discretization on non orthogonal quadrilateral grids for inhomogeneous anisotropic media two classes of discretization methods are proposed for control volume formulations on quadrilateral grids in two space dimensions curvilinear grids are considered as a special case the methods are applicable for any system of conservation laws where the flux is defined by a gradient law like darcy s law for porous media flow a strong feature of the methods is the ability to handle media inhomogeneities in combination with full tensor anisotropy and or non orthogonality of the grid further properties of the methods will be discussed and examples of their use will be presented

an improved bounded semi lagrangian scheme for the turbulent transport of passive scalars an improved bounded semi lagrangian scalar transport scheme based on cubic hermite polynomial reconstruction is proposed in this paper boundedness of the scalar being transported is ensured by applying derivative limiting techniques single sub cell extrema are allowed to exist as they are often physical and help minimize numerical dissipation this treatment is distinct from enforcing strict monotonicity as done by d l williamson and p j rasch 5 and allows better preservation of small scale structures in turbulent simulations the proposed bounding algorithm although a seemingly subtle difference from strict monotonicity enforcement is shown to result in significant performance gain in laminar cases and in three dimensional turbulent mixing layers the scheme satisfies several important properties including boundedness low numerical diffusion and high accuracy performance gain in the turbulent case is assessed by comparing scalar energy and dissipation spectra produced by several bounded and unbounded schemes the results indicate that the proposed scheme is capable of furnishing extremely accurate results with less severe resolution requirements than all the other bounded schemes tested additional simulations in homogeneous isotropic turbulence with scalar timestep size unconstrained by the cfl number show good agreement with spectral scheme results available in the literature detailed analytical examination of gain and phase error characteristics of the original cubic hermite polynomial is also included and points to dissipation and dispersion characteristics comparable to or better than those of a fifth order upwind eulerian scheme

3d object modeling and recognition using local affine invariant image descriptors and multi view spatial constraints this article introduces a novel representation for three dimensional 3d objects in terms of local affine invariant descriptors of their images and the spatial relationships between the corresponding surface patches geometric constraints associated with different views of the same patches under affine projection are combined with a normalized representation of their appearance to guide matching and reconstruction allowing the acquisition of true 3d affine and euclidean models from multiple unregistered images as well as their recognition in photographs taken from arbitrary viewpoints the proposed approach does not require a separate segmentation stage and it is applicable to highly cluttered scenes modeling and recognition results are presented

oscillating singularities on cantor sets a grand canonical multifractal formalism the singular behavior of functions is generally characterized by their holder exponent however we show that this exponent poorly characterizes oscillating singularities we thus introduce a second exponent that accounts for the oscillations of a singular behavior and we give a characterization of this exponent using the wavelet transform we then elaborate on a grand canonical multifractal formalism that describes statistically the fluctuations of both the holder and the oscillation exponents we prove that this formalism allows us to recover the generalized singularity spectrum of a large class of fractal functions involving oscillating singularities

the numerical solution of diffusion problems in strongly heterogeneous non isotropic materials a new second order finite difference algorithm for the numerical solution of diffusion problems in strongly heterogeneous and non isotropic media is constructed on problems with rough coefficients or highly nonuniform grids the new algorithm is superior to all other algorithms we have compared it with for problems with smooth coefficients on smooth grids the method is comparable with other second order methods the new algorithm is formulated for logically rectangular grids and is derived using thesupport operators method a key idea in deriving the method was to replace the usual inner product of vector functions by an inner product weighted by the inverse of the material properties tensor and to use the flux operator defined as the material properties tensor times the gradient rather than the gradient as one of the basic first order operators in the support operators method the discrete analog of the flux operator must also be the negative adjoint of the discrete divergence in an inner product that is a discrete analog of the continuum inner product the resulting method is conservative and the discrete analog of the variable coefficient laplacian is symmetric and negative definite on nonuniform grids in addition on any grid the discrete divergence is zero on constant vectors the null space for the gradient is the constant functions and when the material properties are piecewise constant the discrete flux operator is exact for piecewise linear functions we compare the methods on some of the most difficult examples to be found in the literature

a family of mpfa finite volume schemes with full pressure support for the general tensor pressure equation on cell centered triangular grids a new family of cell centered finite volume schemes is presented for solving the general full tensor pressure equation of subsurface flow in porous media on arbitary unstructured triangulations the new schemes are flux continuous and have full pressure support fps over each subcell with continuous pressure imposed across each control volume sub interface in contrast to earlier formulations the earlier methods are point wise continuous in pressure and flux with triangle pressure support tps which leads to a more limited quadrature range an m matrix analysis identifies bounding limits for the schemes to posses a local discrete maximum principle conditions for the schemes to be positive definite are also derived a range of computational examples are presented for unstructured triangular grids including highly irregular grids and the new fps schemes are compared against the earlier pointwise continuous tps formulations the earlier pointwise tps methods can induce strong spurious oscillations for problems involving strong full tensor anisotropy where the m matrix conditions are violated and can lead to decoupled solutions in such cases unstructured cell centered decoupling is investigated in contrast to tps the new fps formulation leads to well resolved solutions that are essentially free of spurious oscillations a substantial degree of improved convergence behavior for both pressure and velocity is also observed in all convergence tests this is particularly important for problems involving high anisotropy ratios also the new formulation proves to be highly beneficial for an upscaling example where enhancement of convergence is highly significant for certain quadrature points clearly demonstrating further advantages of the new formulation

quasi m matrix multifamily continuous darcy flux approximations with full pressure support on structured and unstructured grids in three dimensions new multifamilies of flux continuous vertex centered finite volume methods are presented for the full tensor pressure equation with general discontinuous coefficients for any cell type in three dimensions the new schemes are flux continuous with full pressure support over each subcell with continuous pressure imposed across each control volume subface in contrast to earlier formulations full pressure continuity across subfaces leads to a quasi positive formulation that minimizes spurious oscillations in discrete pressure solutions for strongly anisotropic full tensor fields the multifamily formulation permits maximum flexibility in quadrature yielding improved solution resolution the earlier methods are pointwise continuous in pressure and flux with tetrahedral pressure support which leads to a more limited quadrature range which is shown to cause spurious oscillations in the solution for strong full tensor fields an m matrix analysis of the three dimensional schemes identifies bounding limits for the schemes to possess a local discrete maximum principle conditions for the schemes to be positive definite are also derived

new tight frames of curvelets and optimal representations of objects with piecewise c2 singularities this paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise c 2 edges conceptually the curvelet transform is a multiscale pyramid with many directions and positions at each length scale and needle shaped elements at fine scales these elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets for instance curvelets obey a parabolic scaling relation which says that at scale 2 j each element has an envelope that is aligned along a ridge of length 2 j 2 and width 2 j we prove that curvelets provide an essentially optimal representation of typical objects f that are c 2 except for discontinuities along piecewise c 2 curves such representations are nearly as sparse as if f were not singular and turn out to be far more sparse than the wavelet decomposition of the object for instance the n term partial reconstruction f c n obtained by selecting the n largest terms in the curvelet series obeys f f c n 2 l2 c n 2 log n 3 n this rate of convergence holds uniformly over a class of functions that are c 2 except for discontinuities along piecewise c 2 curves and is essentially optimal in comparison the squared error of n term wavelet approximations only converges as n 1 as n which is considerably worse than the optimal behavior

enriched multi point flux approximation for general grids it is well known that the two point flux approximation a numerical scheme used in most commercial reservoir simulators has o 1 error when grids are not k orthogonal in the last decade the multi point flux approximations have been developed as a remedy however non physical oscillations can appear when the anisotropy is really strong we found out the oscillations are closely related to the poor approximation of pressure gradient in the flux computation in this paper we propose the control volume enriched multi point flux approximation empfa for general diffusion problems on polygonal and polyhedral meshes non physical oscillations are not observed for realistic and strongly anisotropic heterogeneous material properties described by a full tensor exact linear solutions are recovered for grids with non planar interfaces and a first and second order convergence are achieved for the flux and scalar unknowns respectively

study of a robust feature the pointwise lipschitz regularity the aim of this paper is to highlight the relevance in computer vision of the pointwise lipschitz regularity the regularity gives a measure of the local regularity of the intensity function associated to an image known wavelet methods provide an efficient computation of at contour points of the image from a theoretical point of view we study the effect of geometric deformations and other specific transformations applied to the image showing invariance properties from a practical point of view we assess the robustness of the regularity when the image undergoes various transformations the results we obtain show the lipschitz regularity is a suitable feature for applications in computer vision

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

support operator finite difference algorithms for general elliptic problems abstract an algorithm is developed for discretizing boundary value problems given by a general linear elliptic second order partial differential equation with general mixed or robin boundary conditions in general logically rectangular grids the continuum problem can be written as an operator equation where the operator is self adjoint and positive definite the discrete approximations have the same property consequently the matrices for the discrete problem are symmetric and positive definite also the scheme has a nearest neighbor stencil consequently the most powerful linear solvers can be applied in smooth grids the algorithm produces second order accurate solutions it is the generality of the problem general matrix coefficients general boundary conditions general logically rectangular grids that makes finding such an algorithm difficult the algorithm which is a combination of the method of support operators and the mapping method overcomes certain difficulties of the individual methods producing a high quality algorithm for solving general elliptic problems

quantum deformations of imaginary verma modules we construct quantum deformations of imaginary verma modules over u a 1 1 and show that for generic q imaginary verma modules over u a 1 1 can be deformed to those over the quantum group u q a 1 1 in such a way that the dimensions of the weight spaces are invariant under the deformation we also prove the pbw theorem for u q a 1 1 with respect to the triangular decomposition induced from the root partition corresponding to the imaginary verma modules 1991 mathematics subject classification 17b67 17b65 17b10

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

symmetric positive definite flux continuous full tensor finite volume schemes on unstructured cell centered triangular grids novel cell centered full tensor finite volume methods are presented for general unstructured grids in two spatial dimensions the numerical schemes are flux continuous and based on computing the transmissibilities in a local subcell transform space ensuring that local flux matrices are symmetric as a result the global discretization matrix is shown to be symmetric positive definite for any grid type a symmetric physical space method is also introduced and the symmetric methods are shown to be closely related discrete ellipticity conditions are derived for positive definiteness of the physical space and subcell space schemes computational examples are presented for unstructured triangular grids demonstrating good performance of the scheme the schemes are compared with the so called multipoint flux approximation mpfa o method i aavatsmark t barkve o boe and t mannseth siam j sci comput 19 1998 pp 1700 1716 good agreement between the methods is obtained but the new scheme shows improved behavior in challenging cases

monotone finite volume schemes for diffusion equations on unstructured triangular and shape regular polygonal meshes we consider a non linear finite volume fv scheme for stationary diffusion equation we prove that the scheme is monotone i e it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients the scheme is extended to regular star shaped polygonal meshes and isotropic heterogeneous coefficients

quasi positive families of continuous darcy flux finite volume schemes on structured and unstructured grids new families of flux continuous control volume distributed finite volume schemes are presented for the general full tensor pressure equation arising in porous media and formulated for structured and unstructured grids these schemes offer the practical advantage of being flux continuous while only depending on one degree of freedom per control volume unlike rival approximations such as the mixed finite element method m matrix bounds are presented quasi qm matrices are defined and an optimal quadrilateral scheme is identified anisotropy favoring triangulation is also shown to yield an optimal scheme the new schemes prove to be relatively robust for the cases tested including strongly anisotropic full tensor fields strong oscillations encountered with the earlier formulations are removed or minimized

a quasi positive family of continuous darcy flux finite volume schemes with full pressure support a new family of flux continuous locally conservative finite volume schemes is presented for solving the general tensor pressure equation of subsurface flow in porous media the new schemes have full pressure continuity imposed across control volume faces previous families of flux continuous schemes are point wise continuous in pressure and flux when applying the earlier point wise flux continuous schemes to strongly anisotropic full tensor fields their failure to satisfy a maximum principle as with other fem and finite volume methods can result in loss of local stability for high anisotropy ratios which can cause strong spurious oscillations in the numerical pressure solution an m matrix analysis reveals the upper limits for guaranteeing a maximum principle for general 9 point schemes and aids in the design of schemes that minimize the occurrence of spurious oscillations in the discrete pressure field the full pressure continuity schemes are shown to possess a larger range of flux continuous schemes than the previous point wise counter parts for strongly anisotropic full tensor cases it is shown that the full quadrature range possessed by the new schemes permits these schemes to exploit quadrature points previously out of range that are shown to minimize spurious oscillations in discrete pressure solutions the new formulation leads to a more robust quasi positive family of flux continuous schemes applicable to general discontinuous full tensor fields

texture roughness analysis and synthesis via extended self similar ess model the 2d fractional brownian motion fbm model provides a useful tool to model textured surfaces whose roughness is scale invariant to represent textures whose roughness is scale dependent we generalize the fbm model to the extended self similar ess model in this research we present an estimation algorithm to extract the model parameters from real texture data furthermore a new incremental fourier synthesis algorithm is proposed to generate the 2d realizations of the ess model finally the estimation and rendering methods are combined to synthesize real textured surfaces

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

modelling of heat transport in magnetised plasmas using non aligned coordinates we present discretisation schemes for the heat diffusion equation in strongly magnetised plasmas in 2 d cartesian and 3 d cylindrical geometry the algorithms described do not use field aligned coordinates but show nevertheless a strong reduction of the pollution of perpendicular heat flux caused by parallel heat conduction compared to standard finite element or other finite difference formulations results for test examples show independence of the numerical error from g for values of g g up to 10 9 in plane and 10 1 2 in periodic cylinder geometry simulating toroidal connection the algorithms appear particularly well suited for dynamic mhd calculations where the effort of using exactly aligned coordinates becomes prohibitive

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

discretization on unstructured grids for inhomogeneous anisotropic media part i derivation of the methods discretization methods are proposed for control volume formulations on polygonal and triangular grid cells in two space dimensions the methods are applicable for any system of conservation laws where the flow density is defined by a gradient law like darcy s law for porous media flow a strong feature of the methods is the ability to handle media inhomogeneities in combination with full tensor anisotropy this paper gives a derivation of the methods and the relation to previously published methods is also discussed a further discussion of the methods including numerical examples is given in the companion paper part ii siam j sci comput pp 1717 1736

finite volume scheme for anisotropic diffusion in this paper we apply a special finite volume scheme limited to smooth temperature distributions and cartesian grids to test the importance of connectivity of the finite volumes the area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy we apply the scheme to the anisotropic heat conduction equation and compare its results with those of existing finite volume schemes for anisotropic diffusion also we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines

imaginary verma modules for uq sl 2 ˆ and crystal like bases abstract we consider imaginary verma modules for quantum affine algebra u q sl 2 and define a crystal like base which we call an imaginary crystal basis using the kashiwara algebra k q constructed in earlier work of the authors in particular we prove the existence of imaginary crystal like bases for a suitable category of reduced imaginary verma modules for u q sl 2

automatic panoramic image stitching using invariant features this paper concerns the problem of fully automated panoramic image stitching though the 1d problem single axis of rotation is well studied 2d or multi row stitching is more difficult previous approaches have used human input or restrictions on the image sequence in order to establish matching images in this work we formulate stitching as a multi image matching problem and use invariant local features to find matches between all of the images because of this our method is insensitive to the ordering orientation scale and illumination of the input images it is also insensitive to noise images that are not part of a panorama and can recognise multiple panoramas in an unordered image dataset in addition to providing more detail this paper extends our previous work in the area brown and lowe 2003 by introducing gain compensation and automatic straightening steps

generalized q boson algebras and their integrable modules abstract we define the generalized q boson algebra b associated to a pair of nichols algebras and a skew pairing we study integrable b modules generalizing results by m kashiwara and t nakashima on integrable modules over a q boson kashiwara algebra

discretization on unstructured grids for inhomogeneous anisotropic media part ii discussion and numerical results a companion paper part i siam j sci comput 19 1998 pp 1700 1716 presents discretization methods for control volume formulations in two space dimensions properties of the developed methods are further discussed including rotational invariance and stability under the influence of anisotropy strong anisotropy may have to be handled by use of stretched grid cells numerical examples that demonstrate strengths and weaknesses of the methods are presented the examples focus on inhomogeneity anisotropy and rotational invariance

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

double families of quasi positive darcy flux approximations with highly anisotropic tensors on structured and unstructured grids this paper focuses on flux continuous pressure equation approximation for strongly anisotropic media previous work on families of flux continuous schemes for solving the general geometry permeability tensor pressure equation has focused on single parameter families these schemes have been shown to remove the o 1 errors introduced by standard two point flux reservoir simulation schemes when applied to full tensor flow approximation improved convergence of the schemes has also been established for specific quadrature points however these schemes have conditional m matrices depending on the strength of the off diagonal tensor coefficients when applied to cases involving full tensors arising from strongly anisotropic media the point wise continuous schemes can fail to satisfy the maximum principle and induce severe spurious oscillations in the numerical pressure solution new double family flux continuous locally conservative schemes are presented for the general geometry permeability tensor pressure equation the new double family formulation is shown to expand on the current single parameter range of existing conditional m matrix schemes the conditional m matrix bounds on a double family formulation are identified for both quadrilateral and triangle cell grids a quasi positive qm matrix analysis is presented that classifies the behaviour of the new schemes with respect to double family quadrature in regions beyond the m matrix bounds the extension to double family quadrature is shown to be beneficial resulting in novel optimal anisotropic quadrature schemes the new methods are applied to strongly anisotropic full tensor field problems and yield results with sharp resolution with only minor or practically zero spurious oscillations

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

a new class of unitarizable highest weight representations of infinite dimensional lie algebras ii on donne les details rigoureux pour le probleme de classification on redemontre l unitarite de la representation exceptionnelle on considere les produits tensoriels et les problemes d integrabilite

multi scale finite volume method for elliptic problems in subsurface flow simulation in this paper we present a multi scale finite volume msfv method to solve elliptic problems with many spatial scales arising from flow in porous media the method efficiently captures the effects of small scales on a coarse grid is conservative and treats tensor permeabilities correctly the underlying idea is to construct transmissibilities that capture the local properties of the differential operator this leads to a multi point discretization scheme for the finite volume solution algorithm transmissibilities for the msfv have to be constructed only once as a preprocessing step and can be computed locally therefore this step is perfectly suited for massively parallel computers furthermore a conservative fine scale velocity field can be constructed from the coarse scale pressure solution two sets of locally computed basis functions are employed the first set of basis functions captures the small scale heterogeneity of the underlying permeability field and it is computed in order to construct the effective coarse scale transmissibilities a second set of basis functions is required to construct a conservative fine scale velocity field the accuracy and efficiency of our method is demonstrated by various numerical experiments

quantum deformations of generalized kac moody algebras and their modules abstract we construct quantum groups uq g associated with generalized kac moody algebras g with admissible borcherds cartan matrices we also construct quantum deformations of highest weight modules over u g with integral highest weights we show that for generic q verma modules over u g with integral highest weights and irreducible highest weight modules over u g with dominant integral highest weights can be deformed to those over uq g in such a way that the dimensions of weight spaces are invariant under the deformation in particular for generic q the characters of irreducible highest weight modules over uq g with dominant integral highest weights are given by the weyl kac borcherds formula

simultaneous object recognition and segmentation from single or multiple model views we present a novel object recognition approach based on affine invariant regions it actively counters the problems related to the limited repeatability of the region detectors and the difficulty of matching in the presence of large amounts of background clutter and particularly challenging viewing conditions after producing an initial set of matches the method gradually explores the surrounding image areas recursively constructing more and more matching regions increasingly farther from the initial ones this process covers the object with matches and simultaneously separates the correct matches from the wrong ones hence recognition and segmentation are achieved at the same time the approach includes a mechanism for capturing the relationships between multiple model views and exploiting these for integrating the contributions of the views at recognition time this is based on an efficient algorithm for partitioning a set of region matches into groups lying on smooth surfaces integration is achieved by measuring the consistency of configurations of groups arising from different model views experimental results demonstrate the stronger power of the approach in dealing with extensive clutter dominant occlusion and large scale and viewpoint changes non rigid deformations are explicitly taken into account and the approximative contours of the object are produced all presented techniques can extend any view point invariant feature extractor

nonlinear magnetohydrodynamics simulation using high order finite elements a conforming representation composed of 2d finite elements and finite fourier series is applied to 3d nonlinear non ideal magnetohydrodynamics using a semi implicit time advance the self adjoint semi implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments growth rates for resistive tearing modes with experimentally relevant lundquist number are computed accurately with time steps that are large with respect to the global alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree p two or larger an error diffusion method controls the generation of magnetic divergence error convergence studies show that this approach is effective for continuous basis functions with p 2 where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity is computed accurately with p 3 without mesh alignment a simulation of tearingmode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3d magnetic topologies

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed