fingerprint orientation field reconstruction by weighted discrete cosine transform orientation field represents the topological structure of the interleaved ridge and valley flows in fingerprint images although a number of methods have been proposed for orientation estimation reliable computation of orientation field is still a challenging problem due to the poor quality of some fingerprints this paper proposes a method to reconstruct fingerprint orientation field by weighted discrete cosine transform dct first the dct functions are used to build the basis atoms for linear representation of orientation field then the dct basis atoms of low and high orders are combined with the weights determined by singularity measurements for orientation reconstruction the weighted dct model is further extended for partial fingerprints to gradually and iteratively reconstruct the orientations in noisy or missing parts of fingerprints the proposed method can perform well in smoothing out the noise while maintaining the orientation details in singular regions extensive experiments have been done to compare the proposed method with some existing methods on nist and fvc fingerprint databases in terms of the reconstruction accuracy of orientation field fingerprint indexing performance and fingerprint recognition accuracy experimental results illustrate the effectiveness of the proposed method in reconstructing orientation fields especially for poor quality and partial fingerprints

on the number of nodes in n dimensional cubature formulae of degree 5 for integrals over the ball in this note cubature formulae of degree 5 are studied for n dimensional integrals over the ball with constant weight function we apply the method of reproducing kernel to show that the existence of such formulae attaining the best known lower bound is equivalent to the existence of tight spherical 5 designs the known results concerning spherical 5 designs show that the lower bound for the integral under consideration will not be attained in general the bound will be attained for n 2 3 7 23 and possibly for n 2p 1 2 2 p 5 in all other cases the bound must be increased at least by 1 in particular stroud s formulae for n 4 5 6 7 are minimal

numerical cubature using error correcting codes we present a construction for improving numerical cubature formulas with equal weights and a convolution structure in particular equal weight product formulas using linear error correcting codes the construction is most effective in low degree with extended bch codes using it we obtain several sequences of explicit positive interior cubature formulas with good asymptotics for each fixed degree t as the dimension n to infty using a special quadrature formula for the interval g kuperberg adv in appl math 34 2005 pp 853 870 arxiv math pr 0408360 we obtain an equal weight t cubature formula on the n cube with o n lfloor t 2 rfloor points which is within a constant of the stroud lower bound we also obtain t cubature formulas on the n sphere n ball and gaussian rn with o nt 2 points when t is odd when mu is spherically symmetric and t 5 we obtain o n2 points for each t ge 4 we also obtain explicit positive interior formulas for the n simplex with o nt 1 points for t 3 we obtain o n points these constructions asymptotically improve the nonconstructive tchakaloff bound some related results were recently found independently by victoir siam j numer anal 42 2004 pp 209 227 who also noted that the basic construction more directly uses orthogonal arrays

modeling orientation fields of fingerprints with rational complex functions abstract in this paper a novel model is proposed for the orientation field of fingerprints which can be expressed as the argument of a rational complex function it is suitable for all types of fingerprints experimental results show that it performs much better than the previous works

generating a residual intersection let i be an ideal of height g 0 in a commutative noetherian ring r and let 2i be a proper sub ideal of i generated by 3 g elements if the ideal j 21 i has height at least s then j is called an s residual intersection of i see artin and nagata 1 huneke 19 or huneke and ulrich 22 the case s g corresponds to the theory of linkage and is well understood at least from the homolo cal point of view the cornerstone of this theory is that if i is perfect then a free resolution of r j can be produced from a free resolution of r z and the koszul complex on a set of generators of cu very little is known about resolutions of s residual intersections for s g a few special cases have been resolved s 10 301 and the end of the resolution or in other words a set of generators for the canonical module of r j has been described 22 however in general even the generators of j remain unknown here we show that j can be approximated by a sum of links of i if s g 1 and we give conditions under which this approximation in fact gives a full set of generators of j since these generators arise from comparison maps from koszul complexes to known resolutions at least assuming that the resolution of r i is in some sense known it is feasible to count them compute their degrees in the graded case or even to give explicit formulas for them after stating our main results theorem 2 15 and 2 16 and corollary 2 18 precisely in section 2 we lay out the argument in sections 3 4 and 5 in section 6 we are concerned with the question of when a g t 1 residual intersection j is

asymmetric cubature formulae with few points in high dimension for symmetric measures let mu be a positive measure on mathbb r d invariant under the group of reflections and permutations and let m be a natural number we describe a method to construct cubature formulae of degree m with respect to mu with n positive weights and n points in the support of mu and such that n grows at most like dm with the dimension d we apply this method to classical measures to explicitly construct cubature formulae of degree 5 with the number of points growing at most like d3

definition and extraction of stable points from fingerprint images this paper introduces a new idea to define and extract singular points sps including cores and deltas from fingerprint images by a zone could be in theorem that describes harmonic relationships of a sp and its neighbors according to the theorem we can view sps as stable points attractors and rejectors by their rotations estimate core s direction and restore sp offset the proposed method is validated in the following two hierarchical aspects one is to test the reliability and accuracy of coarse sp detection by means of two indices ri and ac and the other is the accuracy of core s location and the stability of core s direction in terms of improved fingercode matching experiments on partial fvc2004 data sets show that it works well and outperforms three other methods

finding inverse systems from coordinates abstract let i be a homogeneous ideal in r k x 0 x n such that r i is an artinian gorenstein ring a famous theorem of macaulay says that in this instance i is the ideal of polynomial differential operators with constant coefficients that cancel the same homogeneous polynomial f a major question related to this result is to be able to describe f in terms of the ideal i in this note we give a partial answer to this question by analyzing the case when i is the artinian reduction of the ideal of a reduced arithmetically gorenstein zero dimensional scheme p n we obtain f from the coordinates of the points of

global models for the orientation field of fingerprints an approach based on quadratic differentials quadratic differentials naturally define analytic orientation fields on planar surfaces we propose to model orientation fields of fingerprints by specifying quadratic differentials models for all fingerprint classes such as arches loops and whorls are laid out these models are parametrised by few geometrically interpretable parameters which are invariant under euclidean motions we demonstrate their ability in adapting to given observed orientation fields and we compare them to existing models using the fingerprint images of the nist special database 4 we also illustrate that these model allow for extrapolation into unobserved regions this goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region within the framework of quadratic differentials we are able to verify analytically penrose s formula for the singularities on a palm l s penrose dermatoglyphics scientific american vol 221 no 6 pp 73 84 1969 potential applications of these models are the use of their parameters as indices of large fingerprint databases as well as the definition of intrinsic coordinates for single fingerprint images

fingerprint pattern classification abstract this paper presents a new method for fingerprint classification in this method fingerprint images are divided into 32 32 subregions to obtain direction pattern next the relaxation smoothing process with singularity detection and convergency checking is performed starting from the singular regions found feature parameters of the fingerprint are obtained by extracting major flow line traces the result of the experiments shows that this approach is capable of classifying fingerprint patterns into more than ten categories

modelling fingerprint ridge orientation using legendre polynomials the estimation of fingerprint ridge orientation is an essential step in every automatic fingerprint verification system the importance of ridge orientation can be deflected from the fact that it is inevitably used for detecting describing and matching fingerprint features such as minutiae and singular points in this paper we propose a novel method for fingerprint ridge orientation modelling using legendre polynomials one of the main problems it addresses is smoothing orientation data while preserving details in high curvature areas especially singular points we show that singular points which result in a discontinuous orientation field can be modelled by the zero poles of legendre polynomials the models parameters are obtained in a two staged optimization procedure another advantage of the proposed method is a very compact representation of the orientation field using only 56 coefficients we have carried out extensive experiments using a state of the art fingerprint matcher and a singular point detector moreover we compared the proposed method with other state of the art fingerprint orientation estimation algorithms we can report significant improvements in both singular point detection and matching rates

liaison and castelnuovo mumford regularity in this article we establish bounds for the castelnuovo mumford regularity of projective schemes in terms of the degrees of their defining equations the main new ingredient in our proofs is to show that generic residual intersections of complete intersection rational singularities again have rational singularities when applied to the theory of residual intersections this circle of ideas also sheds new light on some known classes of free resolutions of residual ideals

pixel level singular point detection from multi scale gaussian filtered orientation field singular point as a global feature plays an important role in fingerprint recognition inconsistent detection of singular points apparently gives an affect to fingerprint alignment classification and verification accuracy this paper proposes a novel approach to pixel level singular point detection from the orientation field obtained by multi scale gaussian filters initially a robust pixel level orientation field is estimated by a multi scale averaging framework then candidate singular points in pixel level are extracted from the complex angular gradient plane derived directly from the pixel level orientation field the candidate singular points are finally validated via a cascade framework comprised of nested poincare indices and local feature based classification experimental results over the fvc 2000 db2 confirm that the proposed method achieves robust and accurate orientation field estimation and consistent pixel level singular point detection the experimental results exhibit a low computational cost with better performance thus the proposed method can be employed in real time fingerprint recognition

on minimal cubature formulae of small degree for spherically symmetric integrals the aim of this paper is to develop the existence and nonexistence problem of a cubature formula of degree 4k 1 for a spherically symmetric integral which attains the moller lower bound for this purpose we bring together the theory of euclidean design in combinatorics and that of reproducing kernels in numerical analysis we show that if there exists a minimal formula of degree 4k 1 then the nodes are distributed into k 1 concentric spheres including the origin and the weights in the formula are a constant on each concentric sphere we particularly focus on the cases of degrees 5 and 9 we show the equivalence between a minimal formula of degrees 5 and 4 and a spherical tight 5 and 4 design we also prove that there exists no minimal formula of degree 9 for some classical weights such as the gaussian weight on mathbb r d the radial exponential weight on mathbb r d and the jacobi weight on b d

linkage and the koszul homology of ideals 0 introduction let r be a local ring and i an ideal of r associated to i are several graded algebras the symmetric algebra of the module i sym i the rees algebra of i defined to be the algebra r i gn o inf and the associated graded algebra of i gr1 r rii g ii 2 in in 1 i i i our purpose in this paper is to study the behavior of these graded algebras when we change i through linkage recall the definition of linkage found in the paper of peskine and szpiro 22

the resolution of the generic residual intersection of a complete intersection the concept of residual intersection introduced by artin and nagata l in 1972 is a fruitful generalization of linkage as the following two examples attest let i be a strongly cohen macaulay ideal in a cohenmacaulay local ring r if z satisfies the condition g then huneke 6 proposition 4 31 has proved that the extended rees algebra r it t 1 is defined by an ideal which is obtained from i by way of residual intersection since the extended rees algebra is a deformation of both the rees algebra r it and the associated graded algebra gz i it contains considerable information about the analytic properties of i the definitions of residual intersection strongly cohen macaulay and g may be found in section 4 huneke 6 theorem 4 11 has also shown that the ideal i generated by the maximal order minors of a generic n x m matrix is a residual intersection of a generic codimension two cohen macaulay ideal since j is rather poorly behaved with respect to linkage s it is promising that it is close to a well understood ideal once we weaken the tie from linkage to residual intersection

a nonlinear orientation model for global description of fingerprints a nonlinear orientation model for the representation of the orientation matrix of a fingerprint image is presented a general procedure to obtain the set of parameters describing this model is shown particularly a piecewise linear orientation function is analysed the model compared with a previous zero pole model shows substantial decrease in the orientation error the application of this model for efficient identity verification based on the ridge orientation is explored

singular points detection based on zero pole model in fingerprint images an algorithm is proposed which combines zero pole model and hough transform ht to detect singular points orientation of singular points is defined on the basis of the zero pole model which can further explain the practicability of zero pole model contrary to orientation field generation detection of singular points is simplified to determine the parameters of the zero pole model ht uses rather global information of fingerprint images to detect singular points this makes our algorithm more robust to noise than methods that only use local information as the zero pole model may have a little warp from actual fingerprint orientation field poincare index is used to make position adjustment in neighborhood of the detected candidate singular points experimental results show that our algorithm performs well and fast enough for real time application in database nist 4

fisher type inequalities for euclidean t designs the notion of a euclidean t design is analyzed in the framework of appropriate inner product spaces of polynomial functions some fisher type inequalities are obtained in a simple manner by this method the same approach is used to deal with certain analogous combinatorial designs

on cubature formulae of degree 4k 1 attaining moller s lower bound for integrals with circular symmetry the structure of cubature formulae of degree 4k 1 whose number of nodes is equal to moller s lower bound is investigated for integrals with circular symmetry a simple criterion is derived for the existence of such formulae it shows that fork 1 moller s lower bound can always be attained with radon s formulae it also allows to prove that for several integrals with circular symmetry and several values ofk 1 moller s lower bound cannot be attained

on the spatial distribution of fingerprint singularities fingerprint singularities play an important role in several fingerprint recognition and classification systems although some general relationships and constraints about the location of singularities in the different fingerprint classes are well known to the best of our knowledge no statistical models have been developed until now this paper studies the spatial distributions of singularity locations in nature and derives from a representative dataset of labelled samples the probability density functions of the four main fingerprint classes the results obtained can be directly exploited to improve the accuracy of many techniques relying on the position of singularities as confirmed by the results of two experiments on fingerprint classification and synthesis

detection of singular points in fingerprint images abstract this paper describes a technique for the detection of singular points in a fingerprint image the singular points namely the core and the delta points are used as points of registration in fingerprint matching this method makes use of structural information culled from the directional histograms of the directional image of a fingerprint the usage of the histogram allows for a fairly high degree of noise tolerance

on the canonical module of the rees algebra and the associated graded ring of an ideal the investigations of this paper originate in the following question suppose i is an ideal of a local gorenstein ring r m whose associated graded ring gr r is cohenmacaulay under which extra conditions is gr r actually a gorenstein ring hochster shows in 151 that gr r is a gorenstein ring if r is factorial and gr r is a domain hochster s arguments work as well if one only requires r to be a gorenstein ring however the condition that gr r is a domain cannot be weakened much in fact we given an example of a local complete intersection r m whose associated graded ring gr r is a reduced cohen macaulay ring but not a gorenstein ring the question when gr r is a gorenstein ring has a more satisfying answer for ideals i generated by a d sequence for which r i is a cohen macaulay ring d sequences were introduced and studied by huneke their relevance in the study of powers of ideals was shown by huneke in 161 for further investigations on d sequences the reader is referred to 111 now given an ideal i generated by a d sequence and such that r i is cohenmacaulay we show that gr r is a gorenstein ring if and only if i is strongly cohen macaulay again the notion strongly cohen macaulay was introduced by huneke it means that the koszul homology of a system of generators of i is cohen macaulay huneke showed in 191 that any ideal in the linkage class of a complete intersection is strongly cohen macaulay this result provides us with plenty of interesting examples the main subject of the paper however is the study of the canonical module of gr r and of the rees algebra r if r zr 12t2 sr t in 14 the canonical class os of the rees algebra s r zr was determined under the assumption that i is

strongly cohen macaulay schemes and residual intersections this paper studies the local properties of closed subschemes y in cohen macaulay schemes x such that locally the defining ideal of y in x has the property that its koszul homology is cohen macaulay whenever this occurs y is said to be strongly cohen macaulay in x this paper proves several facts about such embeddings chiefly with reference to the residual intersections of y in x the main result states that any residual intersection of y in x is again cohen macaulay introduction our purpose in this paper is to investigate a property of a closed subscheme y in a noetherian cohen macaulay scheme x which we call strong cohen macaulayness this is a local property which we first describe for a local ring let x spec r where r is a cohen macaulay local ring and let y spec r i

constructing cubature formulae of degree 5 with few points this paper is devoted to construct a family of fifth degree cubature formulae for n cube with symmetric measure and n dimensional spherically symmetrical region the formula forn cube contains at most n 2 5n 3 points and for n dimensional spherically symmetrical region contains only n 2 3n 3 points moreover the numbers can be reduced to n 2 3n 1 and n 2 n 1 if n 7 respectively the latter of which is minimal

cubature for the sphere and the discrete spherical harmonic transform using a result of bannai and damerell it is shown that a cubature formula with n points of degree 2s 4 for the surface of the n dimensional sphere u n cannot achieve the classical lower bound of dim mathcal p s where mathcal p s is the space of all polynomials in n variables of at most degree s restricted to u n this implies that for n 2 there does not exist a cubature based discrete n dimensional spherical harmonic transform for degree s 2 with the same number of points as spectral coefficients

rees algebras of linearly presented ideals abstract let i be a height two perfect ideal with a linear presentation matrix in a polynomial ring r k x 1 x d assume that i d 1 and i satisfies the artin nagata condition g d 1 we determine the defining ideal of the rees algebra r i explicitly and we show that r i is cohen macaulay

fingerprint ridge orientation field reconstruction using the best quadratic approximation by orthogonal polynomials in two discrete variables this paper proposes a novel algorithm for reconstructing the fingerprint orientation field fof the basic idea of the algorithm is to reconstruct the ridge orientation by using the best quadratic approximation by orthogonal polynomials in two discrete variables we first estimate the local region orientation by the linear projection analysis lpa based on the vector set of point gradients and then reconstruct the ridge orientation field using the best quadratic approximation by orthogonal polynomials in two discrete variables in the sine domain in this way we solve the problem that is difficult to accurately extract low quality fingerprint image orientation fields the experiments with the database of fvc 2004 show that compared to the state of the art fingerprint orientation estimation algorithms the proposed method is more accurate and more robust against noise and is able to better estimate the fof of low quality fingerprint images with large areas of noise

a new approach for the existence problem of minimal cubature formulas based on the larman rogers seidel theorem in this paper we consider the existence problem of minimal cubature formulas of degree 4k 1 for spherically symmetric integrals we prove that for a minimal formula in sufficiently high dimensional space there exists some concentric sphere on which the inner product of any two distinct points is rational by using this result we prove that for any d ge 2 there exist no d dimensional minimal formulas of degrees 13 and 21 for some special integral

a combination model for orientation field of fingerprints orientation field is a global feature of fingerprints that is very important in automatic fingerprint identification systems afis establishing an accurate and concise model for orientation fields will not only improve the performance of orientation estimation but also make it feasible to apply orientation information in the matching process in this paper a novel model for the orientation field of fingerprints is proposed we use a polynomial model to approximate the orientation field globally and a point charge model at each singular point to improve the approximation locally these two models are combined together by a weight function experimental results are provided to illustrate the fact that this combination model is more accurate and robust with respect to noise compared with the previous works the application of the model is discussed at the end

some constructions of spherical 5 designs abstract spherical designs were introduced by delsarte goethals and seidel in 1977 a spherical t design in rn is a finite set x sn 1 with the property that for every polynomial p with degree t the average value of p on x equals the average value of p on sn 1 this paper contains some existence and nonexistence results mainly for spherical 5 designs in r3 delsarte goethals and seidel proved that if x is a spherical 5 design in r3 then x 12 and if xz sfnc 12 then x consists of the vertices of a regular icosahedron we show that such designs exist with cardinality 16 18 20 22 24 and every integer 26 if x is a spherical 5 design in rn then x n n 1 if x n n 1 then x has been called tight tight spherical 5 designs in rn are known to exist only for n 2 3 7 23 and possibly n u2 2 for odd u 7 any tight spherical 5 design in rn must consist of n n 1 2 antipodal pairs of points we show that for n 3 there are no spherical 5 designs in rn consisting of n n 1 2 1 antipodal pairs of points

numerical invariants of liaison classes 302 c huneke intersection what properties are then enjoyed by v for instance buchweitz was able to show that all such v are strongly nonobstructed see 5 for details the two questions above have been completely answered if x spec r with r a regular local ring and if codim v 2 in this case

a variational formulation for fingerprint orientation modeling orientation pattern is an important feature for characterizing fingerprint and plays critical roles in fingerprint recognition and fingerprint classification this paper proposes a framework for modeling the fingerprint orientation field based on the variational principle where the orientation pattern can be estimated through solving the associated euler lagrange equation compared with existing methods our proposed method has the following features firstly it does not require any prior information about the structure of the acquired fingerprint such as location of singular point s secondly it explicitly provides freedom for modeling the singularity in the orientation field thirdly it has less number of parameters comparison has been made with respect to state of the arts in fingerprint orientation modeling in terms of modeling accuracy fingerprint enhancement and singular point detection advantages of the proposed method are demonstrated

sums of linked ideals it is shown that the sum of two geometrically linked ideals in the linkage class of a complete intersection is again an ideal in the linkage class of a complete intersection conversely every gorenstein ideal of height at least two in the linkage class of a complete intersection can be obtained as a generalized localization of a sum of two geometrically linked ideals in the linkage class of a complete intersection we also investigate sums of doubly linked gorenstein ideals as an application we construct a perfect prime ideal which is strongly nonobstructed but not strongly cohen macaulay and a perfect prime ideal which is not strongly nonobstructed but whose entire linkage class is strongly cohen macaulay