detecting singular patterns in 2d vector fields using weighted laurent polynomial in this paper we propose a method for detecting patterns of interest in vector fields our method detects patterns in a scale and rotation invariant manner it works by approximating the vector field data locally using a laurent polynomial weighted by radial basis functions the proposed representation is able to model both analytic and non analytic flow fields invariance to scale and rotation is achieved by combining the linearity properties of the model coefficients and a scale space parameter of the radial basis functions promising detection results are obtained on a variety of fluid flow sequences

invariant measure for the stochastic navier stokes equations in unbounded 2d domains building upon a recent work by two of the authors and j seidler on bwbw feller property for stochastic nonlinear beam and wave equations we prove the existence of an invariant measure to stochastic 2 d navier stokes with multiplicative noise equations in unbounded domains this answers an open question left after the first author and y li proved a corresponding result in the case of an additive noise

on the stationary solutions and inviscid limit for the generalized proudman johnson equation with o 1 forcing abstract we consider the stationary problem for the generalized proudman johnson equation x x x a x x x x x x x f where a r and 0 are parameters and and f satisfy the periodic boundary conditions on we establish the existence of a time dependent solution and the uniqueness of the stationary solution for some large then we investigate the behavior of solution sequences in the limit 0 fixing a and f where bifurcations appear and new solutions emerge in particular we analyze if there is convergence towards stationary solutions for the corresponding inviscid equation

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

group theoretic characterizations of almost open immersions of curves abstract let p be a prime number and k either a finite field of characteristic p or a generalized sub p adic field let x 1 and x 2 be hyperbolic curves over k in the present paper we introduce a kind of morphism between x 1 and x 2 called an almost open immersion and give some group theoretic characterizations for the set of almost open immersions between x 1 and x 2 via their arithmetic fundamental groups this result generalizes the isom version of grothendieck s anabelian conjecture for curves over k which has been proven by s mochizuki and a tamagawa to the case of almost open immersions

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

rotational invariance based on fourier analysis in polar and spherical coordinates in this paper polar and spherical fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the laplacian with the eigenfunctions being separable in the corresponding coordinates the proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures the theory is compactly presented with an emphasis on the analogy to the normal fourier transform the relation between the polar or spherical fourier transform and the normal fourier transform is explored as examples of applications rotation invariant descriptors based on polar and spherical fourier coefficients are tested on pattern classification problems

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

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

simple systems with anomalous dissipation and energy cascade we analyze a class of dynamical systems of the type dot a n t c n 1 a n 1 t c n a n 1 t f n t n epsilon mathbb n a 0 0 where fn t is a forcing term with f n t not 0 only for n le n star infty and the coupling coefficients cn satisfy a condition ensuring the formal conservation of energy frac12 sum n a n t 2 despite being formally conservative we show that these dynamical systems support dissipative solutions suitably defined and as a result may admit unique statistical steady states when the forcing term fn t is nonzero this claim is demonstrated via the complete characterization of the solutions of the system above for specific choices of the coupling coefficients cn the mechanism of anomalous dissipations is shown to arise via a cascade of the energy towards the modes with higher n this is responsible for solutions with interesting energy spectra namely mathbb e a n 2 scales as n alpha as n here the exponents depend on the coupling coefficients cn and mathbb e denotes expectation with respect to the equilibrium measure this is reminiscent of the conjectured properties of the solutions of the navier stokes equations in the inviscid limit and their accepted relationship with fully developed turbulence hence these simple models illustrate some of the heuristic ideas that have been advanced to characterize turbulence similar in that respect to the random passive scalar or random burgers equation but even simpler and fully solvable

the local pro p anabelian geometry of curves let x be a connected scheme then one can associate after grothendieck to x its algebraic fundamental group 1 x this group 1 x is a profinite group which is uniquely determined up to inner automorphisms by the property that the category of finite discrete sets equipped with a continuous 1 x action is equivalent to the category of finite etale coverings of x moreover the assignment x 1 x is a functor from the category of connected schemes and morphisms of schemes to the category of profinite topological groups and continuous outer homomorphisms i e continuous homomorphisms of topological groups where we identify any two homomorphisms that can be obtained from one another by composition with an inner automorphism

onsager s conjecture on the energy conservation for solutions of euler s equation we give a simple proof of a result conjectured by onsager 1 on energy conservation for weak solutions of euler s equation

enhanced gradient based algorithm for the estimation of fingerprint orientation fields an accurate estimation of fingerprint orientation fields is an essential step in the overall fingerprint recognition process conventional gradient based approaches are popular but very sensitive to noise in this paper we propose a novel implementation to improve the performance of gradient based methods the enhanced algorithm chooses the best orientation estimate from four overlapping neighborhoods of every image block where the voting scheme is based on the reliability measures we test our algorithm on real fingerprint images the experiment results suggest that our enhanced algorithm achieves visibly better noise resistance with modest computation time in comparison with other gradient based methods

singular point detection by shape analysis of directional fields in fingerprints this paper presents a new fingerprint singular point detection method that is type distinguishable and applicable to various fingerprint images regardless of their resolutions the proposed method detects singular points by analyzing the shapes of the local directional fields of a fingerprint image using the predefined rules all types of singular points upper core lower core and delta points can be extracted accurately and delineated in terms of the type of singular points in case of arch type fingerprints there exists no singular point but reference points for arch type fingerprints are required to be detected for registration therefore we propose a new reference point detection method for arch type fingerprints as well the result of the experiments on the two public databases fvc2000 2a fvc2002 2a with different resolutions demonstrates that the proposed method has high accuracy in locating each types of singular points and detecting the reference points of arch type fingerprints without regard to their image resolutions

inviscid limit for damped and driven incompressible navier stokes equations in mathbb r 2 we consider the zero viscosity limit of long time averages of solutions of damped and driven navier stokes equations in mathbb r 2 we prove that the rate of dissipation of enstrophy vanishes stationary statistical solutions of the damped and driven navier stokes equations converge to renormalized stationary statistical solutions of the damped and driven euler equations these solutions obey the enstrophy balance

nonperturbative renormalization group study of the stochastic navier stokes equation we study the renormalization group flow of the average action of the stochastic navier stokes equation with power law forcing using galilean invariance we introduce a nonperturbative approximation adapted to the zero frequency sector of the theory in the parametric range of the holder exponent 4 2e of the forcing where real space local interactions are relevant in any spatial dimension d we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis kolmogorov s 5 3 law is thus recovered for e 2 as also predicted by perturbative renormalization at variance with the perturbative prediction the 5 3 law emerges in the presence of a saturation in the e dependence of the scaling dimension of the eddy diffusivity at e 3 2 when according to perturbative renormalization the velocity field becomes infrared relevant

discontinuous galerkin methods for the stokes equations with nonlinear damping term on general meshes abstract this paper presents the interior penalty discontinuous galerkin ipdg methods to solve the stationary stokes equations with nonlinear damping term the ipdg discrete schemes are established on general meshes the corresponding consistency and stabilization of those schemes are proved subsequently we analyze the existence boundedness and uniqueness of the discrete solutions then the optimal error estimates are derived in the l 2 norm and h 1 like dg norm for the velocity variable and l 2 norm for the pressure variable respectively finally some numerical experiments in two dimensional are reported to demonstrate the theoretical results and show the robustness of our discrete schemes

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

markov random field models for directional field and singularity extraction in fingerprint images a bayesian formulation is proposed for reliable and robust extraction of the directional field in fingerprint images using a class of spatially smooth priors the spatial smoothness allows for robust directional field estimation in the presence of moderate noise levels parametric template models are suggested as candidate singularity models for singularity detection the parametric models enable joint extraction of the directional field and the singularities in fingerprint impressions by dynamic updating of feature information this allows for the detection of singularities that may have previously been missed as well as better aligning the directional field around detected singularities a criteria is presented for selecting an optimal block size to reduce the number of spurious singularity detections the best rates of spurious detection and missed singularities given by the algorithm are 4 9 and 7 1 respectively based on the nist 4 database

abstract framework for the theory of statistical solutions abstract an abstract framework for the theory of statistical solutions is developed for general evolution equations extending the theory initially developed for the three dimensional incompressible navier stokes equations the motivation for this concept is to model the evolution of uncertainties on the initial conditions for systems which have global solutions that are not known to be unique both concepts of statistical solution in trajectory space and in phase space are given and the corresponding results of existence of statistical solution for the associated initial value problems are proved the wide applicability of the theory is illustrated with the very incompressible navier stokes equations a reaction diffusion equation and a nonlinear wave equation all displaying the property of global existence of weak solutions without a known result of global uniqueness

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

walking to singular points of fingerprints singular point is an essential global feature in fingerprint images existing methods for singular points detection generally visit each pixel or each small image block to determine the singular point that is to say existing methods require scanning the image to compute a quantity at each pixel or block and hence they are inevitably time consuming we propose a fast algorithm for detecting singular points by walking directly to them instead of scanning the image walking directional fields wdfs are established from the orientation field then following the walking directions on wdfs we can rapidly walk to the singular points the walking algorithm is extremely fast and easily implemented with acceptable accuracy further more its accuracy can also be improved by combining with state of the art methods we can rapidly walk to a candidate singular point then refine its location using existing more accurate method in the local area experimental results on datasets of spd2010 and fvc validate the high efficiency and satisfactory accuracy of the proposed algorithm highlightswe propose a novel fast method for singular point detection we can walk directly to singular points without scanning fingerprint images simplicity of the idea makes the algorithm easy to be implemented our algorithm can be combined with state of the art method to improve performance

computerized flow field analysis oriented texture fields an approach to the solution of signal to symbol transformation in the domain of flow fields such as oriented texture fields and velocity vector fields is discussed the authors use the geometric theory of differential equations to derive a symbol set based on the visual appearance of phase portraits which are a geometric representation of the solution curves of a system of differential equations they also provide the computational framework to start with a given flow field and derive its symbolic representation specifically they segment the given texture derive its symbolic representation and perform a quantitative reconstruction of the salient features of the original texture based on the symbolic descriptors results of applying this technique to several real texture images are presented this technique is useful in describing complex flow visualization pictures defects in lumber processing defects in semiconductor wafer inspection and optical flow fields

vanishing viscosity limit for global attractors for the damped navier stokes system with stress free boundary conditions abstract we consider the damped and driven navier stokes system with stress free boundary conditions and the damped euler system in a bounded domain r 2 we show that the damped euler system has a strong global attractor in h 1 we also show that in the vanishing viscosity limit the global attractors of the navier stokes system converge in the non symmetric hausdorff distance in h 1 to the strong global attractor of the limiting damped euler system whose solutions are not necessarily unique

systematic methods for the computation of the directional fields and singular points of fingerprints the first subject of the paper is the estimation of a high resolution directional field of fingerprints traditional methods are discussed and a method based on principal component analysis is proposed the method not only computes the direction in any pixel location but its coherence as well it is proven that this method provides exactly the same results as the averaged square gradient method that is known from literature undoubtedly the existence of a completely different equivalent solution increases the insight into the problem s nature the second subject of the paper is singular point detection a very efficient algorithm is proposed that extracts singular points from the high resolution directional field the algorithm is based on the poincare index and provides a consistent binary decision that is not based on postprocessing steps like applying a threshold on a continuous resemblance measure for singular points furthermore a method is presented to estimate the orientation of the extracted singular points the accuracy of the methods is illustrated by experiments on a live scanned fingerprint database

on the euler equations of incompressible fluids euler equations of incompressible fluids use and enrich many branches of mathematics from integrable systems to geometric analysis they present important open physical and mathematical problems examples include the stable statistical behavior of ill posed free surface problems such as the rayleightaylor and kelvin helmholtz instabilities the paper describes some of the open problems related to the incompressible euler equations with emphasis on the blowup problem the inviscid limit and anomalous dissipation some of the recent results on the quasigeostrophic model are also mentioned

note on loss of regularity for solutions of the 3 d incompressible euler and related equations one of the central problems in the mathematical theory of turbulence is that of breakdown of smooth indefinitely differentiable solutions to the equations of motion in 1934 j leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3 d incompressible navier stokes equations the problem is still open we show in this report that breakdown of smooth solutions to the 3 d incompressible slightly viscous i e corresponding to high reynolds numbers or highly turbulent navier stokes equations cannot occur without breakdown in the corresponding solution of the incompressible euler ideal fluid equation we prove then that solutions of distorted euler equations which are equations closely related to the euler equations for short term intervals do breakdown

fingerprint ridge distance computation methodologies abstract the average ridge distance of fingerprint images is used in many problems and applications it is used in fingerprint filter design or in identification and classification procedures this paper addresses the problem of local average ridge distance computation this computation is based on a two step procedure first the average distance is defined in each significant portion of the image and then this information is propagated onto the remaining regions to complete the computation two methods are considered in the first step geometric and spectral in the geometric approach the central points of ridges are estimated on a regular grid and straight lines passing through these points and parallel to the ridge directions are used the second method is based on the computation of harmonic coefficients leading to effective estimates of the average ridge period in order to complete the average distance map a diffusion equation is used so that maps with minimum variations are favored finally some experimental results on nist sdb4 are reported

inviscid limit for the damped boussinesq equation abstract in this paper we consider the limit behavior of solutions to the cauchy problem for damped boussinesq equation in the regime of small viscosity in r n it is shown that the strong solutions of damped boussinesq equation converge to a strong solution of boussinesq equation in any time interval 0 t the key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped boussinesq equation which is a kind of new view we analyze the dispersion by the techniques of high low frequency decomposition and littlewood paley dyadic decomposition stationary phase estimate and some properties of bessel function

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

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

exponential decay of the power spectrum of turbulence the analyticity on a strip of the solutions of navier stokes equations in 2d is shown to explain the observed fast decay of the frequency power spectrum of the turbulent velocity field some subtleties in the application of the wiener khinchine method to turbulence are resolved by showing that the frequency power spectrum of turbulent velocities is in fact a measure exponentially decaying for frequency our approach also shows that the conventional procedures used in analyzing data in turbulence experiments are valid even in the absence of the ergodic property in the flow

equivariant holomorphic filters for contour denoising and rapid object detection it is well known that linear filters are not powerful enough for many low level image processing tasks however it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are at the same time equivariant with respect to translation and rotation this paper proposes a new class of rotation equivariant nonlinear filters that is based on the principle of group integration these filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results the relations of the proposed approach to volterra filters and steerable filters are shown in the context of detection problems the filter may be interpreted as some kind of generalized hough transform the experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images in the detection context our experiments show that the proposed filter is definitely superior to alternative approaches when high localization accuracy is required

asymptotic behavior of strong solutions to the 3d navier stokes equations with a nonlinear damping term abstract this paper deals with the asymptotic behavior of strong solutions to the 3d navier stokes equations with a nonlinear damping term u 1 u 3 first we establish an upper bound for the difference between the solution of our equation and the heat equation in l 2 space then we optimize the upper bound of decay for the solutions and obtain their algebraic lower bound by using fourier splitting method

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

weak solutions renormalized solutions and enstrophy defects in 2d turbulence enstrophy half the integral of the square of vorticity plays a role in 2d turbulence theory analogous to the role of kinetic energy in the kolmogorov theory of 3d turbulence it is therefore interesting to obtain a description of the way enstrophy is dissipated at high reynolds numbers in this article we explore the notions of viscous and transport enstrophy defect which model the spatial structure of the dissipation of enstrophy these notions were introduced by g eyink in an attempt to reconcile the kraichnan batchelor theory of 2d turbulence with current knowledge of the properties of weak solutions of the equations of incompressible and ideal fluid motion three natural questions arise from eyink s theory i existence of the enstrophy defects ii conditions for the equality of transport and viscous enstrophy defects iii conditions for the vanishing of the enstrophy defects in 10 eyink proved a number of results related to these questions and formulated a conjecture on how to answer these problems in a physically meaningful context in the present article we improve and extend some of eyink s results and present a counterexample to his conjecture

fingerprint reference point detection for image retrieval based on symmetry and variation reference point plays an important role in fingerprint identification systems the reference point is widely used for the fingerprint retrieval in large scale databases this paper proposes a novel algorithm for detecting a convex core point as a unique reference point consistently and accurately for all types of fingerprints in order to detect robust core point candidates a modified complex filter called semi radial symmetry filter is proposed to detect correctly rotational symmetries of core points moreover a vertical orientation variation feature called voriv feature is proposed to remove spurious core points and concave core points therefore the proposed technique computes the variation and symmetry combined energy vscome then the reference point is located by searching the global vscome maximum the experimental results on the public database fvc2004 db1 set a show that the proposed technique exhibits a very high robustness and gets the best performance in comparing with other approaches in literature

on inviscid limits for the stochastic navier stokes equations and related models we study inviscid limits of invariant measures for the 2d stochastic navier stokes equations as shown by kuksin j stat phys 115 1 2 469 492 2004 the noise scaling sqrt nu is the only one which leads to non trivial limiting measures which are invariant for the 2d euler equations using a moser type iteration for stochastic drift diffusion equations we show that any limiting measure mu 0 is in fact supported on bounded vorticities relationships of mu 0 to the long term dynamics of 2d euler in l infty with the weak topology are discussed we also obtain a drift independent modulus of continuity for a stationary deterministic model problem which leads us to conjecture that in fact mu 0 is supported on c 0 moreover in view of the batchelor krainchnan 2d turbulence theory we consider inviscid limits for a weakly damped stochastic navier stokes equation in this setting we show that only an order zero noise scaling with respect to leads to a nontrivial limiting measure in the inviscid limit

remarks about the inviscid limit of the navier stokes system in this paper we prove two results about the inviscid limit of the navier stokes system the first one concerns the convergence in hs of a sequence of solutions to the navier stokes system when the viscosity goes to zero and the initial data is in hs the second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions we present here a simple proof which also works in the 3d case the 3d case is new

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

fingerprint classification using fast fourier transform and nonlinear discriminant analysis in this paper we present a new approach for fingerprint classification based on discrete fourier transform dft and nonlinear discriminant analysis utilizing the dft and directional filters a reliable and efficient directional image is constructed from each fingerprint image and then nonlinear discriminant analysis is applied to the constructed directional images reducing the dimension dramatically and extracting the discriminant features the proposed method explores the capability of dft and directional filtering in dealing with low quality images and the effectiveness of nonlinear feature extraction method in fingerprint classification experimental results demonstrates competitive performance compared with other published results