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

structure tensor based analysis of cells and nuclei organization in tissues extracting geometrical information from large 2d or 3d biomedical images is important to better understand fundamental phenomena such as morphogenesis we address the problem of automatically analyzing spatial organization of cells or nuclei in 2d or 3d images of tissues this problem is challenging due to the usually low quality of microscopy images as well as their typically large sizes the structure tensor is a simple and robust descriptor that was developed to analyze textures orientation contrarily to segmentation methods which rely on an object based modeling of images the structure tensor considers the sample at a macroscopic scale like a continuous medium we show that this tool allows quantifying two important features of nuclei in tissues their privileged orientation as well as the ratio between the length of their main axes a quantitative evaluation of the method is provided for synthetic and real 2d and 3d images as an application we analyze the nuclei orientation and anisotropy on multicellular tumor spheroids cryosections this analysis reveals that cells are elongated in a privileged direction that is parallel to the spheroid boundary a matlab toolbox and an icy plugin are available to use the proposed method

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

unified framework for anisotropic interpolation and smoothing of diffusion tensor images to enhance the performance of diffusion tensor imaging dti based fiber tractography this study proposes a unified framework for anisotropic interpolation and smoothing of dti data the critical component of this framework is an anisotropic sigmoid interpolation kernel which is adaptively modulated by the local image intensity gradient profile the adaptive modulation of the sigmoid kernel permits image smoothing in homogeneous regions and meanwhile guarantees preservation of structural boundaries the unified scheme thus allows piece wise smooth continuous and boundary preservation interpolation of dti data so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure the new interpolation method is compared with conventional interpolation methods on the basis of fiber tracking from synthetic and in vivo dti data which demonstrates the effectiveness of this unified framework

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

a caveat concerning independence estimating equations with multivariate binary data clustered binary data occur commonly in both the biomedical and health sciences in this paper we consider logistic regression models for multivariate binary responses where the association between the responses is largely regarded as a nuisance characteristic of the data in particular we consider the estimator based on independence estimating equations iee which assumes that the responses are independent this estimator has been shown to be nearly efficient when compared with maximum likelihood ml and generalized estimating equations gee in a variety of settings the purpose of this paper is to highlight a circumstance where assuming independence can lead to quite substantial losses of efficiency in particular when the covariate design includes within cluster covariates assuming independence can lead to a considerable loss of efficiency in estimating the regression parameters associated with those covariates

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

denoising enhancing images on elastic manifolds the conflicting demands for simultaneous low pass and high pass processing required in image denoising and enhancement still present an outstanding challenge although a great deal of progress has been made by means of adaptive diffusion type algorithms to further advance such processing methods and algorithms we introduce a family of second order in time partial differential equations these equations describe the motion of a thin elastic sheet in a damping environment they are also derived by a variational approach in the context of image processing the new operator enables better edge preservation in denoising applications by offering an adaptive lowpass filter which preserves high frequency components in the pass band better than the adaptive diffusion filter while offering slower error propagation across edges we explore the action of this powerful operator in the context of image processing and exploit for this purpose the wealth of knowledge accumulated in physics and mathematics about the action and behavior of this operator the resulting methods are further generalized for color and or texture image processing by embedding images in multidimensional manifolds a specific application of the proposed new approach to superresolution is outlined

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

hyperconnected attribute filters based on k flat zones in this paper we present a new method for attribute filtering combining contrast and structural information using hyperconnectivity based on k flat zones we improve the ability of attribute filters to retain internal details in detected objects simultaneously we improve the suppression of small unwanted detail in the background we extend the theory of attribute filters to hyperconnectivity and provide a fast algorithm to implement the new method the new version is only marginally slower than the standard max tree algorithm for connected attribute filters and linear in the number of pixels or voxels it is two orders of magnitude faster than anisotropic diffusion the method is implemented in the form of a filtering rule suitable for handling both increasing size and nonincreasing shape attributes we test this new framework on nonincreasing shape filters on both 2d images from astronomy document processing and microscopy and 3d ct scans and show increased robustness to noise while maintaining the advantages of previous methods

an asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations in this paper a numerical method is suggested to solve a class of boundary value problems for a weakly coupled system of singularly perturbed second order ordinary differential equations of reaction diffusion type first in this method an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of the well known perturbation method then initial value problems and terminal value problems tvps are formulated such that their solutions are the terms of this asymptotic expansion these problems are happened to be singularly perturbed problems and therefore exponentially fitted finite difference schemes are used to solve these problems since the boundary value problem is converted into a set of initial and tvps and an asymptotic expansion approximation is used the present method is termed as an asymptotic initial value method necessary error estimates are derived and examples provided to illustrate the method the present method is easy to implement and well suited for parallel computing

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

a riemannian bayesian framework for estimating diffusion tensor images diffusion tensor magnetic resonance imaging dt mri is a non invasive imaging technique allowing to estimate the molecular self diffusion tensors of water within surrounding tissue due to the low signal to noise ratio of magnetic resonance images reconstructed tensor images usually require some sort of regularization in a post processing step previous approaches are either suboptimal with respect to the reconstruction or regularization step this paper presents a bayesian approach for simultaneous reconstruction and regularization of dt mr images that allows to resolve the disadvantages of previous approaches to this end estimation theoretical concepts are generalized to tensor valued images that are considered as riemannian manifolds doing so allows us to derive a maximum a posteriori estimator of the tensor image that considers both the statistical characteristics of the rician noise occurring in mr images as well as the nonlinear structure of tensor valued images experiments on synthetic data as well as real dt mri data validate the advantage of considering both statistical as well as geometrical characteristics of dt mri

hierarchical super resolution based inpainting this paper introduces a novel framework for examplar based inpainting it consists in performing first the inpainting on a coarse version of the input image a hierarchical super resolution algorithm is then used to recover details on the missing areas the advantage of this approach is that it is easier to inpaint low resolution pictures than high resolution ones the gain is both in terms of computational complexity and visual quality however to be less sensitive to the parameter setting of the inpainting method the low resolution input picture is inpainted several times with different configurations results are efficiently combined with a loopy belief propagation and details are recovered by a single image super resolution algorithm experimental results in a context of image editing and texture synthesis demonstrate the effectiveness of the proposed method results are compared to five state of the art inpainting methods

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

the analysis of longitudinal polytomous data generalized estimating equations and connections with weighted least squares in recent years methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual although situations in which the repeated response is binary or poisson have been studied extensively relatively little attention has been given to polytomous categorical response variable in this paper we extend the estimating equations initially developed for clustered discrete data by liang and zeger 1986 biometrika 73 13 22 and subsequently extended by prentice 1988 biometrics 44 1033 1048 to polytomous response variables under certain assumptions we illustrate that these estimating equations simplify to the weighted least squares wls equations formalized by koch et al 1977 biometrics 33 133 158 this connection provides a formal framework for obtaining iterated weighted least squares model parameter estimates cumulative logit models are developed and applied to a representative longitudinal data set simulation results comparing wls an iterative form of wls and independence estimating equations using a robust estimate of the variance are presented

generalized estimating equations for ordinal data a note on working correlation structures generalized estimating equations liang k y and zeger s 1986 biometrika 73 13 22 allow longitudinal or clustered data to be modeled with minimal assumptions about their dependence structures association structures for polytomous data have generally required the estimation of a large number of parameters in many applications involving repeated categorical data an ordinal structure is present a range of association structures and computational methods for ordinal categorical data is described based on the cumulative odds ratio which allows much more parsimonious models this permits the generalized estimating equation methodology to be used for smaller sets of ordinal data and with less effort expended on modeling associations the method is illustrated on sets of ordinal data from medical studies

segmentation and shape tracking of whole fluorescent cells based on the chan vese model we present a fast and robust approach to tracking the evolving shape of whole fluorescent cells in time lapse series the proposed tracking scheme involves two steps first coherence enhancing diffusion filtering is applied on each frame to reduce the amount of noise and enhance flow like structures second the cell boundaries are detected by minimizing the chan vese model in the fast level set like and graph cut frameworks to allow simultaneous tracking of multiple cells over time both frameworks have been integrated with a topological prior exploiting the object indication function the potential of the proposed tracking scheme and the advantages and disadvantages of both frameworks are demonstrated on 2 d and 3 d time lapse series of rat adipose derived mesenchymal stem cells and human lung squamous cell carcinoma cells respectively

cyclic schemes for pde based image analysis we investigate a class of efficient numerical algorithms for many partial differential equations pdes in image analysis they are applicable to parabolic or elliptic pdes that have bounded coefficients and lead to space discretisations with symmetric matrices our schemes are easy to implement and well suited for parallel implementations on gpus since they are based on the explicit diffusion scheme in the parabolic case and the jacobi method in the elliptic case by supplementing these methods with cyclically varying time step sizes or relaxation parameters we achieve efficiency gains of several orders of magnitude we call the resulting algorithms fast explicit diffusion fed and fast jacobi fj methods to achieve a good compromise between efficiency and accuracy we show that one should use parameter cycles that result from factorisations of box filters for these cycles we establish stability results in the euclidean norm our schemes perform favourably in a number of applications including isotropic nonlinear diffusion filters with widely varying diffusivities as well as anisotropic diffusion methods for image filtering inpainting and regularisation in computer vision moreover they are equally suited for higher dimensional problems as well as higher order pdes and they can also be interpreted as efficient first order methods for smooth optimisation problems

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

a computational method for solving boundary value problems for third order singularly perturbed ordinary differential equations singularly perturbed two point boundary value problems spbvps for third order ordinary differential equations odes with a small parameter multiplying the highest derivative are considered a numerical method is suggested in this paper to solve such problems in this method the given bvp is transformed into a system of two odes subject to suitable initial and boundary conditions then the domain of definition of the differential equation a closed interval is divided into two sub intervals which we call the inner region boundary layer and the outer region then the de is solved in these intervals separately the solutions obtained in these intervals are combined to give the solution in the whole interval to obtain boundary conditions at the transition points boundary values inside this interval we use mostly the zeroth order asymptotic expansion of the solution of the bvp or a suitable asymptotic expansion solution first the linear equations are considered and then the semi linear equations to solve semi linear equations newton s method of quasi linearisation is applied examples are provided to illustrate the method the method is easy to implement and suitable for parallel computing

efficient legendre moment computation for grey level images legendre orthogonal moments have been widely used in the field of image analysis because their computation by a direct method is very time expensive recent efforts have been devoted to the reduction of computational complexity nevertheless the existing algorithms are mainly focused on binary images we propose here a new fast method for computing the legendre moments which is not only suitable for binary images but also for grey level images we first establish a recurrence formula of one dimensional 1d legendre moments by using the recursive property of legendre polynomials as a result the 1d legendre moments of order p l p l p 0 can be expressed as a linear combination of l p 1 1 and l p 2 0 based on this relationship the 1d legendre moments l p 0 can thus be obtained from the arrays of l 1 a and l 0 a where a is an integer number less than p to further decrease the computation complexity an algorithm in which no multiplication is required is used to compute these quantities the method is then extended to the calculation of the two dimensional legendre moments l p q we show that the proposed method is more efficient than the direct method

estimating the stenosis probabilities in arteriosclerosis obliterans using generalized estimating equations for each of 211 arteriosclerosis obliterans patients the degree of stenosis of arteries at four sites were examined at hiroshima university hospital to analyse the relationship between the degree of stenosis and age sex and site the generalized estimating equations using a proportional odds model for the stenosis probability with exchangeable correlation was applied to this clustered ordered polytomous data since the correlations between the responses were quite small we could apply the independence estimating equations the best mean model selected by akaike information criterion suggested that age dependency of the stenosis probability was not observed in the central sites but was observed in the peripheral sites and symmetry of the risk of stenosis was seen in the left and right sites details of the analysis will be described

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

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

adaptive smoothing respecting feature directions accurate extraction of the image feature directions is essential to image smoothing and other image processing tasks we show that the gradient based feature direction extraction method can be very erroneous the gradient is too local and it cannot detect oscillations we have developed two new methods the hessian method an approach using higher order differentiations and the gabor 1946 method an approach using space frequency analysis

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

orientation matching minimization for image denoising and inpainting in this paper we propose an orientation matching functional minimization for image denoising and image inpainting following the two step tv stokes algorithm rahman et al in scale space and variational methods in computer vision pp 473 482 springer heidelberg 2007 tai et al in image processing based on partial differential equations pp 3 22 springer heidelberg 2006 bertalmio et al in proc conf comp vision pattern rec pp 355 362 2001 a regularized tangential vector field with zero divergence condition is first obtained then a novel approach to reconstruct the image is proposed instead of finding an image that fits the regularized normal direction from the first step we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction this functional yields a new nonlinear partial differential equation pde for reconstructing denoised and inpainted images the equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field providing reconstructed images which have sharp edges and smooth regions the additive operator splitting aos scheme is used for discretizing euler lagrange equations we present the results of various numerical experiments that illustrate the improvements obtained with the new functional

an anisotropic fourth order diffusion filter for image noise removal fourth order nonlinear diffusion filters used for image noise removal are mainly isotropic filters it means that the spatially varying diffusivity determined by a diffusion function is applied on the image regardless of the orientation of its local features however the optimal choice of parameters in the numerical solver of these filters for having a minimal distortion of the image features results in forming speckle noise on the denoised image and a very slow convergence rate especially when the noise level is moderately high in this paper a new fourth order nonlinear diffusion filter is introduced which has an anisotropic behavior on the image features in the proposed filter it is shown that a suitable choice for a set of diffusivity functions to unevenly control the strength of the diffusion on the directions of the level set and gradient leads to a good edge preservation capability compared to the other diffusion or regularization filters the comparison of the results obtained by the proposed filter with those of the other second and fourth order filters shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

robust scale space filter using second order partial differential equations this paper describes a robust scale space filter that adaptively changes the amount of flux according to the local topology of the neighborhood in a manner similar to modeling heat or temperature flow in physics the robust scale space filter is derived by coupling fick s law with a generalized continuity equation in which the source or sink is modeled via a specific heat capacity the filter plays an essential part in two aspects first an evolution step size is adaptively scaled according to the local structure enabling the proposed filter to be numerically stable second the influence of outliers is reduced by adaptively compensating for the incoming flux we show that classical diffusion methods represent special cases of the proposed filter by analyzing the stability condition of the proposed filter we also verify that its evolution step size in an explicit scheme is larger than that of the diffusion methods the proposed filter also satisfies the maximum principle in the same manner as the diffusion our experimental results show that the proposed filter is less sensitive to the evolution step size as well as more robust to various outliers such as gaussian noise impulsive noise or a combination of the two

variational segmentation of vector valued images with gradient vector flow in this paper we extend the gradient vector flow field for robust variational segmentation of vector valued images rather than using scalar edge information we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4d gradient vector flow equation to reduce the contribution of noise in the structure tensor image channels are weighted according to a blind estimator of contrast the method is applied to biological volume delineation in dynamic pet imaging and validated on realistic monte carlo simulations of numerical phantoms as well as on real images

a maximum entropy method for solving the boundary value problem of second order ordinary differential equations we propose a new method to solve the boundary value problem for a class of second order linear ordinary differential equations which has a non negative solution the method applies the maximum entropy principle to approximating the solution numerically the theoretical analysis and numerical examples show that our method is convergent we propose a new method to solve the boundary value problem for a class of second order linear ordinary differential equations which has a non negative solution the method applies the maximum entropy principle to approximating the solution numerically the theoretical analysis and numerical examples show that our method is convergent

automatic segmentation of mitochondria in em data using pairwise affinity factorization and graph based contour searching in this paper we investigate the segmentation of closed contours in subcellular data using a framework that primarily combines the pairwise affinity grouping principles with a graph partitioning contour searching approach one salient problem that precluded the application of these methods to large scale segmentation problems is the onerous computational complexity required to generate comprehensive representations that include all pairwise relationships between all pixels in the input data to compensate for this problem a practical solution is to reduce the complexity of the input data by applying an over segmentation technique prior to the application of the computationally demanding strands of the segmentation process this approach opens the opportunity to build specific shape and intensity models that can be successfully employed to extract the salient structures in the input image which are further processed to identify the cycles in an undirected graph the proposed framework has been applied to the segmentation of mitochondria membranes in electron microscopy data which are characterized by low contrast and low signal to noise ratio the algorithm has been quantitatively evaluated using two datasets where the segmentation results have been compared with the corresponding manual annotations the performance of the proposed algorithm has been measured using standard metrics such as precision and recall and the experimental results indicate a high level of segmentation accuracy

combining weighted linear project analysis with orientation diffusion for fingerprint orientation field reconstruction this paper presents a novel algorithm for reconstructing the fingerprint orientation field fof the basic idea of the algorithm is to reconstruct the fof by combining weighted linear project analysis with orientation diffusion we first compute the weight values of point gradients according to the similarity of point orientations in the second procedure the qualities of blocks are assessed by the coherence of point orientations and then the block orientation with high quality are estimated by the weighted linear projection analysis based on the vector set of point gradients the fingerprint blocks that will be reconstructed is selected by the priority of them in the third procedure in the end the fof is reconstructed by orientation diffusion based on the reconstruction priorities of blocks to validate the performance the proposed method has been applied to fingerprint enhancement fingerprint singularity detection fingerprint minutiae extraction and fingerprint matching using the fvc2000 and fvc2004 databases the experiments show that the proposed method is more accurate and more reliable and it is more robust against noise

revisiting the relationship between adaptive smoothing and anisotropic diffusion with modified filters anisotropic diffusion has been known to be closely related to adaptive smoothing and discretized in a similar manner this paper revisits a fundamental relationship between two approaches it is shown that adaptive smoothing and anisotropic diffusion have different theoretical backgrounds by exploring their characteristics with the perspective of normalization evolution step size and energy flow based on this principle adaptive smoothing is derived from a second order partial differential equation pde not a conventional anisotropic diffusion via the coupling of fick s law with a generalized continuity equation where a source or sink exists which has not been extensively exploited we show that the source or sink is closely related to the asymmetry of energy flow as well as the normalization term of adaptive smoothing it enables us to analyze behaviors of adaptive smoothing such as the maximum principle and stability with a perspective of a pde ultimately this relationship provides new insights into application specific filtering algorithm design by modeling the source or sink in the pde we introduce two specific diffusion filters the robust anisotropic diffusion and the robust coherence enhancing diffusion as novel instantiations which are more robust against the outliers than the conventional filters

asymptotic initial value methods for two parameter singularly perturbed boundary value problems for second order ordinary differential equations in this paper some numerical methods are presented for singularly perturbed two point boundary value problems for second order ordinary differential equations with two small parameters multiplying the derivatives these methods are distinguished by the fact that initial value problems and or terminal value problems are constructed deduced from the given boundary value problem and then solved by a fitted operator method further error estimates are derived the methods suggested are simple to use and easy to implement the important aspect is that some of the methods suggested are well suited for parallel computing examples are provided to illustrate the methods

bayesian image segmentation using local iso intensity structural orientation image segmentation is a fundamental problem in early computer vision in segmentation of flat shaded nontextured objects in real world images objects are usually assumed to be piecewise homogeneous this assumption however is not always valid with images such as medical images as a result any techniques based on this assumption may produce less than satisfactory image segmentation in this work we relax the piecewise homogeneous assumption by assuming that the intensity nonuniformity is smooth in the imaged objects a novel algorithm that exploits the coherence in the intensity profile to segment objects is proposed the algorithm uses a novel smoothness prior to improve the quality of image segmentation the formulation of the prior is based on the coherence of the local structural orientation in the image the segmentation process is performed in a bayesian framework local structural orientation estimation is obtained with an orientation tensor comparisons between the conventional hessian matrix and the orientation tensor have been conducted the experimental results on the synthetic images and the real world images have indicated that our novel segmentation algorithm produces better segmentations than both the global thresholding with the maximum likelihood estimation and the algorithm with the multilevel logistic mrf model

a scheme with discrete maximum principle and optimized rotation invariance for coherence enhancing diffusion abstract experiments show that the widely employed 3 3 stencil schemes for the coherence enhancing diffusion neither provide acceptable rotational invariance nor do they satisfy the maximum minimum principle at a discrete level we address the problem of rotation invariance by proposing a new 3 3 stencil scheme this scheme also lacks in the discrete maximum principle an enforcement of the discrete maximum principle is presented using a repair technique extensive numerical simulations confirmed the advantage of the repaired scheme over the existing 3 3 stencil schemes in terms of rotational invariance and discrete maximum principle

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

nonlinear image filtering with edge and corner enhancement the authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion the method is designed to enhance not only edges but corners and t junctions as well the method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges such a process is ill posed making the results depend strongly on how the algorithm differs from the diffusion process two ways of modifying the equations using simulations on a variable grid are studied

a smooth locally analytical technique for singularly perturbed two point boundary value problems a locally analytical method for singularly perturbed two point boundary value problems with internal and boundary layers and with turning points is presented the method is based on the linearization of ordinary differential equations in nonoverlapping intervals and results in linear constant coefficients ordinary differential equations which can be integrated analytically thus yielding piecewise analytical solutions by imposing continuity conditions at the end points of each interval plus a smoothness condition at the common end point of two adjacent intervals a global smooth solution is obtained the accuracy of the globally smooth locally analytical method is assessed by comparisons with exact and approximate solutions of several singularly perturbed problems with internal and boundary layers it is shown that the smooth locally analytical method is more precise than second order accurate finite difference discretizations it is also shown that the accuracy of the smooth locally analytical method depends on the kind of nonlinearity and inhomogeneities of singularly perturbed ordinary differential equations but is always higher than that of exponentially fitted techniques based on the local solution of advection diffusion operators

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

computational methods for solving two parameter singularly perturbed boundary value problems for second order ordinary differential equations singularly perturbed two point boundary value problems spbvps for second order ordinary differential equations odes with two small parameters multiplying the derivatives are considered computational methods are suggested in this paper to solve this type of problems one of these methods is fitted operator method fom and the other is bondary value technique bvt in fom we suggest an exponentially fitted finite difference effd scheme throughout the domain of definition of the differential equation and the error estimates are derived in bvt the domain of definition of the differential equation is divided into three subintervals called inner and outer regions then we solve the two parameter spbvp tpspbvp over these regions as two point boundary value problems an exponentially fitted finite difference scheme is used in the inner regions and a classical finite difference scheme in the outer region the data for boundary conditions at the transition points are obtained using zero order asymptotic expansion approximation of the solution of the problem the bvt is well suited for parallel computing numerical examples are given to illustrate the method

flux based anisotropic diffusion applied to enhancement of 3 d angiogram we present a new approach to anisotropic diffusion based on a multidirectional diffusion flux the diffusion flux is decomposed in an orthogonal basis effectively enabling enhancement of contours as well as diffusion along the contours to this end we have selected a three dimensional basis that depicts the directions of principal curvature and has an interesting interpretation in the context of the vessels the diffusion function associated to each vector of the basis depends on the first order derivative of the intensity in this direction instead of the traditional norm of the smoothed gradient accordingly we present the results of a restoration of computed tomography data of the liver

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

image deblurring in the presence of impulsive noise consider the problem of image deblurring in the presence of impulsive noise standard image deconvolution methods rely on the gaussian noise model and do not perform well with impulsive noise the main challenge is to deblur the image recover its discontinuities and at the same time remove the impulse noise median based approaches are inadequate because at high noise levels they induce nonlinear distortion that hampers the deblurring process distinguishing outliers from edge elements is difficult in current gradient based edge preserving restoration methods the suggested approach integrates and extends the robust statistics line process half quadratic and anisotropic diffusion points of view we present a unified variational approach to image deblurring and impulse noise removal the objective functional consists of a fidelity term and a regularizer data fidelity is quantified using the robust modified l 1 norm and elements from the mumford shah functional are used for regularization we show that the mumford shah regularizer can be viewed as an extended line process it reflects spatial organization properties of the image edges that do not appear in the common line process or anisotropic diffusion this allows to distinguish outliers from edges and leads to superior experimental results

tubular structure segmentation based on minimal path method and anisotropic enhancement we present a new interactive method for tubular structure extraction the main application and motivation for this work is vessel tracking in 2d and 3d images the basic tools are minimal paths solved using the fast marching algorithm this allows interactive tools for the physician by clicking on a small number of points in order to obtain a minimal path between two points or a set of paths in the case of a tree structure our method is based on a variant of the minimal path method that models the vessel as a centerline and surface this is done by adding one dimension for the local radius around the centerline the crucial step of our method is the definition of the local metrics to minimize we have chosen to exploit the tubular structure of the vessels one wants to extract to built an anisotropic metric the designed metric is well oriented along the direction of the vessel admits higher velocity on the centerline and provides a good estimate of the vessel radius based on the optimally oriented flux this measure is required to be robust against the disturbance introduced by noise or adjacent structures with intensity similar to the target vessel we obtain promising results on noisy synthetic and real 2d and 3d images and we present a clinical validation

left invariant diffusions on the space of positions and orientations and their application to crossing preserving smoothing of hardi images hardi high angular resolution diffusion imaging is a recent magnetic resonance imaging mri technique for imaging water diffusion processes in fibrous tissues such as brain white matter and muscles in this article we study left invariant diffusion on the group of 3d rigid body movements i e 3d euclidean motion group se 3 and its application to crossing preserving smoothing of hardi images the linear left invariant convection diffusions are forward kolmogorov equations of brownian motions on the space of positions and orientations in 3d embedded in se 3 and can be solved by 3 s 2 convolution with the corresponding green s functions we provide analytic approximation formulas and explicit sharp gaussian estimates for these green s functions in our design and analysis for appropriate nonlinear convection diffusions on hardi data we explain the underlying differential geometry on se 3 we write our left invariant diffusions in covariant derivatives on se 3 using the cartan connection this cartan connection has constant curvature and constant torsion and so have the exponential curves which are the auto parallels along which our left invariant diffusion takes place we provide experiments of our crossing preserving euclidean invariant diffusions on artificial hardi data containing crossing fibers

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

a class of nonlocal tensor telegraph diffusion equations applied to coherence enhancement abstract in this paper we propose a nonlocal tensor telegraph diffusion equation which could be applied to enhancement of coherent flow like structures the telegraph diffusion equation interpolates between diffusion equation and wave equation which lead to a mixed behaviour of diffusion and wave propagation and thus it can preserve edges in a highly oscillatory region replacing scalar valued diffusivity function by diffusion tensor enables real anisotropic diffusion processes which may reveal advantages to enhance the flow like structures in addition the nonlocal technique makes our model robust to noise the existence uniqueness and stability of the solution of our model are proved in this paper the experimental results indicate superiority of the proposed model over the existing methods

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

graph spectral image smoothing using the heat kernel a new method for smoothing both gray scale and color images is presented that relies on the heat diffusion equation on a graph we represent the image pixel lattice using a weighted undirected graph the edge weights of the graph are determined by the gaussian weighted distances between local neighboring windows we then compute the associated laplacian matrix the degree matrix minus the adjacency matrix anisotropic diffusion across this weighted graph structure with time is captured by the heat equation and the solution i e the heat kernel is found by exponentiating the laplacian eigensystem with time image smoothing is accomplished by convolving the heat kernel with the image and its numerical implementation is realized by using the krylov subspace technique the method has the effect of smoothing within regions but does not blur region boundaries we also demonstrate the relationship between our method standard diffusion based pdes fourier domain signal processing and spectral clustering experiments and comparisons on standard images illustrate the effectiveness of the method