shape preserving local histogram modification a novel approach for shape preserving contrast enhancement is presented in this paper contrast enhancement is achieved by means of a local histogram equalization algorithm which preserves the level sets of the image this basic property is violated by common local schemes thereby introducing spurious objects and modifying the image information the scheme is based on equalizing the histogram in all the connected components of the image which are defined based both on the grey values and spatial relations between pixels in the image and following mathematical morphology constitute the basic objects in the scene we give examples for both grey value and color images

a semi classical trace formula at a non degenerate critical level abstract we study the semi classical trace formula at a critical energy level for a h pseudodifferential operator whose principal symbol has a unique non degenerate critical point for that energy this leads to the study of hamiltonian systems near equilibrium and near the non zero periods of the linearized flow the contributions of these periods to the trace formula are expressed in terms of degenerate oscillatory integrals the new results obtained are formulated in terms of the geometry of the energy surface and the classical dynamics on this surface

the semi classical trace formula and propagation of wave packets abstract we study spectral and propagation properties of operators of the form s h n j 0 h j p j where j p j is a differential operator of order j on a manifold m asymptotically as h 0 the estimates are in terms of the flow t of the classical hamiltonian h x p n j 0 p j x p on t m where p j is the principal symbol of p j we present two sets of results i the semiclassical trace formula on the asymptotic behavior of eigenvalues and eigenfunctions of s h in terms of periodic trajectors of h ii associated to certain isotropic submanifolds t m we define families of functions h and prove that t exp iths is a family of the same kind associated to t

the radiation condition at infinity for the high frequency helmholtz equation with source term a wave packet approach abstract we consider the high frequency helmholtz equation with a given source term and a small absorption parameter 0 the high frequency or semi classical parameter is 0 we let and go to zero simultaneously we assume that the zero energy is non trapping for the underlying classical flow we also assume that the classical trajectories starting from the origin satisfy a transversality condition a generic assumption under these assumptions we prove that the solution u radiates in the outgoing direction uniformly in in particular the function u when conveniently rescaled at the scale close to the origin is shown to converge towards the outgoing solution of the helmholtz equation with coefficients frozen at the origin this provides a uniform version in of the limiting absorption principle writing the resolvent of the helmholtz equation as the integral in time of the associated semi classical schrodinger propagator our analysis relies on the following tools i for very large times we prove and use a uniform version of the egorov theorem to estimate the time integral ii for moderate times we prove a uniform dispersive estimate that relies on a wave packet approach together with the above mentioned transversality condition iii for small times we prove that the semi classical schrodinger operator with variable coefficients has the same dispersive properties as in the constant coefficients case uniformly in

semiclassical measure for the solution of the dissipative helmholtz equation we study the semiclassical measures for the solution of a dissipative helmholtz equation with a source term concentrated on a bounded submanifold the potential is not assumed to be non trapping but trapped trajectories have to go through the region where the absorption coefficient is positive in that case the solution is microlocally written around any point away from the source as a sum finite or infinite of lagragian distributions moreover we prove and use the fact that the outgoing solution of the dissipative helmholtz equation is microlocally zero in the incoming region

semiclassical resolvent estimates for n body schrodinger operators in this paper we prove for a generalized n body schrodinger operator that the non trapping condition on the classical hamiltonian and all classical subhamiltonians is both necessary and sufficient for obtaining good semiclassical bounds on the boundary values of the resolvent and their energy derivatives we accomplish this by generalizing gerard s geometrical construction of an escape function for three body problems to n body problems this work is motivated by a recent paper of ch gerard 3 in which he proved for three body problems that if the classical hamiltonian and all classical sub hamiltonians are non trapping at the energy e then the resolvent of the corresponding semiclassical schrodinger operator satisfies the estimates

semiclassical asymptotics gauge fields and quantum chaos a gauge field is given by a connection on a principal bundle p m we consider the semiclassical behavior of a family of schrodinger operators associated with a gauge field in the limit as h 0 we relate the spectral theory of such operators to behavior of the hamiltonian flow on the natural phase space associated to a gauge field examining in particular situations where this flow exhibits chaotic behavior

semiclassical spectral invariants for schrodinger operators in this article we show how to compute the semi classical spectral measure associated with the schrodinger operator on r n and by examining the rst few terms in the asymptotic expansion of this measure obtain inverse spectral results in one and two dimensions in particular we show that for the schrodinger operator on r 2 with a radially symmetric electric potential v and magnetic potential b both v and b are spectrally determined we also show that in one dimension there is a very simple explicit identity relating the spectral measure of the schrodinger operator with its birkho canonical form

contributions of non extremum critical points to the semi classical trace formula we study the semi classical trace formula at a critical energy level for a h pseudo differential operator on rn whose principal symbol has a totally degenerate critical point for that energy we compute the contribution to the trace formula of isolated non extremum critical points under a condition of real principal type the new contribution to the trace formula is valid for all time in a compact subset of r but the result is modest since we have restrictions on the dimension

ergodicite et limite semi classique consider a self adjoint quantic hamiltonian p h p x hdx whereh 0 is the planck s constant andp some smooth classical observable on the phase space r2n when the classical flow on a compact energy shell p is ergodic we prove that in the limith 0 almost all the eigenfunctions ofp h whose energy is near of are distributed according to the liouville measure on p

convexity of solutions and brunn minkowski inequalities for hessian equations in r3 by using minkowski addition of convex functions we prove convexity and rearrangement properties of solutions to some hessian equations in r 3 and brunn minkowski and isoperimetric inequalities for related functionals

time averaging for the strongly confined nonlinear schrodinger equation using almost periodicity abstract we study the limiting behavior of a nonlinear schrodinger equation describing a 3 dimensional gas that is strongly confined along the vertical z direction the confinement induces fast oscillations in time that need to be averaged out since the hamiltonian in the z direction is merely assumed confining without any further specification the associated spectrum is discrete but arbitrary and the fast oscillations induced by the nonlinear equation entail countably many frequencies that are arbitrarily distributed for that reason averaging cannot rely on small denominator estimates or like to overcome these difficulties we prove that the fast oscillations are almost periodic in time with values in a sobolev like space that we completely identify we then exploit the existence of long time averages for almost periodic functions to perform the necessary averaging procedure in our nonlinear problem

a retinex model based on absorbing markov chains the retinex algorithm developed by land and mccann provides an abstract model of the mechanism of color sensation in the human vision system at the basis of model lies the fact that the color appearance of a point does not depend only on its color value but rather on the comparison among itself and other pixels according to the model separately for each chromatic channel an image pixel receives suitably filtered information about the brightness of other image regions based on which its own brightness is eventually re scaled the original formulation land and mccann 1971 uses a path based sampling approach the information is transported by memoryless random walks starting from randomly chosen points along the path the information is filtered based on the brightness of the travelled regions by a specific path function computed through chains of ratios of pixel intensities such a function is path dependent and retains the value of the brightest point found along the path the overall correction to a pixel depends on the specific realizations of two sampling processes the starting point sampling process and the path sampling process as a consequence of the sampling this algorithm is known to be intrinsically noisy this draw back can be overcome by passing from the path sampling algorithm to the probabilistic representation of the corresponding diffusion process in this paper we start from the random path simulative model of retinex we respell the standard path based sampling process representation of the retinex model as formalized in provenzi et al 2005 and we show that despite the overall path dependence the model can be given a representation in terms of absorbing markov chains by means of the embedding into a suitable state space we derive the corresponding analytic model accounting for the combined effects of path function path sampling process and starting point sampling process finally we provide a numerical algorithm for working out its solution using such a model the output brightness of a pixel can be computed based on the solution of a simple sparse linear system we show that the output of the random walk sampling algorithm and the markov chain based algorithm agree to an extent that can be controlled by few model parameters we have found also that the markov chain based algorithm is more efficient than the basic random path sampling in obtaining noise free images those analytic probabilistic models and simulative models can be used as complementary tools for studying the retinex mechanism and for identifying and comparing variants

calcul fonctionnel par la transformation de mellin et operateurs admissibles mellin s transform is used to establish a functional calculus of a class of pseudodifferential operators depending on a small parameter h 0 we apply for exeample this result to prove the semi classical behaviour of the discrete spectrum of schrodinger operators h2 v and of dirac operators h j 13 jdj 4 v

issues about retinex theory and contrast enhancement we present an interpretation of land s retinex theory that we show to be consistent with the original formulation the proposed model relies on the computation of the expectation value of a suitable random variable weighted with a kernel function thus the name kernel based retinex kbr for the corresponding algorithm kbr shares the same intrinsic characteristics of the original retinex it can reduce the effect of a color cast and enhance details in low key images but since it can only increase pixel intensities it is not able to enhance over exposed pictures comparing the analytical structure of kbr with that of a recent variational model of color image enhancement we are able to perform an analysis of the action of kbr on contrast showing the need to anti symmetrize its equation in order to produce a two sided contrast modification able to enhance both under and over exposed pictures the anti symmetrized kbr equations show clear correspondences with other existing color correction models in particular ace whose relationship with retinex has always been difficult to clarify finally from an image processing point of view we mention that both kbr and its antisymmetric version are free from the chromatic noise due to the use of paths in the original retinex implementation and that they can be suitably approximated in order to reduce their computational complexity from mathcal o n 2 to mathcal o n log n being n the number of input pixels

a microscopic convexity principle for nonlinear partial differential equations we study microscopic convexity property of fully nonlinear elliptic and parabolic partial differential equations under certain general structure condition we establish that the rank of hessian 2u is of constant rank for any convex solution u of equation f 2u u u x 0 the similar result is also proved for parabolic equations some of geometric applications are also discussed

existence of c local solutions for the monge ampere equation on considere l equation de monge ampere det u ij f y u u dans un ouvert de r n on demontre l existence de solutions c locales

approximation semi classique de l equation de heisenberg we study the semi classical approximation for the solution of heisenberg equation in terms of pseudo differential operators and establish a semi classical version of egorov s theorem as an application of these results we get the classical limit of quantum mechanical correlation functions for a class of non bounded observables

star a structure and texture aware retinex model retinex theory is developed mainly to decompose an image into the illumination and reflectance components by analyzing local image derivatives in this theory larger derivatives are attributed to the changes in reflectance while smaller derivatives are emerged in the smooth illumination in this paper we utilize exponentiated local derivatives with an exponent gamma of an observed image to generate its structure map and texture map the structure map is produced by been amplified with gamma 1 while the texture map is generated by been shrank with gamma to this end we design exponential filters for the local derivatives and present their capability on extracting accurate structure and texture maps influenced by the choices of exponents gamma the extracted structure and texture maps are employed to regularize the illumination and reflectance components in retinex decomposition a novel structure and texture aware retinex star model is further proposed for illumination and reflectance decomposition of a single image we solve the star model by an alternating optimization algorithm each sub problem is transformed into a vectorized least squares regression with closed form solutions comprehensive experiments on commonly tested datasets demonstrate that the proposed star model produce better quantitative and qualitative performance than previous competing methods on illumination and reflectance decomposition low light image enhancement and color correction the code is publicly available at https github com csjunxu star

interior curvature estimates and the asymptotic plateau problem in hyperbolic space we show that for a very general class of curvature functions defined in the positive cone the problem of finding a complete strictly locally convex hypersurface in h satisfying f 0 1 with a prescribed asymptotic boundary at infinity has at least one smooth solution with uniformly bounded hyperbolic principal curvatures moreover if is euclidean starshaped the solution is unique and also euclidean starshaped while if is mean convex the solution is unique we also show via a strong duality theorem that analogous results hold in de sitter space a novel feature of our approach is a global interior curvature estimate

existence and convexity of local solutions to degenerate hessian equations abstract in this work we prove the existence of convex solutions to the following k hessian equation s k u k y g y u d u in the neighborhood of a point y 0 u 0 p 0 r n r r n where g c g y 0 u 0 p 0 0 k c is nonnegative near y 0 k y 0 0 and rank d y 2 k y 0 n k 1

time delay operators in semiclassical limit ii short range potentials this work is a continuation of 27 we prove that quantum timedelay operator localized in a nontrapping energy interval is in fact an h pseudodifferential operator with the h principal symbol given by the classical timedelay function composed with the incoming wave operator in classical mechanics the classical limit of time delay operator is also given

a perceptually inspired variational framework for color enhancement basic phenomenology of human color vision has been widely taken as an inspiration to devise explicit color correction algorithms the behavior of these models in terms of significative image features such as e g contrast and dispersion can be difficult to characterize to cope with this we propose to use a variational formulation of color contrast enhancement that is inspired by the basic phenomenology of color perception in particular we devise a set of basic requirements to be fulfilled by an energy to be considered as perceptually inspired showing that there is an explicit class of functionals satisfying all of them we single out three explicit functionals that we consider of basic interest showing similarities and differences with existing models the minima of such functionals is computed using a gradient descent approach we also present a general methodology to reduce the computational cost of the algorithms under analysis from o n2 to o n logn being n the number of pixels of the input image

the convexity of solution of a class hessian equation in bounded convex domain in r 3 we use the deformation methods to obtain the convexity of solution of a class hessian equation in bounded convex domain in r 3 c 2008 elsevier inc all rights reserved

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

perceptual color correction through variational techniques in this paper we present a discussion about perceptual based color correction of digital images in the framework of variational techniques we propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original the variational formulation permits a more flexible local control of contrast adjustment and attachment to data we show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement ace a particular perceptual based model of color enhancement moreover we prove that a numerical approximation of the euler lagrange equation reduces the computational complexity of ace from o n2 to o nlogn where n is the total number of pixels in the image

influence of normalization and color space to color texture classification abstract color texture classification has recently attracted significant attention due to its multiple applications the color texture images depend on the texture surface and its albedo the illumination the camera and its viewing position a key problem to get an acceptable performance is the ambient illumination which can vary the perceived structures in the surface given a color texture classification problem it would be desirable to know which is the best approach to solve the problem making the minimal assumptions about the illumination conditions the present work does an exhaustive evaluation of the state of the art color texture classification methods considering 5 different color spaces 12 normalization methods to achieve illumination invariances 19 texture feature vectors and 23 pure color feature vectors our experiments allow to conclude that parallel approaches are better than integrative approaches for color texture classification achieving the first positions in the friedman ranking multiresolution local binary patterns mlbp are the best intensity texture features followed by wavelet and gabor filters combined with luminance chrominance color spaces lab and lab2000hl and for pure color classification the best are first order statistics fos calculated in rgb color space for intensity texture features the learning methods work better on the four smallest datasets although they could not be tested in other four bigger datasets due to its huge computational cost nor with color texture classification normalization and color spaces slightly increase the average accuracy of color texture classification although the differences achieved using normalization are not statistically significant in a paired t test lab2000hl and rgb are the best color spaces but the former is the slowest one regarding elapsed time the best vector features mlbp for intensity texture daub4 daubechies filters using mean and variance statistics for color texture and fos for pure color are nearly the fastest or are in the middle interval of all the tested methods

a semi classical trace formula for schrodinger operators in the case of a critical energy level let 2 2 v x be a schrodinger operator on rn with smooth potentialv x as x the spectrum of is discrete and one can study the asymptotic of the smoothed spectral density e k ek e as 0 here ek k nis the spectrum of and c 0 r we shall investigate the case whereeis a critical value of the symbolhof and extending the work of brummelhuis paul and uribe in 3 we will prove the existence of a full asymptotic expansion for in terms of and ln and compute the leading coefficient we will consider new weyl type estimates for the counting function nec k n ek e

breit wigner formulas for the scattering phase and the total scattering cross section in the semi classical limit in this paper we prove results in resonance scattering for the schrodinger operatorpv h2 v v being a smooth short range potential onrn more precisely for energy near a trapping energy level 0 for the classical system defined by the hamiltonianp x 2 v x we prove that the scattering phase and the scattering cross sections associated to pv p0 have the breit wigner form lorentzian line shape in the limith 0

a pde formalization of retinex theory in 1964 edwin h land formulated the retinex theory the first attempt to simulate and explain how the human visual system perceives color his theory and an extension the reset retinex were further formalized by land and mccann several retinex algorithms have been developed ever since these color constancy algorithms modify the rgb values at each pixel to give an estimate of the color sensation without a priori information on the illumination unfortunately the retinex land mccann original algorithm is both complex and not fully specified indeed this algorithm computes at each pixel an average of a very large set of paths on the image for this reason retinex has received several interpretations and implementations which among other aims attempt to tune down its excessive complexity in this paper it is proved that if the paths are assumed to be symmetric random walks the retinex solutions satisfy a discrete poisson equation this formalization yields an exact and fast implementation using only two ffts several experiments on color images illustrate the effectiveness of the retinex original theory

a brunn minkowski inequality for the hessian eigenvalue in three dimensional convex domain abstract we use the deformation methods to obtain the strictly log concavity of solution of a class hessian equation in bounded convex domain in r 3 as an application we get the brunn minkowski inequality for the hessian eigenvalue and characterize the equality case in bounded strictly convex domain in r 3

equivariant spectral asymptotics for h pseudodifferential operators we prove equivariant spectral asymptotics for h pseudodifferential operators for compact orthogonal group actions generalizing results of el houakmi and helffer comportement semi classique en presence de symetries action d un groupe de lie compact asymp anal 5 2 91 113 1991 and cassanas reduced gutzwiller formula with symmetry case of a lie group j math pures appl 85 6 719 742 2006 using recent results for certain oscillatory integrals with singular critical sets p ramacher singular equivariant asymptotics and weyl s law on the distribution of eigenvalues of an invariant elliptic operator j reine angew math crelles j to be published we can deduce a weak equivariant weyl law furthermore we can prove a complete asymptotic expansion for the gutzwiller trace formula without any additional condition on the group action by a suitable generalization of the dynamical assumptions on the hamilton flow

quantum normal forms moyal star product and bohr sommerfeld approximation a normal form transformation is carried out on one dimensional quantum hamiltonians that transforms them into functions of the quantum harmonic oscillator the method works with the weyl transform or symbol of the hamiltonian the moyal star product is used to carry out the normal form transformation at the level of symbols diagrammatic techniques are developed for handling the expressions that result from higher order terms in the moyal series once the normal form is achieved the bohr sommerfeld formula for the eigenvalues including higher order corrections follows easily

a variational framework for retinex retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for non uniform lighting this is in general an ill posed problem in this paper we propose a variational model for the retinex problem that unifies previous methods similar to previous algorithms it assumes spatial smoothness of the illumination field in addition knowledge of the limited dynamic range of the reflectance is used as a constraint in the recovery process a penalty term is also included exploiting a priori knowledge of the nature of the reflectance image the proposed formulation adopts a bayesian view point of the estimation problem which leads to an algebraic regularization term that contributes to better conditioning of the reconstruction problem based on the proposed variational model we show that the illumination estimation problem can be formulated as a quadratic programming optimization problem an efficient multi resolution algorithm is proposed it exploits the spatial correlation in the reflectance and illumination images applications of the algorithm to various color images yield promising results

semi classical asymptotics for local spectral densities and time delay problems in scattering processes abstract we study the semi classical asymptotics for local spectral densities of schrodinger operators 1 2 h 2 v and apply the obtained result to the time delay problem in potential scattering theory it is shown that for a class of central potentials the time delay in quantum mechanics converges to the corresponding one in classical mechanics in the semi classical limit in a non trapping energy region however such a convergence is not expected in a trapping energy region

calcul fonctionnel sur les operateurs admissibles et application abstract let h v h h 2 2 v lim x v x under suitable conditions we prove that h v h is a pseudodifferential operator whose symbol has an asymptotic a h j 0 h j a j more general pseudodifferential operator s classes are also considered we apply this result to study the semi classical behaviour of the spectrum of h v as h 0 so we improve recent results obtained by j chazarain and by the author in collaboration with b helffer furthermore we give a precise meaning to the formal development considered in b grammaticos and a voros work ann physics 123 1979 359 380

clustering for the spectrum ofh pseudodifferential operators with periodic flow on an energy surface abstract we study the repartition of the eigenvalues of anh pseudodifferential operator in a small neighbourhood of an energy where the hamiltonian flow associated with the principal symbol of the operator is periodic the proof is based on a geometric lemma and perturbation techniques to obtain the results from the known theorem in the case of a periodic flow in an energy band b helffer and d robert ann inst h poincare41 1984 291 331

time decay of scattering solutions and resolvent estimates for semiclassical schrodinger operators we study the semiclassical schrodinger operator h2 v x h 0 1 and establish various results on the time decay of scattering solutions and the semiclassical bounds for the powers of the resolvent for short range potentials the time decay results obtained in this paper are the best possible and this enables us to conclude the equivalence between the non trapping condition in classical mechanics and the uniform time decay of wave functions in quantum mechanics

feynman path integrals and the trace formula for the schrodinger operators we study schrodinger operators of the form h frac h 2 2 delta frac 1 2 x cdot a 2 x v x on d wherea2 is a strictly positive symmetricd d matrix andv x is a continuous real function which is the fourier transform of a bounded measure if n are the eigenvalues ofh we show that the theta function theta t sum limits n exp left frac i h t lambda n right is explicitly expressible in terms of infinite dimensional oscillatory integrals feynman path integrals over the hilbert space of closed trajectories we use these explicit expressions to give the asymptotic behaviour of t for smallh in terms of classical periodic orbits thus obtaining a trace formula for the schrodinger operators this then yields an asymptotic expansion of the spectrum ofh in terms of the periodic orbits of the corresponding classical mechanical system these results extend to the physical case the recent work on poisson and trace formulae for compact manifolds

scattering phase asymptotics with fractal remainders for a riemannian manifold m g which is isometric to the euclidean space outside of a compact set and whose trapped set has liouville measure zero we prove weyl type asymptotics for the scattering phase with remainder depending on the classical escape rate and the maximal expansion rate for axiom a geodesic flows this gives a polynomial improvement over the known remainders we also show that the remainder can be bounded above by the number of resonances in some neighbourhoods of the real axis and provide similar asymptotics for hyperbolic quotients using the selberg zeta function

semiclassical estimates on resolvents of schrodinger operators with homogeneous electric field abstract we are interested in the limiting absorption principle for schrodinger operators of the form h h h 2 x 1 v x 0 h h 0 for a large class of potentials v we establish various estimates for the resolvents of h h at non trapping energy the proof is based on a simple commutator technique our results seem to be new even in the case of h 1

microscopic derivation of ginzburg landau theory we give the first rigorous derivation of the celebrated ginzburg landau gl theory starting from the microscopic bardeen cooper schrieffer bcs model close to the critical temperature gl arises as an effective theory on the macroscopic scale the relevant scaling limit is semiclassical in nature and semiclassical analysis with minimal regularity assumptions plays an important part in our proof

semiclassical asymptotics for the spectral function of long range schrodinger operators we obtain semiclassical asymptotics for the spectral function of schrodinger operators with long range potentials we study the case of non trapping energy levels and also the case of a potential well inside an island where resonances due to trapped trajectories appear

a proof of the gutzwiller semiclassical trace formula using coherent states decomposition the gutzwiller trace formula links the eigenvalues of the schrodinger operator as planck s constant goes to zero the semiclassical regime with the closed orbits of the corresponding classical mechanical system gutzwiller gave a heuristic proof of this trace formula using the feynman integral representation for the propagator of later using the theory of fourier integral operators mathematicians gave rigorous proofs of the formula in various settings here we show how the use of coherent states allows us to give a simple and direct proof

a probabilistic method for image enhancement with simultaneous illumination and reflectance estimation in this paper a new probabilistic method for image enhancement is presented based on a simultaneous estimation of illumination and reflectance in the linear domain we show that the linear domain model can better represent prior information for better estimation of reflectance and illumination than the logarithmic domain a maximum a posteriori map formulation is employed with priors of both illumination and reflectance to estimate illumination and reflectance effectively an alternating direction method of multipliers is adopted to solve the map problem the experimental results show the satisfactory performance of the proposed method to obtain reflectance and illumination with visually pleasing enhanced results and a promising convergence rate compared with other testing methods the proposed method yields comparable or better results on both subjective and objective assessments

space time picture of semiclassical resonances this paper addresses the theory of quasiclassical resonances for schrodinger operators with potentials smooth outside some possible local singularities we introduce the notion of quasiresonance similar to that of quasimode but incorporating a condition revealing its scattering nature and describe its space time behaviour the definition is given in terms of the original schrodinger operator and uses a description of its frequency set the result on the space time behaviour justifies the intuitive picture of resonances as metastable states or bound states with finite life times we demonstrate how quasiresonances arise in several natural situations

remarques sur le principe d incertitude on considere un systeme d observables a j x on suppose que toutes les derivees d ordre 1 des a j sont bornees sur r 2n soit 1 2 1 les deux proprietes suivantes sont equivalentes a il existe c 0 et h 0 0 tels que h ch h 0 h 0 g r n 0 b il existe c 1 0 tel qu on ait 2 1 1 a i x c 1 x r 2n

on the classical limit of berry s phase integrable systems berry s phase is given by integration of a characteristic two form we consider integrable systems defined by weyl quantized classical hamiltonians it is shown that the limit of i times this tow form is the curvature of the classical connection whose holonomy is the hannay angels a result of this type was derived by berry b2

a semi classical trace formula at a totally degenerate critical level we study the semi classical trace formula at a critical energy level for an h pseudo differential operator on open image in new window n whose principal symbol has a totally degenerate critical point for that energy this problem is studied for a large time behavior and under the hypothesis that the principal symbol of the operator has a local extremum at the critical point

sharp semiclassical estimates for the number of eigenvalues below a totally degenerate critical level we consider the semiclassical asymptotic behaviour of the number of eigenvalues smaller than e for elliptic operators in l2 rd we describe a method of obtaining remainder estimates related to the volume of the region of the phase space in which the principal symbol takes values belonging to the intervals e e h where e is close to e if the volume of this region is o h then we obtain remainder estimates o h1 d with no assumptions on the hessian of the principal symbol at the critical level moreover we do not assume that the coefficients are smooth all results hold if second order derivatives of coefficients are holder continuous

on the geometry of semiclassical limits on dirichlet spaces abstract this paper is a contribution to semiclassical analysis for abstract schrodinger type operators on locally compact spaces let x be a metrizable separable locally compact space let be a radon measure on x with a full support let t x y p t x y be a strictly positive pointwise consistent heat kernel and assume that the generator h p 0 of the corresponding self adjoint contraction semigroup in l 2 x induces a regular dirichlet form then given a function 0 1 0 such that the limit lim t 0 p t x x t exists for all x x we prove that for every potential w x r one has lim t 0 t tr e t h p w e w x lim t 0 p t x x t d x for the schrodinger type operator h p w provided w satisfies very mild conditions at that are essentially only made to guarantee that the sum of quadratic forms h p w t is self adjoint and bounded from below for small t and to guarantee that e w x lim t 0 p t x x t d x the proof is probabilistic and relies on a principle of not feeling the boundary for p t x x in particular this result implies a new semiclassical limit result for partition functions valid on arbitrary connected geodesically complete riemannian manifolds and one also recovers a previously established semiclassical limit result for possibly locally infinite connected weighted graphs

contrast enhancement based on intrinsic image decomposition in this paper we propose to introduce intrinsic image decomposition priors into decomposition models for contrast enhancement since image decomposition is a highly ill posed problem we introduce constraints on both reflectance and illumination layers to yield a highly reliable solution we regularize the reflectance layer to be piecewise constant by introducing a weighted ell 1 norm constraint on neighboring pixels according to the color similarity so that the decomposed reflectance would not be affected much by the illumination information the illumination layer is regularized by a piecewise smoothness constraint the proposed model is effectively solved by the split bregman algorithm then by adjusting the illumination layer we obtain the enhancement result to avoid potential color artifacts introduced by illumination adjusting and reduce computing complexity the proposed decomposition model is performed on the value channel in hsv space experiment results demonstrate that the proposed method performs well for a wide variety of images and achieves better or comparable subjective and objective quality compared with the state of the art methods