texture is modeled using spatial correlation functions defined within and between sensor bands using a linear model for surface spectral reflectance with the same number of parameters as the number of sensor classes we show that illumination and geometry changes in the scene correspond to a linear transformation of the correlation functions and a linear transformation of their coordinates a several step algorithm that includes scale estimation and correlation moment computation is used to achieve the invariance the key to the method is the new result that illumination rotation and scale changes in the scene correspond to a specific transformation of correlation function zernike moment matrices these matrices can be estimated from a color image this relationship is used to derive an efficient algorithm for recognition the algorithm is substantiated using classification results on over 200 images of color textures obtained under various illumination conditions and geometric configurations

fast computation of jacobi fourier moments for invariant image recognition the jacobi fourier moments jfms provide a wide class of orthogonal rotation invariant moments orims which are useful for many image processing pattern recognition and computer vision applications they however suffer from high time complexity and numerical instability at high orders of moment in this paper a fast method based on the recursive computation of radial kernel function of jfms is proposed which not only reduces time complexity but also improves their numerical stability fast recursive method for the computation of jacobi fourier moments is proposed the proposed method not only reduces time complexity but also improves numerical stability of moments better image reconstruction is achieved with lower reconstruction error proposed method is useful for many image processing pattern recognition and computer vision applications

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

geometrically invariant image watermarking using polar harmonic transforms this paper presents an invariant image watermarking scheme by introducing the polar harmonic transform pht which is a recently developed orthogonal moment method similar to zernike moment zm and pseudo zernike moment pzm approaches pht is defined on a circular domain the magnitudes of phts are invariant to image rotation and scaling furthermore the phts are free of numerical instability so they are more suitable for watermarking in this paper the invariant properties of phts are investigated during embedding a subset of the accurate phts are modified according to the binary watermark sequence then a compensation image is formatted by reconstructing the modified pht vector the final watermarked image is obtained by adding the compensation image to the original image in the decoder the watermark can be retrieved from the magnitudes of the phts directly experimental results illustrate that the proposed scheme outperforms zm pzm based schemes in terms of embedding capacity and watermark robustness and is also robust to both geometric and signal processing based attacks

index parity of closed geodesics and rigidity of hopf fibrations the diameter rigidity theorem of gromoll and grove 1987 states that a riemannian manifold with sectional curvature 1 and diameter 2 is either homeomorphic to a sphere locally isometric to a rank one symmetric space or it has the cohomology ring of the cayley plane ca the reason that they were only able to recognize the cohomology ring of ca is due to an exceptional case in another theorem gromoll and grove 1988 a riemannian submersion m b b with connected fibers that is defined on the euclidean sphere m is metrically congruent to a hopf fibration unless possibly m b 15 8 we will rule out the exceptional cases in both theorems our argument relies on a rather unusal application of morse theory for that purpose we give a general criterion which allows to decide whether the morse index of a closed geodesic is even or odd

generalized cylinders in semi riemannian and spin geometry we use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory it has the advantage of being very simple and the result directly extends to semi riemannian manifolds and to embeddings into spaces of constant curvature we also give a new way to identify spinors for different metrics and to derive the variation formula for the dirac operator moreover we show that generalized killing spinors for codazzi tensors are restrictions of parallel spinors finally we study the space of lorentzian metrics and give a criterion when two lorentzian metrics on a manifold can be joined in a natural manner by a 1 parameter family of such metrics

local birth of homoclinic chaos abstract local generation of chaotic behaviours associated with a sil nikov homoclinic orbit is studied near the codimension two bifurcation at the double stationary oscillatory instability of eigenvalues 0 we develop a perturbative calculation of the sil nikov homoclinic orbit and of its bifurcation locus starting from a conservative vector field flat nonanalytic behaviours due to non axisymmetric perturbations of the normal form are discussed and we show that the codimension one locus of sil nikov homoclinicity is unavoidable near bicriticality under certain conditions the results are applied to rossler s model quasiperiodic regimes born at the double instability are also studied and illustrated in the rossler model

interaction of steady and periodic bifurcating modes with imperfection effects in reaction diffusion systems asymptotic solutions for two dimensional reaction diffusion systems are obtained under suitable conditions a trivial solution independent of both time and space is assumed to exist and the linearized system about this solution is considered the analysis is restricted to the case where this linearized system possesses one real eigenvalue and a complex pair of eigenvalues all with real part approximately equal to zero steady periodic and doubly periodic bifurcating solutions are found with special attention given to the effects of imperfection in one of the parameters

multi level dense descriptor and hierarchical feature matching for copy move forgery detection in this paper a multi level dense descriptor mldd extraction method and a hierarchical feature matching method are proposed to detect copy move forgery in digital images the mldd extraction method extracts the dense feature descriptors using multiple levels while the extracted dense descriptor consists of two parts the color texture descriptor and the invariant moment descriptor after calculating the mldd for each pixel the hierarchical feature matching method subsequently detects forgery regions in the input image first the pixels that have similar color textures are grouped together into distinctive neighbor pixel sets next each pixel is matched with pixels in its corresponding neighbor pixel set through its geometric invariant moments then the redundant pixels from previously generated matched pixel pairs are filtered out by the proposed adaptive distance and orientation based filtering method finally some morphological operations are applied to generate the final detected forgery regions experimental results show that the proposed scheme can achieve much better detection results compared with the existing state of the art cmfd methods even under various challenging conditions such as geometric transforms jpeg compression noise addition and down sampling

detection of composite edges the paper presents a new parametric model based approach to high precision composite edge detection using orthogonal zernike moment based operators it deals with two types of composite edges a generalized step and b pulse staircase edges a 2 d generalized step edge is modeled in terms of five parameters two gradients on two sides of the edge the distance from the center of the candidate pixel the orientation of the edge and the step size at the location of the edge a 2 d pulse staircase edge is modeled in terms of two steps located at two positions within the mask and the edge orientation a pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity two complex and two real zernike moment based masks are designed to determine parameters of both the 2 d edge models for a given edge model estimated parameter values at a point are used to detect the presence or absence of that type of edge extensive noise analysis is performed to demonstrate the robustness of the proposed operators experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment based step edge detection technique and canny s 1986 edge detector

fast generic polar harmonic transforms generic polar harmonic transforms have recently been proposed to extract rotation invariant features from images and their usefulness has been demonstrated in a number of pattern recognition problems however direct computation of these transforms from their definition is inefficient and is usually slower than some efficient computation strategies that have been proposed for other methods this paper presents a number of novel computation strategies to compute these transforms rapidly the proposed methods are based on the inherent recurrence relations among complex exponential and trigonometric functions used in the definition of the radial and angular kernels of these transforms the employment of these relations leads to recursive and addition chain based strategies for fast computation of harmonic function based kernels experimental results show that the proposed method is about 10 times faster than direct computation and 5 times faster than fast computation of zernike moments using the q recursive strategy thus among all existing rotation invariant feature extraction methods polar harmonic transforms are the fastest

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

affine transformations and parallel lightlike vector fields on compact lorentzian 3 manifolds we describe the compact lorentzian 3 manifolds admitting a parallel lightlike vector field the classification of compact lorentzian 3 manifolds admitting non isometric affine diffeomorphisms follows together with the complete description of these morphisms such a lorentzian manifold is in some sense an equivariant deformation of a flat one