spectral shift function for trapping energies in the semiclassical limit semiclassical asymptotics of the spectral shift function ssf for schrodinger operator is studied at trapping energies it is shown that the ssf converges to sum of a smooth function and a step function which is essentially the counting function of resonances in particular the weyl asymptotics is proved

semiclassical analysis of low lying eigenvalues iv the flea on the elephant abstract the two lowest eigenvalues e 0 e 1 of a symmetric double well tunnelling problem 2 v as are considered and they are compared to the two lowest eigenvalues e 0 e 1 of 2 v w where w is supported away from the well bottoms of v we determine the leading exponential splitting of various differences of the four numbers e 0 e 1 e 0 e 1 related problems are discussed

semiclassical analysis of low lying eigenvalues ii tunneling we discuss the leading asymptotics of eigenvalue splittings of 2 x2v in the limit as x o and where v is a non negative potential with several zeros for example if eo x e1 x are the two lowest eigenvalues in a situation where v has precisely two zeros a and b related by a symmetry then limx x lin e1 x eo x is given as the distance from a to b in a certain riemann metric

affine invariant pattern recognition using multiscale autoconvolution this paper presents a new affine invariant image transform called multiscale autoconvolution msa the proposed transform is based on a probabilistic interpretation of the image function the method is directly applicable to isolated objects and does not require extraction of boundaries or interest points and the computational load is significantly reduced using the fast fourier transform the transform values can be used as descriptors for affine invariant pattern classification and in this article we illustrate their performance in various object classification tasks as shown by a comparison with other affine invariant techniques the new method appears to be suitable for problems where image distortions can be approximated with affine transformations

2d affine invariant contour matching using b spline model this paper presents a new affine invariant matching algorithm based on b spline modeling which solves the problem of the nonuniqueness of b spline in curve matching this method first smoothes the b spline curve by increasing the degree of the curve it is followed by a reduction of the curve degree using the least square error lse approach to construct the curvature scale space css image css matching is then carried out our method combines the advantages of b spline that are continuous curve representation and the robustness of css matching with respect to noise and affine transformation it avoids the need for other matching algorithms that have to use the resampled points on the curve thus the curve matching error is reduced the proposed algorithm has been tested by matching similar shapes from a prototype database the experimental results showed the robustness and accuracy of the proposed method in b spline curve matching

spectral flow and level spacing of edge states for quantum hall hamiltonians we consider a non relativistic particle on the surface of a semi infinite cylinder of circumference l submitted to a perpendicular magnetic field of strength b and to the potential of impurities of maximal amplitude w this model is of importance in the context of the integer quantum hall effect in the regime of strong magnetic field or weak disorder b w it is known that there are chiral edge states which are localized within a few magnetic lengths close to and extended along the boundary of the cylinder and whose energy levels lie in the gaps of the bulk system these energy levels have a spectral flow uniform in l as a function of a magnetic flux which threads the cylinder along its axis through a detailed study of this spectral flow we prove that the spacing between two consecutive levels of edge states is bounded below by 2 l 1 with 0 independent of l and of the configuration of impurities this implies that the level repulsion of the chiral edge states is much stronger than that of extended states in the usual anderson model and their statistics cannot obey one of the gaussian ensembles our analysis uses the notion of relative index between two projections and indicates that the level repulsion is connected to topological aspects of quantum hall systems

the method of normalization to determine invariants the determination of invariant characteristics is an important problem in pattern recognition many invariants are known which have been obtained either by normalization or by other methods this paper shows that the method of normalization is much more general and allows one to derive a lot of sets of invariants from the second list as well to this end the normalization method is generalized and is presented in such a way that it is easy to apply thus unifying and simplifying the determination of invariants furthermore this paper discusses the advantages and disadvantages of the invariants obtained by normalization their main advantage is that the normalization process provides us with a standard position of the object because of the generality of the method also new invariants are obtained such as normalized moments more stable than known ones legendre descriptors and zernike descriptors to affine transformations two dimensional fourier descriptors and affine moment invariants obtained by combining hu s moment invariants and normalized moments

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

a shape based inversion algorithm applied to microwave imaging of breast tumors we propose a new shape based inversion algorithm to identify an anomaly embedded in an inhomogeneous layered geometry we apply our approach to microwave breast imaging where the geometry consists of several inhomogeneous layers and the potential tumor is embedded in the innermost layer in addition to the tumor identification we estimate the irregular transition layer between the breast inner layers our inversion algorithm is based on a low dimensional parametric form of the relevant geometries and uses multiple frequency multi source data to estimate the unknowns several numerical examples are provided to evaluate the effectiveness of our approach and demonstrate its robustness both to the initial choice of parameter values and uncertainty in the complex dielectric properties of the media even with the complex geometry and the simplified inverse model

new approach to the semiclassical limit of quantum mechanics i multiple tunnelings in one dimension we propose a new approach for the estimate of the rate of degeneracy of the lowest eigenvalues of the schrodinger operator in the presence of tunneling based on the theory of diffusion processes our method provides lower and upper bounds for the energy splittings and the rates of localization of the wave functions and enables us to discuss cases which as far as we know have never been treated rigorously in the literature in particular we give an analysis of the effect on eigenvalues and eigenfunctions of localized deformations of 1 symmetric double well potentials 2 potentials periodic and symmetric over a finite interval theses situations are characterized by a remarkable dependence on such deformations our probabilistic techniques are inspired by the theory of small random perturbations of dynamical systems

foundations of semi differential invariants this paper elaborates the theoretical foundations of a semi differential framework for invariance semi differential invariants combine coordinates and their derivatives with respect to some contour parameter at several points of the image contour thus allowing for an optimal trade off between identification of points and the calculation of derivatives a systematic way of generating complete and independent sets of such invariants is presented it is also shown that invariance under reparametrisation can be cast in the same framework the theory is illustrated by a complete analysis of 2d affine transformations in a companion paper pauwels et al 1995 these affine semi differential invariants are implemented in the computer program form flat object recognition method for the recognition of planar contours under pseudo perspective projection

hasse principles for higher dimensional fields for rather general excellent schemes x k kato deflned complexes of gerstenbloch ogus type involving the galois cohomology groups of all residue flelds of x for arithmetically interesting schemes i e schemes over global or local flelds or over their rings of integers he developed a web of conjectures on some of these complexes generalizing the fundamental exact sequence of brauer groups for a global fleld he proved these conjectures for low dimensions we prove kato s conjecture with inflnite coe cients over number flelds in particular it gives a hasse principle for function flelds f over a number fleld k involving the corresponding function flelds fv over the completions kv of k we get a conditional result over global flelds k of positive characteristic assuming resolution of singularities this is unconditional for dim x 3 due to recent results on resolution there are also applications to other cases considered by kato

on eigenfunction decay for two dimensional magnetic schrodinger operators for two dimensional schrodinger operators with a nonzero constant magnetic field perturbed by a magnetic field and a scalar potential both vanishing arbitrarily slow at infinity it is proved that eigenfunctions corresponding to the discrete spectrum decay faster than any exponential under more restrictive conditions on the perturbations even quicker decay is obtained

viewpoint independent matching of planar curves in 3d space we present a new approach to match planar curves using the weak perspective projection model this is based on a set of shape parameters that can be extracted from a closed or open contour derived from the original image as a s boundary code in order to reduce the complexity and increase the robustness ofthe matching process the original parameters are reduced to a set ofthree intermediate variables each ofwhich can be calculated independently these variables are contained within a system oflinear equations which de4ne the angles and the ratio ofthe heights ofcorresponding point pairs on the two contours with respect to a 5oating coordinate system the shape matching process is scale and orientation independent and the original parameters that describe the relative pose ofthe two contours in 3d space can be recovered subsequently the approach can be applied to featured and featureless contours to whole and partial contours and is demonstrated on images ofcontours and mechanical parts and tools to recover identity and pose

a generalization of serre s condition mathrm f f with applications to the finiteness of unramified cohomology in this paper we introduce a condition mathrm f m on a field k for a positive integer m that generalizes serre s condition f and which still implies the finiteness of the galois cohomology of finite galois modules annihilated by m and algebraic k tori that split over an extension of degree dividing m as well as certain groups of etale and unramified cohomology various examples of fields satisfying mathrm f m including those that do not satisfy f are given

estimation of general 2d affine motion using fourier descriptors abstract in the present paper a general affine motion estimation algorithm using the fourier descriptors is proposed it is able to estimate in addition to the translation scaling and rotation the stretching parameters or equivalently the scale the shift and the four coefficients of the general affine matrix a modified claire test sequence will serve as a useful test to evaluate the proposed motion algorithm this sequence was selected by international expert groups and was provided by the centre national d etudes des telecommunications cnet france

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

extended edge states in finite hall systems we study edge states of a random schrodinger operator for an electron submitted to a magnetic field in a finite macroscopic two dimensional system of linear dimensions equal to l the y direction is l periodic and in the x direction the electron is confined by two smoothly increasing parallel boundary potentials we prove that with large probability for an energy range in the first spectral gap of the bulk hamiltonian the spectrum of the full hamiltonian consists only on two sets of eigenenergies whose eigenfuntions have average velocities which are strictly positive negative uniformly with respect to the size of the system our result gives a well defined meaning to the notion of edge states for a finite cylinder with two boundaries and extends previous studies on systems with only one boundary

combined blur and affine moment invariants and their use in pattern recognition abstract the paper is devoted to the recognition of objects and patterns deformed by imaging geometry as well as by unknown blurring we introduce a new class of features invariant simultaneously to blurring with a centrosymmetric psf and to affine transformation as we prove in the paper they can be constructed by combining affine moment invariants and blur invariants derived earlier combined invariants allow to recognize objects in the degraded scene without any restoration

learning affine transformations under the assumption of weak perspective two views of the same planar object are related through an affine transformation in this paper we consider the problem of training a simple neural network to learn to predict the parameters of the affine transformation although the proposed scheme has similarities with other neural network schemes its practical advantages are more profound first of all the views used to train the neural network are not obtained by taking pictures of the object from different viewpoints instead the training views are obtained by sampling the space of affine transformed views of the object this space is constructed using a single view of the object fundamental to this procedure is a methodology based on singular value decomposition svd and interval arithmetic ia for estimating the ranges of values that the parameters of affine transformation can assume second the accuracy of the proposed scheme is very close to that of a traditional least squares approach with slightly better space and time requirements a front end stage to the neural network based on principal components analysis pca shows to increase its noise tolerance dramatically and also to guides us in deciding how many training views are necessary in order for the network to learn a good noise tolerant mapping the proposed approach has been tested using both artificial and real data

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

logarithmic hodge witt sheaves on normal crossing varieties in this paper we define two kinds homological and cohomological of etale logarithmic hodge witt sheaves on normal crossing varieties over a perfect field of positive characteristic and discuss some fundamental properties in particular puity and duality

the reduced c algebra of the p adic group gl n abstract the reduced c algebra of the p adic group gl n is morita equivalent to an abelian c algebra the structure of this abelian c algebra is described in terms of unramified unitary characters of levi subgroups the k groups k0 and k1 are both free abelian of infinite rank generators are essentially parametrized by two items of langlands data

perturbation theory for shape resonances and large barrier potentials we develop a systematic perturbation and resonance theory for the one dimensional schrodinger equation of the form d 2 dx 2 u x lambda v x e psi x 0 0 leqq x infty where the barrier potentialv x is supported only wherex 1 and is non negative there and is a real parameter tending to infinity we prove that every eigenvalue turns into a resonance or an eigenvalue for finite

exponential splitting of bound states in a waveguide with a pair of distant windows we consider the laplacian in a straight planar strip with dirichlet boundary which has two neumann windows of the same length the centres of which are 2l apart and study the asymptotic behaviour of the discrete spectrum as l it is shown that there are pairs of eigenvalues around each isolated eigenvalue of a single window strip and their distances vanish exponentially in the limit l we derive an asymptotic expansion also in the case where a single window gives rise to a threshold resonance which the presence of the other window turns into a single isolated eigenvalue

perceptually relevant and piecewise linear matching of silhouettes in this paper a novel alignment method for silhouettes is proposed this method is based on the establishment of correspondences between landmarks on their boundaries and in turn on the establishment of correspondences of the boundary pieces in between these landmarks the method yields more correct correspondences than conventional methods that scale the arc length descriptions of silhouettes to align them the selection of landmarks is investigated as to the robustness of their localization and their perceptual relevance matching of silhouettes is then achieved by quantifying the dissimilarity of a pair of silhouette boundaries based on a novel dissimilarity metric the matching procedure is evaluated based on retrieval experiments and it is concluded that the precision of the results is higher than that obtained by conventional pointwise comparison methods

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

skew symmetry detection via invariant signatures we propose a new approach to skew symmetry detection based on the theory of invariant signatures for planar objects invariant signatures associated to object boundaries are generalizations of the curvature versus arclength description of curves invariant under geometric transformations more complex than the euclidean ones we show that symmetries of objects and hence of closed boundaries translate into simple structures in the invariant signature functions and are therefore in principle readily detectable

cramer rao bounds for 2 d target shape estimation in nonlinear inverse scattering problems with application to passive radar we present new methods for computing fundamental performance limits for two dimensional 2 d parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging we evaluate cramer rao lower bounds crb on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory the crb provides an unbeatable performance limit for any unbiased estimator and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator mle the resultant crbs are used to define an asymptotic global confidence region centered around the true boundary in which the boundary estimate lies with a prescribed probability these global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated target and facilitate geometric inferences numerical simulations are performed using the layer approach and the nystrom method for computation of domain derivatives and using fourier descriptors for target shape parameterization this analysis demonstrates the accuracy and generality of the proposed methods

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

vertex based features for recognition of projectively deformed polygons the paper deals with features of a general polygon which are invariant with respect to projective transform first some properties of the area of a triangle under projective transform are discussed new projective triangular invariants of polygons are derived as the quotient of two different products of the areas of triangles formed by the vertices of the polygon the features are proved to be invariant to numbering of the vertices of the polygon the number of projective triangular invariants for polygons with a given number of vertices is derived a method for reduction of the number of invariants in the case of polygons with a high number of vertices is presented numerical experiments dealing with three octagons and one polygon with 18 vertices deformed by projective transforms are described

schwarps locally projective image warps based on 2d schwarzian derivatives image warps or just warps capture the geometric deformation existing between two images of a deforming surface the current approach to enforce a warp s smoothness is to penalize its second order partial derivatives bookstein in ieee trans pattern anal mach intell 11 567 585 1989 rueckert et al in ieee trans med imaging 18 712 721 1999 because this favors locally affine warps this fails to capture the local projective component of the image deformation this may have a negative impact on applications such as image registration and deformable 3d reconstruction we propose a novel penalty designed to smooth the warp while capturing the deformation s local projective structure our penalty is based on equivalents to the schwarzian derivatives which are projective differential invariants exactly preserved by homographies we propose a methodology to derive a set of partial differential equations with only homographies as solutions we call this system the schwarzian equations and we explicitly derive them for 2d functions using differential properties of homographies we name as schwarp a warp which is estimated by penalizing the residual of schwarzian equations experimental evaluation shows that schwarps outperform existing warps in modeling and extrapolation power and lead to better results in three deformable reconstruction methods namely shape reconstruction in shape from template camera calibration in shape from template and non rigid structure from motion

the local projective shape of smooth surfaces and their outlines this article examines projectively invariant local geometric properties of smooth curves and surfaces oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines it is applied to two problems 1 the projective generalization of koenderink s famous characterization of convexities concavities and inflections of the apparent contours of solids bounded by smooth surfaces and 2 the image based construction of rim meshes which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it

quantum particle in a hierarchical potential with tunnelling over arbitrarily large scales the authors introduce a notion of hierarchical potential by iterating a basic elementary geometric construction over an increasing sequence of length scales they then show that a quantum particle in such a potential exhibits a subdiffusive behaviour characterised by r2 or c ln t beta if the initial state is a normalised wavepacket superposition of states of sufficiently low energy

on exponential asymptotics for nonseparable wave equations iii approximate spectral bands of periodic potentials on strips short waves in a periodic potential on a periodic strip in two dimensions are stud ied in the parameter range where the spectrum has banded structure the exponentially precise ebk theory of parts i and ii is applied to a restricted class of such wave problems to indicate why their continuous spectra can be complicated and how the spectral structure can be elucidated quantitatively the results indicate the direction in which the analog for partial differential equations of the basic floquet theorem for ordinary differential equations may be found

recognition of planar shapes by a semi differential invariant for moving triangles consider the recognition of planar contours of several moving triangles using pictures taken by camera our new idea is that we take pictures of not only rotated triangles but also image trajectories of circles placed properly we apply this method to the recognition of three dimensional tetrahedrons by showing that each angle between two face planes is measured only from the circles on face triangles in addition to recognizing face triangles the method uses the semi differential invariance for pseudo perspective projection which can recognize local figures

comportement semi classique pour l operateur de schrodinger a potentiel periodique abstract in this paper the schrodinger operator with a periodic potential is considered let v a smooth periodic function we study the semi classical behavior for a continuum spectrum of h2 v h 0 we are interested by localization and width of bands we give the interaction matrix up to an exponentially small error measured by agmon s distance between the wells a detailed investigation of the spectrum is made for the case where v has one nondegenerate minima per unit cell we also investigate the spectral properties of h2 v v where v is a smooth positive perturbation with compact support

recognition of planar shapes under affine distortion methods for the recognition ofplanar shapes from arbitrary viewpoints are described the adopted model of projection is orthographic the invariant descriptions derived for this group are one dimensional shape signatures comparable to the well known curvature as a function of arc length description of euclidean geometry since the use of such differential invariants in the affine case would lead to unacceptably high orders of derivatives affine invariant descriptions based onsemi differential invariants are proposed as an alternative a systematic discussion of different types of these invariants is given the usefulness and viability of this methodology is demonstrated on a database containing more than 40 objects

the shape resonance for a class of schrodinger operatorsh 2 2m v onl 2 n with potentials having minima embedded in the continuum of the spectrum and non trapping tails we show the existence of shape resonances exponentially close to the real axis as 0 the resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

spectral stability under tunneling we study the spectral properties of multiple well schrodinger operators on n we give in particular upper bounds on energy shifts due to tunnel effect and localization properties of wave packets our methods are based on agmon type estimates for resolvents in classically forbidden regions and geometric perturbation theory our results are valid also for an infinite number of wells arbitrary spectral type and in non semi classical regimes

intermixture of extended edge and localized bulk energy levels in macroscopic hall systems we study the spectrum of a random schrodinger operator for an electron subjected to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to l the y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials the eigenvalues of the hamiltonian are classified according to their associated quantum mechanical diamagnetic current in the y direction here we look at an interval of energies inside the first landau band of the random operator for the infinite plane in this energy interval with large probability there exist l eigenvalues with positive or negative currents of 1 between each of these there exist l2 eigenvalues with infinitesimal current e b log l 2 we explain the relevance of this analysis of boundary diamagnetic currents to the integer quantum hall effect

finiteness theorems for the shifted witt and higher grothendieck witt groups of arithmetic schemes abstract for smooth varieties over finite fields we prove that the shifted aka derived witt groups of surfaces are finite and the higher grothendieck witt groups aka hermitian k theory of curves are finitely generated for more general arithmetic schemes we give conditional results for example finite generation of the motivic cohomology groups implies finite generation of the grothendieck witt groups

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

affine invariants of convex polygons in this correspondence we prove that the affine invariants for image registration and object recognition proposed recently by yang and cohen see ibid vol 8 no 7 p 934 46 july 1999 are algebraically dependent we show how to select an independent and complete set of the invariants the use of this new set leads to a significant reduction of the computing complexity without decreasing the discrimination power

etale duality for constructible sheaves on arithmetic schemes in this note we relate the following three topics for arithmetic schemes a general duality for etale constructible torsion sheaves a theory of etale homology and the arithmetic complexes of gersten bloch ogus type defined by k kato kct in brief there is an absolute duality using certain dualizing sheaves on these schemes we describe and characterize the dualizing sheaves to some extent relate them to symbol maps define etale homology via the dualizing sheaves and show that the niveau spectral sequence for the latter constructed by the method of bloch and ogus bo leads to the complexes defined by kato some of these relations may have been expected by experts and some have been used implicitly in the literature although we do not know any explicit reference for statements or proofs moreover the main results are used in a crucial way in a paper by two of us js so a major aim is to fill a gap in the literature and a special emphasis is on precise formulations including the determination of signs but the general picture developed here may be of interest itself

affine invariant geometry for non rigid shapes shape recognition deals with the study geometric structures modern surface processing methods can cope with non rigidity by measuring the lack of isometry deal with similarity or scaling by multiplying the euclidean arc length by the gaussian curvature and manage equi affine transformations by resorting to the special affine arc length definition in classical equi affine differential geometry here we propose a computational framework that is invariant to the full affine group of transformations similarity and equi affine thus by construction it can handle non rigid shapes technically we add the similarity invariant property to an equi affine invariant one and establish an affine invariant pseudo metric as an example we show how diffusion geometry can encapsulate the proposed measure to provide robust signatures and other analysis tools for affine invariant surface matching and comparison

lower bounds on the width of stark wannier type resonances we prove that the schrodinger operator d2 dx2 fx w x onl2 r withw bounded and analytic in a strip has no resonances in a region ime exp c f

edge and impurity effects on quantization of hall currents we consider the edge hall conductance and show it is invariant under perturbations located in a strip along the edge decaying perturbations far from the edge are also allowed this enables us to prove for the edge conductances a general sum rule relating currents due to the presence of two different media located respectively on the left and on the right half plane as a particular interesting case we put forward a general quantization formula for the difference of edge hall conductances in semi infinite samples with and without a confining wall it implies in particular that the edge hall conductance takes its ideal quantized value under a gap condition for the bulk hamiltonian or under some localization properties for a random bulk hamiltonian provided one first regularizes the conductance we shall discuss this regularization issue our quantization formula also shows that deviations from the ideal value occurs if a semi infinite distribution of impurity potentials is repulsive enough to produce current carrying surface states on its boundary

the faraday effect revisited thermodynamic limit abstract this paper is the second in a series revisiting the effect of faraday rotation we formulate and prove the thermodynamic limit for the transverse electric conductivity of bloch electrons as well as for the verdet constant the main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and agmon combes thomas uniform exponential decay estimates

low energy asymptotics for schrodinger operators with slowly decreasing potentials low energy behavior of schrodinger operators with potentials which decay slowly at infinity is studied it is shown that if the potential is positive then the zero energy is very regular and the resolvent is smooth near 0 this implies rapid local decay for the solutions of the schrodinger equation on the other hand if the potential is negative then the resolvent has discontinuity at zero energy thus one cannot expect local decay faster than ordert 1 ast

eigenvalues in gaps and decoupling by neumann boundary conditions abstract continuing earlier investigations we show the existence of eigenvalues of schrodinger operators h w r inside a spectral gap of h v under suitable conditions on v and w our method of proof is based on a decoupling of regions in r v by means of dirichlet or neumann boundary conditions where in particular the use of neumann boundary conditions in the decoupling process leads to a new asymptotic results for eigenvalue counting functions

stark ladder resonances for small electric fields we prove the existence of resonances in the semi classical regime of smallh for stark ladder hamiltonians h h f equiv h 2 frac d 2 dx 2 v fx in one dimension the potentialv is a real periodic function with period which is the restriction to of a function analytic in a strip about the electric field strengthf satisfies the bounds v f 0 in general the imaginary part of the resonances are bounded above by open image in new window for some 0 0 independent ofh andf forh sufficiently small this is an extension of the oppenheimer formula for the stark effect to the case of periodic potentials

an affine symmetric image model and its applications natural images contain considerable redundancy some of which is successfully captured using recently developed directional wavelets in this paper an affine symmetric image model is considered it provides a flexible scheme to exploit geometric redundancy a patch of texture from an image is rotated scaled and sheared to approximate other similar parts in the image revealing the self similarity relation the general scheme is derived as follows a texture model is required that identifies structural patterns then the affine symmetry is exploited between structural textures at a local level the objective being to find the minimum residual error by estimating the affine transform relating two patches of texture having developed a local model the methodology is extended to the whole image to estimate the global affine relation this global model is further developed in a multiresolution framework for multiscale analysis by which the self similarity of the image is exploited across space and scale the multiresolution model can be applied to a series of practical problems experimental evaluation demonstrates the effectiveness of the approach in affine invariant texture segmentation and image approximation

pose estimation of 3d free form contours in this article we discuss the 2d 3d pose estimation problem of 3d free form contours in our scenario we observe objects of any 3d shape in an image of a calibrated camera pose estimation means to estimate the relative position and orientation containing a rotation and translation of the 3d object to the reference camera system the fusion of modeling free form contours within the pose estimation problem is achieved by using the conformal geometric algebra the conformal geometric algebra is a geometric algebra which models entities as stereographically projected entities in a homogeneous model this leads to a linear description of kinematics on the one hand and projective geometry on the other hand to model free form contours in the conformal framework we use twists to model cycloidal curves as twist depending functions and interpret n times nested twist generated curves as functions generated by 3d fourier descriptors this means we use the twist concept to apply a spectral domain representation of 3d contours within the pose estimation problem we will show that twist representations of objects can be numerically efficient and easily be applied to the pose estimation problem the pose problem itself is formalized as implicit problem and we gain constraint equations which have to be fulfilled with respect to the unknown rigid body motion several experiments visualize the robustness and real time performance of our algorithms

2 d object recognition using invariant contour descriptor and projective refinement abstract this paper presents an efficient model based recognition method to recognize 2 d objects and to obtain correspondences between models and scene boundaries with a subpixel positioning error as a shape signature for a contour we propose a descriptor consisting of five point invariants which are used to index a hash table also we propose a projective refinement as a verification method to compute exact correspondences between models and scene contour points this method repeatedly computes projective transformation using a weighted pseudo inverse we present an error model for five point invariants which are used to define a similarity between two descriptors to determine a searching bound in indexing and to obtain the weights in the projective refinement in experiments using seriously distorted images of forty models this method led to the recognition of planar curved objects a transformation using the correspondence between the model and scene points on contours was also obtained

quasi invariant parameterisations and matching of curves in images in this paper we investigate quasi invariance on a smooth manifold and show that there exist quasi invariant parameterisations which are not exactly invariant but approximately invariant under group transformations and do not require high order derivatives the affine quasi invariant parameterisation is investigated in more detail and exploited for defining general affine semi local invariants from second order derivatives only the new invariants are implemented and used for matching curve segments under general affine motions and extracting symmetry axes of objects with 3d bilateral symmetry

application of affine invariant fourier descriptors to recognition of 3 d objects the method of fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation translation rotation scaling and shearing the method is based on a parameterized boundary description which is transformed to the fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions as is demonstrated by processing silhouettes of aircraft maneuvering in three space

perceptually motivated image features using contours dong et al examined the ability of 51 computational feature sets to estimate human perceptual texture similarity however none performed well for this task while it is well known that the human visual system is extremely adept at exploiting longer range aperiodic and periodic contour characteristics in images none of the investigated feature sets exploit higher order statistics hos over larger image regions 19 times 19 pixels we therefore hypothesise that long range hos in the form of contour data are useful for perceptual texture similarity estimation we present the results of a psychophysical experiment that shows that contour data are more important than local image patches or global second order data to human observers for this task inspired by this finding we propose a set of perceptually motivated image features pmif that encode the long range hos computed from spatial and angular distributions of contour segments we use two perceptual texture similarity estimation tasks to compare pmif against the 51 feature sets referred to above and four commonly used contour representations this new feature set is also examined in the context of two additional tasks sketch based image retrieval and natural scene recognition the results show that the proposed feature set performs better or at least comparably to all the other feature sets we attribute this promising performance to the fact that the proposed feature set exploits both short range and long range hos

convergent expansions for tunneling a new method to compute effects of tunneling in one dimensional multiple well is developed a tunneling parameter built with physical quantities is introduced to measure the splitting between eigenvalues due to tunneling these splittings are given by convergent series in term of this tunneling parameter for a wide class of double well