eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

the relative neighborhood graph with an application to minimum spanning trees le graphe de voisinage relatif rng d un ensemble v de points dans un espace euclidien est un graphe v e tel que p q appartient a e si et seulement si il n existe pas de point z de v tel que d p z d p q et d q z d p q on montre que 1 le rng de n points du plan peut etre trouve en temps o n log n lequel est optimal a une constante multiplicative pres 2 le rng ainsi que l arbre minimum des sommets d un polygone a n sommets convexe peut etre trouve en un temps o n 3 sous l hypothese que trois points d entree ne forment pas un triangle isocele le rng de n points dans un espace dimension r peut etre trouve en un temps o n 2 pour r 3

two methods for discretizing a delta function supported on a level set this paper presents two new methods for discretizing a dirac delta function which is concentrated on the zero level set of a smooth function u r n r the function u is only known at the discrete set of points belonging to a regular mesh covering r n these two methods are used to approximate integrals over the manifold defined by the level set both methods are conceptually simple and easy to implement we present the results of numerical experiments indicating that as the mesh size h goes to zero the rate of convergence is at least o h for the first method and o h 2 for the second method we perform a limited analysis of the proposed algorithms including a proof of convergence for both methods

enhanced local texture feature sets for face recognition under difficult lighting conditions making recognition more reliable under uncontrolled lighting conditions is one of the most important challenges for practical face recognition systems we tackle this by combining the strengths of robust illumination normalization local texture based face representations distance transform based matching kernel based feature extraction and multiple feature fusion specifically we make three main contributions 1 we present a simple and efficient preprocessing chain that eliminates most of the effects of changing illumination while still preserving the essential appearance details that are needed for recognition 2 we introduce local ternary patterns ltp a generalization of the local binary pattern lbp local texture descriptor that is more discriminant and less sensitive to noise in uniform regions and we show that replacing comparisons based on local spatial histograms with a distance transform based similarity metric further improves the performance of lbp ltp based face recognition and 3 we further improve robustness by adding kernel principal component analysis pca feature extraction and incorporating rich local appearance cues from two complementary sources gabor wavelets and lbp showing that the combination is considerably more accurate than either feature set alone the resulting method provides state of the art performance on three data sets that are widely used for testing recognition under difficult illumination conditions extended yale b cas peal r1 and face recognition grand challenge version 2 experiment 4 frgc 204 for example on the challenging frgc 204 data set it halves the error rate relative to previously published methods achieving a face verification rate of 88 1 at 0 1 false accept rate further experiments show that our preprocessing method outperforms several existing preprocessors for a range of feature sets data sets and lighting conditions

integrated coverage and connectivity in wireless sensor networks a two dimensional percolation problem while sensing coverage reflects the surveillance quality provided by a wireless sensor network wsn network connectivity enables data gathered by sensors to reach a central node called the sink given an initially uncovered field and as more and more sensors are continuously added to a wsn the size of partial covered areas increases at some point the situation abruptly changes from small fragmented covered areas to a single large covered area we call this abrupt change as the sensing coverage phase transition scpt also given an originally disconnected wsn and as more and more sensors are added the number of connected components changes such that the wsn suddenly becomes connected at some point we call this sudden change as the network connectivity phase transition ncpt the nature of such phase transitions is a central topic in percolation theory of boolean models in this paper we propose a probabilistic approach to compute the covered area fraction at critical percolation for both of the scpt and ncpt problems because sensing coverage and network connectivity are not totally orthogonal we also propose a model for percolation in wsns called correlated disk model which provides a basis for solving the scpt and ncpt problems together

a high order elliptic pde based level set reinitialisation method using a discontinuous galerkin discretisation abstract in this paper an efficient high order accurate level set reinitialisation method is proposed based on the elliptic reinitialisation method basting and kuzmin 2013 1 which is discretised spatially using the discontinuous galerkin dg symmetric interior penalty method sipg in order to achieve this a number of improvements have been made to the elliptic reinitialisation method including reformulation of the underlying minimisation problem driving the solution adoption of a lagrange multiplier approach for enforcing a dirichlet boundary condition on the implicit level set interface and adoption of a narrow band approach numerical examples confirm the high order accuracy of the resultant method by demonstrating experimental orders of convergence congruent with optimal convergence rates for the sipg method that is h p 1 and h p in the l 2 and dg norms respectively furthermore the degree to which the level set function satisfies the eikonal equation improves proportionally to h p and the often ignored homogeneous dirichlet boundary condition on the interface is shown to be satisfied accurately with a rate of convergence of at least h 2 for all polynomial orders

high order numerical methods to a type of delta function integrals we study second to fourth order numerical methods to a type of delta function integrals in one to three dimensions these delta function integrals arise from recent efficient level set methods for computing the multivalued solutions of nonlinear pdes we show that the natural quadrature approach with usual discrete delta functions and support size formulas to the two dimensional delta function integrals suffer from nonconvergence we then design high order numerical methods to this type of delta function integrals based on interpolation approach numerical examples are presented to verify the efficiency and accuracy of our methods

orthogonal neighborhood preserving discriminant analysis for face recognition in this paper we propose a new linear subspace analysis algorithm called orthogonal neighborhood preserving discriminant analysis onpda given a set of data points in the ambient space a weight matrix is firstly built which describes the relationship between the data points then optimal between class scatter matrix and within class scatter matrix are defined such that the neighborhood structure can be preserved in order to improve the discriminating power a new method is presented for orthogonalizing the basis eigenvectors we evaluate the performance of the proposed algorithm for face recognition with the use of different databases consistent and promising results demonstrate the effectiveness of our algorithm

numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting abstract fictitious domain methods such as the finite cell method simplify the discretization process significantly as the mesh is decoupled from the geometrical description however this simplification in the mesh generation results in broken cells which is why special integration methods are required usually adaptive integration schemes are applied resulting in a large number of integration points and thus an expensive numerical integration especially for nonlinear applications to perform the numerical integration more efficiently we propose an adaptive integration method using moment fitting thereby we present a moment fitting approach based on lagrange polynomials through gauss legendre points to circumvent having to solve the moment fitting equation system the performance of this integration method is shown by studying several numerical examples of the finite cell method for small and large strain problems in elastoplasticity

a novel local pattern descriptor local vector pattern in high order derivative space for face recognition in this paper a novel local pattern descriptor generated by the proposed local vector pattern lvp in high order derivative space is presented for use in face recognition based on the vector of each pixel constructed by computing the values between the referenced pixel and the adjacent pixels with diverse distances from different directions the vector representation of the referenced pixel is generated to provide the 1d structure of micropatterns with the devise of pairwise direction of vector for each pixel the lvp reduces the feature length via comparative space transform to encode various spatial surrounding relationships between the referenced pixel and its neighborhood pixels besides the concatenation of lvps is compacted to produce more distinctive features to effectively extract more detailed discriminative information in a given subregion the vector of lvp is refined by varying local derivative directions from the n th order lvp in n 1 th order derivative space which is a much more resilient structure of micropatterns than standard local pattern descriptors the proposed lvp is compared with the existing local pattern descriptors including local binary pattern lbp local derivative pattern ldp and local tetra pattern ltrp to evaluate the performances from input grayscale face images in addition extensive experiments conducting on benchmark face image databases feret cas peal cmu pie extended yale b and lfw demonstrate that the proposed lvp in high order derivative space indeed performs much better than lbp ldp and ltrp in face recognition

highly accurate surface and volume integration on implicit domains by means of moment fitting summary we introduce a new method for the numerical integration over curved surfaces and volumes defined by a level set function the method is based on the solution of a small linear system based on a simplified variant of the moment fitting equations numerical experiments suggest that the accuracy of the resulting quadrature rules exceeds the accuracy of traditional methods by orders of magnitude using moments up to an order of p the measured experimental orders of convergence exceed hp consequently their construction is very efficient because only coarse computational grids are required the conceptual simplicity allows for the application on very general grid types which is demonstrated by numerical experiments on quadrilateral triangular and hexahedral grids copyright 2013 john wiley sons ltd

high order x fem and levelsets for complex microstructures uncoupling geometry and approximation in this contribution a strategy is proposed for uncoupling geometrical description and approximation with the x fem the strategy is based on an uniform coarse mesh that defines a high order approximation of the mechanical fields and an adapted mesh that defines the geometrical features by means of levelsets the connection between the geometry and the approximation is obtained by sharing the quadtree trees of the two meshes numerical examples involving level set based parts convergence studies mechanical computations and numerical homogenization show good promise for this approach

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

a numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions we present a numerical algorithm for the construction of efficient high order quadratures in two and higher dimensions quadrature rules constructed via this algorithm possess positive weights and interior nodes resembling the gaussian quadratures in one dimension in addition rules can be generated with varying degrees of symmetry adaptable to individual domains we illustrate the performance of our method with numerical examples and report quadrature rules for polynomials on triangles squares and cubes up to degree 50 these formulae are near optimal in the number of nodes used and many of them appear to be new

gabor based kernel pca with doubly nonlinear mapping for face recognition with a single face image in this paper a novel gabor based kernel principal component analysis pca with doubly nonlinear mapping is proposed for human face recognition in our approach the gabor wavelets are used to extract facial features then a doubly nonlinear mapping kernel pca dkpca is proposed to perform feature transformation and face recognition the conventional kernel pca nonlinearly maps an input image into a high dimensional feature space in order to make the mapped features linearly separable however this method does not consider the structural characteristics of the face images and it is difficult to determine which nonlinear mapping is more effective for face recognition in this paper a new method of nonlinear mapping which is performed in the original feature space is defined the proposed nonlinear mapping not only considers the statistical property of the input features but also adopts an eigenmask to emphasize those important facial feature points therefore after this mapping the transformed features have a higher discriminating power and the relative importance of the features adapts to the spatial importance of the face images this new nonlinear mapping is combined with the conventional kernel pca to be called doubly nonlinear mapping kernel pca the proposed algorithm is evaluated based on the yale database the ar database the orl database and the yaleb database by using different face recognition methods such as pca gabor wavelets plus pca and gabor wavelets plus kernel pca with fractional power polynomial models experiments show that consistent and promising results are obtained

the finite cell method for three dimensional problems of solid mechanics this article presents a generalization of the recently proposed finite cell method to three dimensional problems of linear elasticity the finite cell method combines ideas from embedding or fictitious domain methods with the p version of the finite element method besides supporting a fast simple generation of meshes it also provides high convergence rates mesh generation for a boundary representation of solids and for voxel based data obtained from ct scans is addressed in detail in addition the implementation of non homogeneous neumann boundary conditions and the computation of cell matrices based on a composed integration is presented the performance of the proposed method is demonstrated by three numerical examples including the elastostatic computation of a human bone biopsy

a completed modeling of local binary pattern operator for texture classification in this correspondence a completed modeling of the local binary pattern lbp operator is proposed and an associated completed lbp clbp scheme is developed for texture classification a local region is represented by its center pixel and a local difference sign magnitude transform ldsmt the center pixels represent the image gray level and they are converted into a binary code namely clbp center clbp c by global thresholding ldsmt decomposes the image local differences into two complementary components the signs and the magnitudes and two operators namely clbp sign clbp s and clbp magnitude clbp m are proposed to code them the traditional lbp is equivalent to the clbp s part of clbp and we show that clbp s preserves more information of the local structure than clbp m which explains why the simple lbp operator can extract the texture features reasonably well by combining clbp s clbp m and clbp c features into joint or hybrid distributions significant improvement can be made for rotation invariant texture classification

discretization of dirac delta functions in level set methods discretization of singular functions is an important component in many problems to which level set methods have been applied we present two methods for constructing consistent approximations to dirac delta measures concentrated on piecewise smooth curves or surfaces both methods are designed to be convenient for level set simulations and are introduced to replace the commonly used but inconsistent regularization technique that is solely based on a regularization parameter proportional to the mesh size the first algorithm is based on a tensor product of regularized one dimensional delta functions it is independent of the irregularity relative to the grid in the second method the regularization is constructed from a one dimensional regularization that is extended to multi dimensions with a variable support depending on the orientation of the singularity relative to the computational grid convergence analysis and numerical results are given

delta function approximations in level set methods by distance function extension in a k tornberg b engquist numerical approximations of singular source terms in differential equations j comput phys 200 2004 462 488 it was shown for simple examples that the then m

higher order xfem for curved strong and weak discontinuities the extended finite element method xfem enables the accurate approximation of solutions with jumps or kinks within elements optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces higher order convergence for arbitrary curved interfaces relies on two major issues i an accurate quadrature of the galerkin weak form for the cut elements and ii a careful formulation of the enrichment which should preclude any problems in the blending elements for i we employ a strategy of subdividing the elements into subcells with only one curved side reference elements that are higher order on only one side are then used to map the integration points to the real element for ii we find that enrichments for strong discontinuities are easily extended to higher order accuracy in contrast problems in blending elements may hinder optimal convergence for weak discontinuities different formulations are investigated including the corrected xfem numerical results for several test cases involving strong or weak curved discontinuities are presented quadratic and cubic approximations are investigated optimal convergence rates are achieved using the standard xfem for the case of a strong discontinuity close to optimal convergence rates for the case of a weak discontinuity are achieved using the corrected xfem copyright 2009 john wiley sons ltd

the nitsche xfem dg space time method and its implementation in three space dimensions in a recent paper c lehrenfeld and a reusken siam j numer anal 51 2013 pp 958 983 a new finite element discretization method for a class of two phase mass transport problems is presented and analyzed the transport problem describes mass transport in a domain with an evolving interface across the evolving interface a jump condition has to be satisfied the discretization in that paper is a space time approach which combines a discontinuous galerkin dg technique in time with an extended finite element method xfem using the nitsche method the jump condition is enforced in a weak sense while the emphasis in that paper was on the analysis and one dimensional numerical experiments the main contribution of this paper is the discussion of implementation aspects for the spatially three dimensional case as the space time interface is typically given only implicitly as the zero level of a level set function we construct a piecewise planar approximation of the space time interface this disc

equivalent polynomials for quadrature in heaviside function enriched elements summary one of the advantages of partition of unity fems like the extended fem is the ability of modeling discontinuities independent of the mesh structure the enrichment of the element functional space with discontinuous or non differentiable functions requires when the element stiffness is computed partitioning into subdomains for quadrature however the arbitrary intersection between the base mesh and the discontinuity plane generates quadrature subdomains of complex shape this is particularly true in three dimensional problems where quite sophisticate methodologies have been presented in the literature for the element stiffness evaluation the present work addresses the problem of heaviside function enrichments and is based on the replacement of the discontinuous enrichment function with the limit of an equivalent polynomial defined on the entire element domain this allows for the use of standard gaussian quadrature in the elements crossed by the discontinuity the work redefines conceptually the first version of the equivalent polynomial methodology introduced in 2006 allowing a much broader applicability as a consequence equivalent polynomials can be computed for all continuum element families in one two and three dimensions copyright 2014 john wiley sons ltd

robust second order accurate discretizations of the multi dimensional heaviside and dirac delta functions we present a robust second order accurate method for discretizing the multi dimensional heaviside and the dirac delta functions on irregular domains the method is robust in the following ways 1 integrations of source terms on a co dimension one surface are independent of the underlying grid and therefore stable under perturbations of the domain s boundary 2 the method depends only on the function value of a level function not on its derivatives we present the discretizations in tabulated form to make their implementations straightforward we present numerical results in two and three spatial dimensions to demonstrate the second order accuracy in the l 1 norm in the case of the solution of pdes with singular source terms in the case of evaluating the contribution of singular source terms on interfaces the method is also second order accurate in the l norm

rotation invariant texture classification using feature distributions abstract a distribution based classification approach and a set of recently developed texture measures are applied to rotation invariant texture classification the performance is compared to that obtained with the well known circular symmetric autoregressive random field csar model approach a difficult classification problem of 15 different brodatz textures and seven rotation angles is used in experiments the results show much better performance for our approach than for the csar features a detailed analysis of the confusion matrices and the rotation angles of misclassified samples produces several interesting observations about the classification problem and the features used in this study

high order numerical methods to two dimensional delta function integrals in level set methods in this paper we design and analyze a class of high order numerical methods to delta function integrals appearing in level set methods in two dimensional case the methods comprise approximating the mesh cell restrictions of the delta function integral in each mesh cell the two dimensional delta function integral can be rewritten as a one dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral and thus is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals proposed in x wen high order numerical methods to a type of delta function integrals j comput phys 226 2007 1952 1967 we establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub algorithms and has better accuracy under an assumption on the zero level set of the level set function which holds generally numerical examples are presented showing that the second to fourth order methods implemented in this paper achieve or exceed the expected accuracy and demonstrating the advantage of using our high order numerical methods

generalized gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method new gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method for discontinuous functions we construct gauss like quadrature rules over arbitrarily shaped elements in two dimensions without the need for partitioning the finite element a point elimination algorithm is used in the construction of the quadratures which ensures that the final quadratures have minimal number of gauss points for weakly singular integrands we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques

a high order and interface preserving discontinuous galerkin method for level set reinitialization abstract a high order numerical method for interface preserving level set reinitialization is presented in this paper in the interface cells the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved in the non interface cells we compute the gradient of the level set function by solving a hamilton jacobi equation as a conservation law system using the discontinuous galerkin method following the work by hu and shu siam j sci comput 21 1999 660 690 the missing constant is then recovered by the continuity of the level set function while taking into account the characteristics to handle highly distorted initial conditions we develop a hybrid numerical flux that combines the lax friedrichs flux and the penalty flux our method is stable for non trivial test cases and handles singularities away from the interface very well when derivative singularities are present on the interface a second derivative limiter is designed to suppress the oscillations at least n 1 th order accuracy in the interface cells and nth order in the whole domain are observed for smooth solutions when nth degree polynomials are used two dimensional test cases are presented to demonstrate superior properties such as accuracy long term stability interface preserving capability and easy treatment of contact lines we also show some preliminary results on the pinch off process of a pendant drop where topological changes of the fluid interface are involved our method is readily extendable to three dimensions and adaptive meshes

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

high order local ternary patterns with locality preserving projection for smoke detection and image classification it is a challenging task to recognize smoke from visual scenes due to large variations in the color texture shapes of smoke to improve detection accuracy we propose a novel feature extraction method by encoding high order directional derivatives at each pixel we first quantize the directional derivatives into ternary values to generate local ternary patterns ltp for the sake of simplification each ltp code is usually decomposed into an upper lbp code and a lower lbp code but this leads to loss of information hence we use joint histograms to preserve the co occurrence of upper and lower lbp codes for each order ltp then we concatenate all joint histograms from different orders to propose high order local ternary patterns hltp to improve computational efficiency we apply locality preserving projection lpp to reduce the dimension of hltp to further improve performance we present a noise resistant mechanism to remove noisy derivatives and then propose hltp based on magnitudes of noise removed derivatives and values of center pixels hltpmc finally the support vector machine svm is used for training and classification experiments on large scale smoke data sets show that our method can achieve detection rates above 94 with false alarm rates below 1 33 experiments on a multi class brodatz texture data set also achieved good performance with low dimensional features so our method has powerful discriminative capabilities and compact feature representation for multi class image classification

high order numerical quadratures to one dimensional delta function integrals we study high order numerical quadratures to one dimensional delta function integrals in this paper this is motivated by the fact that traditional numerical quadratures give only first order accuracy in general we provide criteria on discrete delta functions and support size formulas which ensure any desired accuracy of the numerical quadratures discrete delta functions and support size formulas satisfying these criteria are designed numerical examples are presented to verify the performed analysis and the high order accuracy of the proposed numerical quadratures

quadrature schemes for arbitrary convex concave volumes and integration of weak form in enriched partition of unity methods abstract quadrature schemes are constructed based on moment fitting equations to integrate polynomials over arbitrary convex concave volumes that arise among others in enriched partition of unity finite element methods epum the building block of the scheme involves the divergence theorem of multivariable calculus which is used to integrate the base functions an efficient and robust point distribution method is proposed and the quadrature weights at the corresponding points are obtained by solving a least squares problem the method is applied initially to integrate given polynomial functions over complex volumes and further to simulate simple three dimensional fluid dynamic problems which involve very complex volumes when solved with epum accuracy of the present quadrature construction scheme is demonstrated by comparing the results with the available exact numerical solutions and efficiency of the method is proved by comparing the computational time with that of the widely used tessellation method

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

a geometric transversal approach to analyzing track coverage in sensor networks this paper presents a new coverage formulation addressing the quality of service of sensor networks that cooperatively detect targets traversing a region of interest the problem of track coverage consists of finding the positions of n sensors such that a lebesgue measure on the set of tracks detected by at least k sensors is optimized this paper studies the geometric properties of the network addressing a deterministic track coverage formulation and binary sensor models it is shown that the tracks detected by a network of heterogeneous omnidirectional sensors are the geometric transversals of non translates families of circles a novel methodology based on cone theory is presented for representing and measuring sets of transversals in closed form then the solution of the track coverage problem can be formulated as a nonlinear program nlp the numerical results show that this approach can improve track coverage by up to two orders of magnitude compared to grid and random deployments also it can be used to reduce the number of sensors required to achieve a desired detection performance by up to 50 and to optimally replenish or reposition existing sensor networks

geometric integration over irregular domains with application to level set methods we present a geometric approach for calculating integrals over irregular domains described by a level set function this procedure can be used to evaluate integrals over a lower dimensional interface and may be used to evaluate the contribution of singular source terms this approach produces results that are second order accurate and robust to the perturbation of the interface location on the grid moreover since we use a cell wise approach this procedure can be easily extended to quadtree and octree grids we demonstrate the second order accuracy and the robustness of the method in two and three spatial dimensions

orthogonal laplacianfaces for face recognition following the intuition that the naturally occurring face data may be generated by sampling a probability distribution that has support on or near a submanifold of ambient space we propose an appearance based face recognition method called orthogonal laplacianface our algorithm is based on the locality preserving projection lpp algorithm which aims at finding a linear approximation to the eigenfunctions of the laplace beltrami operator on the face manifold however lpp is nonorthogonal and this makes it difficult to reconstruct the data the orthogonal locality preserving projection olpp method produces orthogonal basis functions and can have more locality preserving power than lpp since the locality preserving power is potentially related to the discriminating power the olpp is expected to have more discriminating power than lpp experimental results on three face databases demonstrate the effectiveness of our proposed algorithm

an application of chain code based local descriptor and its extension to face recognition local descriptors are widely used technique of feature extraction to obtain information about both local and global properties of an object here we discuss an application of the chain code based local descriptor to face recognition by focusing on various datasets and considering different variants of this description method we augment the generic form of the descriptor by adding a possibility of grouping pixels into blocks i e effectively describing larger neighborhoods the results of experiments show the efficiency of the approach we demonstrate that the obtained results are comparable or even better than those delivered by other important algorithms in the class of methods based on the bag of visual words paradigm an extension of chain code based local descriptor ccbld is proposed ccbld is applied to face recognition task bag of visual words paradigm is realized through the dictionary of chain codes test results show that ccbld is comparable or outperforms other local descriptors the approach is tested using cas peal colorferet fg net and other datasets

the numerical approximation of a delta function with application to level set methods it is shown that a discrete delta function can be constructed using a technique developed by anita mayo the fast solution of poisson s and the biharmonic equations on irregular regions siam j sci comput 21 1984 285 299 for the numerical solution of elliptic equations with discontinuous source terms this delta function is concentrated on the zero level set of a continuous function in two space dimensions this corresponds to a line and a surface in three space dimensions delta functions that are first and second order accurate are formulated in both two and three dimensions in terms of a level set function the numerical implementation of these delta functions achieves the expected order of accuracy

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

a nonlinear optimization procedure for generalized gaussian quadratures we present a new nonlinear optimization procedure for the computation of generalized gaussian quadratures for a broad class of square integrable functions on intervals while some of the components of this algorithm have been previously published we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works the new algorithm successfully computes generalized gaussian quadratures in a number of instances in which the previous algorithms fail four applications of our scheme to computational physics are presented the construction of discrete plane wave expansions for the helmholtz green s function the design of linear array antennae the computation of a quadrature for the discretization of laplace boundary integral equations on certain domains with corners and the construction of quadratures for the discretization of laplace and helmholtz boundary integral equations on smooth surfaces

coverage in wireless ad hoc sensor networks sensor networks pose a number of challenging conceptual and optimization problems such as location deployment and tracking one of the fundamental problems in sensor networks is the calculation of the coverage in meguerdichian et al 2001 it is assumed that the sensor has uniform sensing ability we provide efficient distributed algorithms to optimally solve the best coverage problem raised in the above mentioned article in addition we consider a more general sensing model the sensing ability diminishes as the distance increases as energy conservation is a major concern in wireless or sensor networks we also consider how to find an optimum best coverage path with the least energy consumption and how to find an optimum best coverage path that travels a small distance in addition we justify the correctness of the method proposed above that uses the delaunay triangulation to solve the best coverage problem and show that the search space of the best coverage problem can be confined to the relative neighborhood graph which can be constructed locally

histogram of gabor phase patterns hgpp a novel object representation approach for face recognition a novel object descriptor histogram of gabor phase pattern hgpp is proposed for robust face recognition in hgpp the quadrant bit codes are first extracted from faces based on the gabor transformation global gabor phase pattern ggpp and local gabor phase pattern lgpp are then proposed to encode the phase variations ggpp captures the variations derived from the orientation changing of gabor wavelet at a given scale frequency while lgpp encodes the local neighborhood variations by using a novel local xor pattern lxp operator they are both divided into the nonoverlapping rectangular regions from which spatial histograms are extracted and concatenated into an extended histogram feature to represent the original image finally the recognition is performed by using the nearest neighbor classifier with histogram intersection as the similarity measurement the features of hgpp lie in two aspects 1 hgpp can describe the general face images robustly without the training procedure 2 hgpp encodes the gabor phase information while most previous face recognition methods exploit the gabor magnitude information in addition fisher separation criterion is further used to improve the performance of hgpp by weighing the subregions of the image according to their discriminative powers the proposed methods are successfully applied to face recognition and the experiment results on the large scale feret and cas peal databases show that the proposed algorithms significantly outperform other well known systems in terms of recognition rate

a high order discontinuous galerkin method for compressible flows with immersed boundaries summary we present a higher order discretization scheme for the compressible euler and navier stokes equations with immersed boundaries our approach makes use of a discontinuous galerkin dg discretization in a domain that is implicitly defined by means of a level set function the zero iso contour of this level set function is considered as an additional domain boundary where we weakly enforce boundary conditions in the same manner as in boundary fitted cells in order to retain the full order of convergence of the scheme it is crucial to perform volume and surface integrals in boundary cells with high accuracy this is achieved using a linear moment fitting strategy moreover we apply a non intrusive cell agglomeration technique that averts problems with very small and ill shaped cuts the robustness accuracy and convergence properties of the scheme are assessed in several two dimensional test cases for the steady compressible euler and navier stokes equations approximation orders range from zero to four even though the approach directly generalizes to even higher orders in all test cases with a sufficiently smooth solution the experimental order of convergence matches the expected rate for dg schemes this article is protected by copyright all rights reserved

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features

high order numerical methods to three dimensional delta function integrals in level set methods in this paper we propose a class of high order numerical methods to delta function integrals appearing in level set methods in the three dimensional case by extending the idea for designing high order methods to two dimensional delta function integrals in x wen j comput phys 228 2009 pp 4273 4290 the methods comprise approximating the mesh cell restrictions of the delta function integral in each mesh cell the three dimensional delta function integral can be rewritten as a two dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral a key idea in designing high order methods in this paper is that the high order accuracy of the methods is not ensured in each mesh cell and the methods are designed in a consistent way to foster error cancelations in mesh cells where high order accuracy is not ensured in the individual cell this issue is essentially related to the construction of integral area for the two dimensional ordinary integral in each mesh cell which is achieved by considering the intersection points between the zero level set and the edges or sides of the mesh cell the mesh cell restrictions of the three dimensional delta function integral are then approximated by applying standard two dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals numerical examples are presented showing that our methods in this paper achieve or exceed the expected second to fourth order accuracy and demonstrating the stability of shifting mesh for our methods and the advantage of using our high order numerical methods