asymptotic equivalence of nonparametric regression and white noise the principal result is that under conditions to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems and conversely this asymptotic equivalence is in a global and uniform sense any normalized risk function attainable in one problem is asymptotically attainable in the other with the difference in normalized risks converging to zero uniformly over the entire parameter space the results are constructive a recipe is provided for producing these asymptotically equivalent procedures some implications and generalizations of the principal result are also discussed

fractional laplacian phase transitions and boundary reactions a geometric inequality and a symmetry result we deal with symmetry properties for solutions of nonlocal equations of the type sv f v in rn where s 0 1 and the operator s is the so called fractional laplacian the study of this nonlocal equation is made via a careful analysis of the following degenerate elliptic equation div x u 0on rn 0 x ux f u on rn 0 where 1 1 y rn x 0 and u u y x this equation is related to the fractional laplacian since the dirichlet to neumann operator u r n 1 x ux r n 1 is 1 2 more generally we study the so called boundary reaction equations given by div x u g x u 0on rn 0 x ux f u on rn 0 under some natural assumptions on the diffusion coefficient and on the nonlinearities f and g we prove a geometric formula of poincare type for stable solutions from which we derive a symmetry result in the spirit of a conjecture of de giorgi

serrin s overdetermined problem and constant mean curvature surfaces for all n 9 we find smooth entire epigraphs in rn namely smooth domains of the form x rn xn f x1 xn 1 which are not half spaces and in which a problem of the form u f u 0 in has a positive bounded solution with 0 dirichlet boundary data and constant neumann boundary data on this answers negatively for large dimensions a question by berestycki caffarelli and nirenberg in 1971 serrin proved that a bounded domain where such an overdetermined problem is solvable must be a ball in analogy to a famous result by alexandrov that states that an embedded compact surface with constant mean curvature cmc in euclidean space must be a sphere in lower dimensions we succeed in providing examples for domains whose boundary is close to large dilations of a given cmc surface where serrin s overdetermined problem is solvable

layer solutions in a half space for boundary reactions r n 1 are denoted by y y1 yn 1 our main goal is to study bounded solutions of 1 1 that are monotone increasing say from 1 to 1 in one of the y variables we call them layer solutions of 1 1 and we study their existence uniqueness symmetry and variational properties as well as their asymptotic behavior the interest in such increasing solutions comes from some models of boundary phase transitions when the nonlinearity f is given by f u sin cu for some constant c problem 1 1 in a half plane is called the peierls nabarro problem and it appears as a model of dislocations in crystals see 21 36 the peierls nabarro problem is also central to the analysis of boundary vortices in the paper 28 which studies a model for soft thin films in micromagnetism recently derived by kohn and slastikov 26 see also 27 our main result theorem 1 2 characterizes the nonlinearities f for which there exists a layer solution of 1 1 in dimension n 2 we prove that the necessary and sufficient condition is that the potential g defined by g f has two and only two absolute minima in the interval 1 1 located at 1 under the additional hypothesis g 1 0 we also establish the uniqueness of a layer solution up to translations in the y variable the proofs of both the necessity and the sufficiency of the condition on g for existence use new ingredients which we develop in this article a first one is a nonlocal estimate as well as a conserved or hamiltonian quantity satisfied by every layer solution in dimension 2 see theorem 1 3 the estimate can be seen as

asymptotic equivalence for nonparametric regression with multivariate and random design we show that nonparametric regression is asymptotically equivalent in le cam s sense to a sequence of gaussian white noise experiments as the number of observations tends to infinity we propose a general constructive framework based on approximation spaces which allows asymptotic equivalence to be achieved even in the cases of multivariate and random design

from constant mean curvature hypersurfaces to the gradient theory of phase transitions given a nondegenerate minimal hypersurface in a riemannian manifold we prove that for all e small enough there exists ue a critical point of the allen cahn energy ee u e2 u 2 1 u2 2 whose nodal set converges to as e tends to 0 moreover if is a volume nondegenerate constant mean curvature hypersurface then the same conclusion holds with the function ue being a critical point of ee under some volume constraint

embedded minimal surfaces of finite topology in this paper we prove that any complete embedded minimal surface m in r 3 with finite topology and compact boundary possibly empty is conformally a compact riemann surface m with boundary punctured in a finite number of interior points and that m can be represented in terms of meromorphic data on its conformal completion m in particular we demonstrate that m is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior ofm

rotation invariant local frequency descriptors for texture classification this paper presents a novel rotation invariant method for texture classification based on local frequency components the local frequency components are computed by applying 1 d fourier transform on a neighboring function defined on a circle of radius r at each pixel we observed that the low frequency components are the major constituents of the circular functions and can effectively represent textures three sets of features are extracted from the low frequency components two based on the phase and one based on the magnitude the proposed features are invariant to rotation and linear changes of illumination moreover by using low frequency components the proposed features are very robust to noise while the proposed method uses a relatively small number of features it outperforms state of the art methods in three well known datasets brodatz outex and curet in addition the proposed method is very robust to noise and can remarkably improve the classification accuracy especially in the presence of high levels of noise

solutions to the overdetermined boundary problem for semilinear equations with position dependent nonlinearities abstract we show that a wide range of overdetermined boundary problems for semilinear equations with position dependent nonlinearities admits nontrivial solutions the result holds true both on r n and on compact riemannian manifolds as a byproduct of the proofs we also obtain some rigidity or partial symmetry results for solutions to overdetermined problems on riemannian manifolds of nonconstant curvature

a rigidity result for overdetermined elliptic problems in the plane let f 0 r be a locally lipschitz function and r 2 a c 1 domain whose boundary is unbounded and connected if there exists a positive bounded solution to the overdetermined elliptic problem u f u 0 in u 0 on u 1 on we prove that is a half plane in particular we obtain a partial answer to a question raised by h berestycki l caffarelli and l nirenberg in 1997

symmetry of some entire solutions to the allen cahn equation in two dimensions abstract in this paper we prove even symmetry and monotonicity of certain solutions of allen cahn equation in a half plane we also show that entire solutions with finite morse index and four ends must be evenly symmetric with respect to two orthogonal axes a classification scheme of general entire solutions with finite morse index is also presented using energy quantization

on stable solutions for boundary reactions a de giorgi type result in dimension 4 1 we prove that every bounded stable solution of begin aligned delta 1 2 u f u 0 qquad text in mathbb r 3 end aligned is a 1d profile i e u x phi e cdot x for some e in mathbb s 2 where phi mathbb r rightarrow mathbb r is a nondecreasing bounded stable solution in dimension one equivalently stable critical points of boundary reaction problems in mathbb r d 1 mathbb r d 1 cap x d 1 ge 0 of the form begin aligned int x d 1 ge 0 frac 1 2 nabla u 2 dx dx d 1 int x d 1 0 f u dx end aligned are 1d when d 3 these equations have been studied since the 1940 s in crystal dislocations also as it happens for the allen cahn equation the associated energies enjoy a gamma convergence result to the perimeter functional in particular when f u u 3 u or equivalently when f u frac 1 4 1 u 2 2 our result implies the analogue of the de giorgi conjecture for the half laplacian in dimension 4 namely that monotone solutions are 1d note that our result is a pde version of the fact that stable embedded minimal surfaces in mathbb r 3 are planes it is interesting to observe that the corresponding statement about stable solutions to the allen cahn equation namely when the half laplacian is replaced by the classical laplacian is still unknown for d 3

asymptotic equivalence of density estimation and gaussian white noise signal recovery in gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation having all the essential traits in a pure form the equivalence has mostly been stated informally but an approximation in the sense of le cam s deficiency distance would make it precise the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss in nonparametrics a first result of this kind has recently been established for gaussian regression we consider the analogous problem for the experiment given by n i i d observations having density f on the unit interval our basic result concerns the parameter space of densities which are in a holder ball with exponent 1 2 and which are uniformly bounded away from zero we show that an i i d sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift f l 2 and variance 1 4n l this represents a nonparametric analog of le cam s heteroscedastic gaussian approximation in the finite dimensional case the proof utilizes empirical process techniques related to the hungarian construction white noise models on f and log f are also considered allowing for various automatic asymptotic risk bounds in the i i d model from white noise

rotation invariant texture classification using lbp variance lbpv with global matching local or global rotation invariant feature extraction has been widely used in texture classification local invariant features e g local binary pattern lbp have the drawback of losing global spatial information while global features preserve little local texture information this paper proposes an alternative hybrid scheme globally rotation invariant matching with locally variant lbp texture features using lbp distribution we first estimate the principal orientations of the texture image and then use them to align lbp histograms the aligned histograms are then in turn used to measure the dissimilarity between images a new texture descriptor lbp variance lbpv is proposed to characterize the local contrast information into the one dimensional lbp histogram lbpv does not need any quantization and it is totally training free to further speed up the proposed matching scheme we propose a method to reduce feature dimensions using distance measurement the experimental results on representative databases show that the proposed lbpv operator and global matching scheme can achieve significant improvement sometimes more than 10 in terms of classification accuracy over traditional locally rotation invariant lbp method

asymptotic equivalence of spectral density estimation and gaussian white noise we consider the statistical experiment given by a sample y 1 y n of a stationary gaussian process with an unknown smooth spectral density f asymptotic equivalence in the sense of le cam s deficiency distance to two gaussian experiments with simpler structure is established the first one is given by independent zero mean gaussians with variance approximately f i where i is a uniform grid of points in nonparametric gaussian scale regression this approximation is closely related to well known asymptotic independence results for the periodogram and corresponding inference methods the second asymptotic equivalence is to a gaussian white noise model where the drift function is the log spectral density this represents the step from a gaussian scale model to a location model and also has a counterpart in established inference methods that is log periodogram regression the problem of simple explicit equivalence maps markov kernels allowing to directly carry over inference appears in this context but is not solved here

a statistical approach to texture classification from single images we investigate texture classification from single images obtained under unknown viewpoint and illumination a statistical approach is developed where textures are modelled by the joint probability distribution of filter responses this distribution is represented by the frequency histogram of filter response cluster centres textons recognition proceeds from single uncalibrated images and the novelty here is that rotationally invariant filters are used and the filter response space is low dimensional classification performance is compared with the filter banks and methods of leung and malik ijcv 2001 schmid cvpr 2001 and cula and dana ijcv 2004 and it is demonstrated that superior performance is achieved here classification results are presented for all 61 materials in the columbia utrecht texture database we also discuss the effects of various parameters on our classification algorithm such as the choice of filter bank and rotational invariance the size of the texton dictionary as well as the number of training images used finally we present a method of reliably measuring relative orientation co occurrence statistics in a rotationally invariant manner and discuss whether incorporating such information can enhance the classifier s performance

asymptotic equivalence for nonparametric generalized linear models we establish that a non gaussian nonparametric regression model is asymptotically equivalent to a regression model with gaussian noise the approximation is in the sense of le cam s deficiency distance the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss our result concerns a sequence of independent but not identically distributed observations with each distribution in the same real indexed exponential family the canonical parameter is a value f ti of a regression function f at a grid point ti nonparametric glm when f is in a holder ball with exponent we establish global asymptotic equivalence to observations of a signal f t in gaussian white noise where is related to a variance stabilizing transformation in the exponential family the result is a regression analog of the recently established gaussian approximation for the i i d model the proof is based on a functional version of the hungarian construction for the partial sum process

contrast context histogram an efficient discriminating local descriptor for object recognition and image matching in this paper we propose a new invariant local descriptor called the contrast context histogram cch for image matching and object recognition by representing the contrast distributions of a local region it serves as a distinctive local descriptor of the region our experiments demonstrate that contrast based local descriptors can represent local regions with more compact histogram bins because of its high matching accuracy and efficient computation the cch has the potential to be used in a number of real time applications

equivalence theory for density estimation poisson processes and gaussian white noise with drift this paper establishes the global asymptotic equivalence between a poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function this equivalence is also extended to density estimation models by poissonization the asymptotic equivalences are established by constructing explicit equivalence mappings the impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models

stability of hypersurfaces of constant mean curvature in riemannian manifolds hypersurfaces m n with constant mean curvature in a riemannian manifold overline m n 1 display many similarities with minimal hypersurfaces of overline m n 1 they are both solutions to the variational problem of minimizing the area function for certain variations in the first case however the admissible variations are only those that leave a certain volume function fixed for precise definitions see sect 2 this isoperimetric character of the variational problem associated to hypersurfaces of constant mean curvature introduces additional complications in the treatment of stability of such hypersurfaces

gaussian mrf rotation invariant features for image classification features based on markov random field mrf models are sensitive to texture rotation this paper develops an anisotropic circular gaussian mrf acgmrf model for retrieving rotation invariant texture features to overcome the singularity problem of the least squares estimate method an approximate least squares estimate method is designed and implemented rotation invariant features are obtained from the acgmrf model parameters using the discrete fourier transform the acgmrf model is demonstrated to be a statistical improvement over three published methods the three methods include a laplacian pyramid an isotropic circular gmrf icgmrf and gray level cooccurrence probability features

overdetermined elliptic problems in topological disks abstract we introduce a method based on the poincare hopf index theorem to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk applications to some well known nonlinear elliptic pdes are provided our result can be seen as the analogue of hopf s uniqueness theorem for constant mean curvature spheres but for the general analytic context of overdetermined elliptic problems

asymptotic nonequivalence of nonparametric experiments when the smoothness index is an example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments density problem white noise with drift and nonparametric regression when the smoothness index of the unknown nonparametric function class is 1 2

tight conditions for consistency of variable selection in the context of high dimensionality we address the issue of variable selection in the regression model with very high ambient dimension textit i e when the number of variables is very large the main focus is on the situation where the number of relevant variables called intrinsic dimension and denoted by d is much smaller than the ambient dimension d without assuming any parametric form of the underlying regression function we get tight conditions making it possible to consistently estimate the set of relevant variables these conditions relate the intrinsic dimension to the ambient dimension and to the sample size the procedure that is provably consistent under these tight conditions is based on comparing quadratic functionals of the empirical fourier coefficients with appropriately chosen threshold values the asymptotic analysis reveals the presence of two quite different re gimes the first regime is when d is fixed in this case the situation in nonparametric regression is the same as in linear regression textit i e consistent variable selection is possible if and only if log d is small compared to the sample size n the picture is different in the second regime d to infty as n to infty where we prove that consistent variable selection in nonparametric set up is possible only if d log log d is small compared to log n we apply these results to derive minimax separation rates for the problem of variable selection

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

a general halfspace theorem for constant mean curvature surfaces in this paper we prove a general halfspace theorem for constant mean curvature surfaces under certain hypotheses we prove that in an ambient space m 3 any constant mean curvature h 0 surface on one side of a constant mean curvature h 0 surface sigma 0 is an equidistant surface to sigma 0 the main hypotheses of the theorem are that sigma 0 is parabolic and the mean curvature of the equidistant surfaces to sigma 0 evolves in a certain way

regularity of flat level sets in phase transitions we consider local minimizers of the ginzburg landau energy functional 1 2 u 2 1 4 1 u 2 2 dx and prove that if the 0 level set is included in a flat cylinder then in the interior it is included in a flatter cylinder as a consequence we prove a conjecture of de giorgi which states that level sets of global solutions of u u 3 u such that u 1 n u 0 lim u x x n 1 x n are hyperplanes in dimension n 8

asymptotic equivalence of nonparametric diffusion and euler scheme experiments the main goal of the asymptotic equivalence theory of le cam 1986 is to approximate general statistical models by simple ones we develop here a global asymptotic equivalence result for nonparametric drift estimation of a discretely observed diffusion process and its euler scheme the asymptotic equivalences are established by constructing explicit equivalence mappings the impact of such asymptotic equivalence results is that it justifies the use in many applications of the euler scheme instead of the diffusion process we especially investigate the case of diffusions with non constant diffusion coefficient to obtain asymptotic equivalence experiments obtained by random change of times are introduced

unbounded periodic solutions to serrin s overdetermined boundary value problem we study the existence of nontrivial unbounded domains omega in mathbb r n such that the overdetermined problem delta u 1 quad rm in omega quad u 0 quad partial nu u rm const quad rm on partial omega admits a solution u by this we complement serrin s classification result from 1971 which yields that every bounded domain admitting a solution of the above problem is a ball in mathbb r n the domains we construct are periodic in some variables and radial in the other variables and they bifurcate from a straight generalized cylinder or slab we also show that these domains are uniquely self cheeger relative to a period cell for the problem

the gibbs thompson relation within the gradient theory of phase transitions this paper discusses the asymptotic behavior as 0 of the chemical potentials associated with solutions of variational problems within the van der waals cahn hilliard theory of phase transitions in a fluid with free energy per unit volume given by 2 2 w where is the density the main result is that is asymptotically equal to e d o with e the interfacial energy per unit surface area of the interface between phases the constant sum of principal curvatures of the interface and d the density jump across the interface this result is in agreement with a formula conjectured by m gurtin and corresponds to the gibbs thompson relation for surface tension proved by g caginalp within the context of the phase field model of free boundaries arising from phase transitions

asymptotic equivalence theory for nonparametric regression with random design this paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function the asymptotic equivalence is established by constructing explicit equivalence mappings between the nonparametric regression and the whitenoise experiments which provide synthetic observations and synthetic asymptotic solutions from any one of the two experiments with asymptotic properties identical to the true observations and given asymptotic solutions from the other the impact of such asymptotic equivalence results is that an investigation in one nonparametric problem automatically yields asymptotically analogous results in all other asymptotically equivalent nonparametric problems 1 introduction the purpose of this paper is to establish the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function we establish this asymptotic equivalence by constructing explicit equivalence mappings between the nonparametric regression and the white noise problems as in brown and low 1996 for their asymptotic equivalence results the equivalence mapping from the nonparametric regression to the white noise provides synthetic observations of the white noise from the nonparametric regression such that the distributions of the synthetic observations are asymptotically equivalent to those of the true observations of the white noise for any asymptotic solution to a white noise problem the application of the solution to the synthetic observations provides an asymptotic solution to the corresponding nonparametric regression problem with identical asymptotic properties likewise the equivalence mapping from the white noise produces synthetic observations of the nonparametric regression problem and synthetic asymptotic solutions to white noise problems based on those of the corresponding nonparametric regression problems the impact of such asymptotic equivalence results is that an investigation in one nonparametric problem automatically yields asymptotically analogous results in

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

local binary features for texture classification local binary patterns lbp have emerged as one of the most prominent and widely studied local texture descriptors truly a large number of lbp variants has been proposed to the point that it can become overwhelming to grasp their respective strengths and weaknesses and there is a need for a comprehensive study regarding the prominent lbp related strategies new types of descriptors based on multistage convolutional networks and deep learning have also emerged in different papers the performance comparison of the proposed methods to earlier approaches is mainly done with some well known texture datasets with differing classifiers and testing protocols and often not using the best sets of parameter values and multiple scales for the comparative methods very important aspects such as computational complexity and effects of poor image quality are often neglected in this paper we provide a systematic review of current lbp variants and propose a taxonomy to more clearly group the prominent alternatives merits and demerits of the various lbp features and their underlying connections are also analyzed we perform a large scale performance evaluation for texture classification empirically assessing forty texture features including thirty two recent most promising lbp variants and eight non lbp descriptors based on deep convolutional networks on thirteen widely used texture datasets the experiments are designed to measure their robustness against different classification challenges including changes in rotation scale illumination viewpoint number of classes different types of image degradation and computational complexity the best overall performance is obtained for the median robust extended local binary pattern mrelbp feature for textures with very large appearance variations fisher vector pooling of deep convolutional neural networks is clearly the best but at the cost of very high computational complexity the sensitivity to image degradations and computational complexity are among the key problems for most of the methods considered highlightsa taxonomy and comprehensive survey of lbp variants characteristics of and connections between lbp variants are provided a comprehensive experimental evaluation of 32 lbp methods comparison of 32 lbp variants with 8 deep convnets features evaluation of robustness to rotation illumination scale and noise changes comparison of computational complexity of forty variants

entire solutions of semilinear elliptic equations in r 3 and a conjecture of de giorgi this paper is concerned with the study of bounded solutions of semilinear elliptic equations u f u in the whole space r under the assumption that u is monotone in one direction say nu in r n the goal is to establish the one dimensional character or symmetry of u namely that u only depends on one variable or equivalently that the level sets of u are hyperplanes this type of symmetry question was raised by de giorgi in who made the following conjecture we quote literally page of dg

texture classification using dominant neighborhood structure this paper proposes a new approach to extract global image features for the purpose of texture classification the proposed texture features are obtained by generating an estimated global map representing the measured intensity similarity between any given image pixel and its surrounding neighbors within a certain window the intensity similarity map is an average representation of the texture image dominant neighborhood similarity the estimated dominant neighborhood similarity is robust to noise and referred to as image dominant neighborhood structure the global rotation invariant features are then extracted from the generated image dominant neighborhood structure features obtained from the local binary patterns lbps are then extracted in order to supply additional local texture features to the generated features from the dominant neighborhood structure both features complement each other the experimental results on representative texture databases show that the proposed method is robust to noise and can achieve significant improvement in terms of the obtained classification accuracy in comparison to the lbp method in addition the method classification accuracy is comparable to the two recent lbp extensions dominant lbp and completed lbp

dominant local binary patterns for texture classification this paper proposes a novel approach to extract image features for texture classification the proposed features are robust to image rotation less sensitive to histogram equalization and noise it comprises of two sets of features dominant local binary patterns dlbp in a texture image and the supplementary features extracted by using the circularly symmetric gabor filter responses the dominant local binary pattern method makes use of the most frequently occurred patterns to capture descriptive textural information while the gabor based features aim at supplying additional global textural information to the dlbp features through experiments the proposed approach has been intensively evaluated by applying a large number of classification tests to histogram equalized randomly rotated and noise corrupted images in outex brodatz meastex and curet texture image databases our method has also been compared with six published texture features in the experiments it is experimentally demonstrated that the proposed method achieves the highest classification accuracy in various texture databases and image conditions

exploring space frequency co occurrences via local quantized patterns for texture representation local binary pattern lbp has shown its power in texture classification and face recognition however the lbp operator is performed in the original image space and it lacks deeper pixel interactions to capture a richer description in this paper we propose to explore space frequency co occurrences via local quantized patterns for texture representation the proposed method proceeds in two channels in each channel the multi resolution spatial maps are first obtained by specific spatial filtering and local frequency features spectral maps are subsequently extracted by applying the local fourier transform to the spatial map two types of quantization via global thresholding are employed to quantize the spatial and spectral maps into three and two levels respectively the quantized patterns are then jointly encoded to construct a space frequency co occurrence histogram finally the two channel histograms are combined to characterize the texture without resort to the texton based representation our method directly encodes the joint information in the space and frequency domains while preserving the robustness to image rotation illumination scale and viewpoint changes extensive experiments have been conducted on three well known texture databases and our method achieves the best classification results compared with state of the art approaches investigated highlightstwo channel space frequency feature spaces are designed to obtain invariant features two types of quantization via global thresholding are developed the joint space frequency coding is explored to capture a richer description our method outperforms the state of the art on three well known texture datasets

a complement to le cam s theorem this paper examines asymptotic equivalence in the sense of le cam between density estimation experiments and the accompanying poisson experiments the significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other the equivalence given here is established under a weak assumption on the parameter space f in particular a sharp besov smoothness condition is given on f which is sufficient for poissonization namely if f is in a besov ball b p g m with ap 1 2 examples show poissonization is not possible whenever ap 0

the liouville property and a conjecture of de giorgi we consider bounded entire solutions of the nonlinear pde u u u 3 0i n r d and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes the proof uses a liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form operator c 2000 john wiley sons inc

rotation invariant multiresolution texture analysis using radon and wavelet transforms a new rotation invariant texture analysis technique using radon and wavelet transforms is proposed this technique utilizes the radon transform to convert the rotation to translation and then applies a translation invariant wavelet transform to the result to extract texture features a k nearest neighbors classifier is employed to classify texture patterns a method to find the optimal number of projections for the radon transform is proposed it is shown that the extracted features generate an efficient orthogonal feature space it is also shown that the proposed features extract both of the local and directional information of the texture patterns the proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the radon transform step to test and evaluate the method we employed several sets of textures along with different wavelet bases experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture analysis methods

geometry and topology of some overdetermined elliptic problems we study necessary conditions on the geometry and the topology of domains in r2 that support a positive solution to a classical overdetermined elliptic problem u f u 0in u 0on u constanton the ideas and tools we use come from constant mean curvature surface theory in particular we obtain a partial answer to a question posed by h berestycki l caffarelli and l nirenberg in 1997 we investigate also some boundedness properties of the solution u some of our results generalize to higher dimensions

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

entire solutions of the allen cahn equation and complete embedded minimal surfaces of finite total curvature in r 3 we consider minimal surfaces m which are complete embedded and have finite total curvature in mathbb r 3 and bounded entire solutions with finite morse index of the allen cahn equation delta u f u 0 in mathbb r 3 here f w with w bi stable and balanced for instance w u frac 1 4 1 u 2 2 we assume that m has m ge 2 ends and additionally that m is non degenerate in the sense that its bounded jacobi fields are all originated from rigid motions this is known for instance for a catenoid and for the costa hoffman meeks surface of any genus we prove that for any small alpha gt 0 the allen cahn equation has a family of bounded solutions depending on m 1 parameters distinct from rigid motions whose level sets are embedded surfaces lying close to the blown up surface m alpha alpha 1 m with ends possibly diverging logarithmically from m alpha we prove that these solutions are l infty non degenerate up to rigid motions and find that their morse index coincides with the index of the minimal surface our construction suggests parallels of de giorgi conjecture for general bounded solutions of finite morse index

tusnady s inequality revisited tusnady s inequality is the key ingredient in the kmt hungarian coupling of the empirical distribution function with a brownian bridge we present an elementary proof of a result that sharpens the tusnady inequality modulo constants our method uses the beta integral representation of binomial tails simple taylor expansion and some novel bounds for the ratios of normal tail probabilities

adaptive nonparametric confidence sets we construct honest confidence regions for a hilbert space valued parameter in various statistical models the confidence sets can be centered at arbitrary adaptive estimators and have diameter which adapts optimally to a given selection of models the latter adaptation is necessarily limited in scope we review the notion of adaptive confidence regions and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation applications include the finite normal mean model the white noise model density estimation and regression with random design institute of mathematical statistics 2006

robust volumetric texture classification of magnetic resonance images of the brain using local frequency descriptor this paper presents a method for robust volumetric texture classification it also proposes 2d and 3d gradient calculation methods designed to be robust to imaging effects and artifacts using the proposed 2d method the gradient information is extracted on the xyz orthogonal planes at each voxel and used to form a local coordinate system the local coordinate system and the local 3d gradient computed by the proposed 3d gradient calculator are then used to define volumetric texture features it is shown that the presented gradient calculation methods can be efficiently implemented by convolving with 2d and 3d kernels the experimental results demonstrate that the proposed gradient operators and the texture features are robust to imaging effects and artifacts such as blurriness and noise in 2d and 3d images the proposed method is compared with three state of the art volumetric texture classification methods the 3d gray level cooccurance matrix 3d local binary patterns and second orientation pyramid on magnetic resonance imaging data of the brain the experimental results show the superiority of the proposed method in accuracy robustness and speed

3d solid texture classification using locally oriented wavelet transforms many image acquisition techniques used in biomedical imaging material analysis and structural geology are capable of acquiring 3d solid images computational analysis of these images is complex but necessary since it is difficult for humans to visualize and quantify their detailed 3d content one of the most common methods to analyze 3d data is to characterize the volumetric texture patterns texture analysis generally consists of encoding the local organization of image scales and directions which can be extremely diverse in 3d current state of the art techniques face many challenges when working with 3d solid texture where most approaches are not able to consistently characterize both scale and directional information 3d riesz wavelets can deal with both properties one key property of riesz filterbanks is steerability which can be used to locally align the filters and compare textures with arbitrary local orientations this paper proposes and compares three novel local alignment criteria for higher order 3d riesz wavelet transforms the estimations of local texture orientations are based on higher order extensions of regularized structure tensors an experimental evaluation of the proposed methods for the classification of synthetic 3d solid textures with alterations such as rotations and noise demonstrated the importance of local directional information for robust and accurate solid texture recognition these alignment methods achieved an accuracy of 0 95 in the rotated data three times more than the unaligned riesz descriptor that achieved 0 32 the accuracy obtained is better than all other techniques that are published and tested on the same database

on adaptive estimation of linear functionals adaptive estimation of linear functionals over a collection of parameter spaces is considered a between class modulus of continuity a geometric quantity is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single para meter space a general construction of optimally adaptive estimators based on an ordered modulus of continuity is given the results are complemented by several illustrative examples

asymptotic equivalence of nonparametric autoregression and nonparametric regression it is proved that nonparametric autoregression is asymptotically equivalent in the sense of le cam s deficiency distance to nonparametric regression with random design as well as with regular nonrandom design

texture classification by modeling joint distributions of local patterns with gaussian mixtures texture classification generally requires the analysis of patterns in local pixel neighborhoods statistically the underlying processes are comprehensively described by their joint probability density functions jpdfs even for small neighborhoods however stable estimation of jpdfs by joint histograms jhsts is often infeasible since the number of entries in the jhst exceeds by far the number of pixels in a typical texture region moreover evaluation of distance functions between jhsts is often computationally prohibitive practically the number of entries in a jhst is therefore reduced by considering only two pixel patterns leading to 2d jhsts known as cooccurrence matrices or by quantization of the gray levels in local patterns to only two gray levels yielding local binary patterns lbps both approaches result in a loss of information we introduce here a framework for supervised texture classification which reduces or avoids this information loss local texture neighborhoods are first filtered by a filter bank without further quantization the jpdf of the filter responses is then described parametrically by gaussian mixture models gmms we show that the parameters of the gmms can be reliably estimated from small image regions moreover distances between the thus modelled jpdfs of different texture patterns can be computed efficiently in closed form from their model parameters we furthermore extend this texture descriptor to achieve full invariance to rotation we evaluate the framework for different filter banks on the brodatz texture set we first show that combining the lbp difference filters with the gmm based density estimator outperforms the classical lbp approach and its codebook extensions when replacing these rather elementary difference filters by the wavelet frame transform wft the performance of the framework on all 111 brodatz textures exceeds the one obtained more recently by spin image and rift descriptors by lazebnik et al

flattening results for elliptic pdes in unbounded domains with applications to overdetermined problems semilinear elliptic pdes are dealt with either in the half space or in overdetermined settings we obtain several new results and also give new proofs of celebrated theorems by exploiting some geometric analysis of level sets a geometric inequality and a pointwise gradient estimate

deficiency distance between multinomial and multivariate normal experiments the deficiency distance between a multinomial and a multivariate normal experiment is bounded under a condition that the parameters are bounded away from zero this result can be used as a key step in establishing asymptotic normal approximations to nonparametric density estimation experiments the bound relies on the recursive construction of explicit markov kernels that can be used to reproduce one experiment from the other the distance is then bounded using classic local limit bounds between binomial and normal distributions some extensions to other appropriate normal experiments are also presented

completed local binary count for rotation invariant texture classification in this brief a novel local descriptor named local binary count lbc is proposed for rotation invariant texture classification the proposed lbc can extract the local binary grayscale difference information and totally abandon the local binary structural information although the lbc codes do not represent visual microstructure the statistics of lbc features can represent the local texture effectively in addition a completed lbc clbc is also proposed to enhance the performance of texture classification experimental results obtained from three databases demonstrate that the proposed clbc can achieve comparable accurate classification rates with completed local binary pattern

a liouville theorem for the euler equations in the plane this paper is concerned with qualitative properties of bounded steady flows of an ideal incompressible fluid with no stagnation point in the two dimensional plane mathbb r 2 we show that any such flow is a shear flow that is it is parallel to some constant vector the proof of this liouville type result is firstly based on the study of the geometric properties of the level curves of the stream function and secondly on the derivation of some estimates on the at most logarithmic growth of the argument of the flow in large balls these estimates lead to the conclusion that the streamlines of the flow are all parallel lines

asymptotic equivalence and adaptive estimation for robust nonparametric regression asymptotic equivalence theory developed in the literature so far are only for bounded loss functions this limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded in this paper we develop asymptotic equivalence results for robust nonparametric regression with unbounded loss functions the results imply that all the gaussian nonparametric regression procedures can be robustified in a unified way a key step in our equivalence argument is to bin the data and then take the median of each bin the asymptotic equivalence results have significant practical implications to illustrate the general principles of the equivalence argument we consider two important nonparametric inference problems robust estimation of the regression function and the estimation of a quadratic functional in both cases easily implementable procedures are constructed and are shown to enjoy simultaneously a high degree of robustness and adaptivity other problems such as construction of confidence sets and nonparametric hypothesis testing can be handled in a similar fashion

the root unroot algorithm for density estimation as implemented via wavelet block thresholding we propose and implement a density estimation procedure which begins by turning density estimation into a nonparametric regression problem this regression problem is created by binning the original observations into many small size bins and by then applying a suitable form of root transformation to the binned data counts in principle many common nonparametric regression estimators could then be applied to the transformed data we propose use of a wavelet block thresholding estimator in this paper finally the estimated regression function is un rooted by squaring and normalizing the density estimation procedure achieves simultaneously three objectives computational efficiency adaptivity and spatial adaptivity a numerical example and a practical data example are discussed to illustrate and explain the use of this procedure theoretically it is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the besov classes the estimator also automatically adapts to the local smoothness of the underlying function and attains the local adaptive minimax rate for estimating functions at a point there are three key steps in the technical argument poissonization quantile coupling and oracle risk bound for block thresholding in the non gaussian setting some of the technical results may be of independent interest

symmetry of traveling wave solutions to the allen cahn equation in mathbb r 2 in this paper we prove even symmetry of monotone traveling wave solutions to the balanced allen cahn equation in the entire plane related results for the unbalanced allen cahn equation are also discussed

an overdetermined problem of anisotropic equations in convex cones abstract in this paper we study some overdetermined boundary value problems for anisotropic elliptic pdes in a bounded domain in a convex cone of r n by using some integral identities and maximum principle we prove the corresponding wulff shape characterizations which includes the classical serrin s overdetermined boundary value problem

bifurcating extremal domains for the first eigenvalue of the laplacian abstract we prove the existence of a smooth family of non compact domains s r n 1 n 1 bifurcating from the straight cylinder b n r for which the first eigenfunction of the laplacian with 0 dirichlet boundary condition also has constant neumann data at the boundary for each s e e the overdetermined system u u 0 in s u 0 on s u const on s has a bounded positive solution the domains s are rotationally symmetric and periodic with respect to the r axis of the cylinder they are of the form s x t r n r x 1 s cos 2 t s t o s 2 where t s t 0 o s and t 0 is a positive real number depending on n for n 2 these domains provide a smooth family of counter examples to a conjecture of berestycki caffarelli and nirenberg we also give rather precise upper and lower bounds for the bifurcation period t 0 this work improves a recent result of the second author

on de giorgi s conjecture in dimension n 9 a celebrated conjecture due to de giorgi states that any bounded solution of the equation u 1 u 2 u 0 in r n with ynu 0 must be such that its level setsfu g are all hyperplanes at least for dimension n 8 a counterexample for n 9 has long been believed to exist starting from a minimal graph which is not a hyperplane found by bombieri de giorgi and giusti in r n n 9 we prove that for any small 0 there is a bounded solution u y with yn u 0 which resembles tanh a t p 2 a where t t y denotes a choice of signed distance to the blown up minimal graph 1 this solution is a counterexample to de giorgi s conjecture for n 9

one dimensional symmetry of bounded entire solutions of some elliptic equations this paper is about one dimensional symmetry properties for some entire and bounded solutions of u f u 0 in ir we consider solutions u such that 1 u 1 and u x1 xn 1 as xn uniformly with respect to x1 xn 1 under some conditions on f we prove that the solutions only depend on the variable xn we also discuss more general elliptic operators the qualitative properties then strongly depend on the coefficients of the operator these results extend to higher dimensions and to more general operators a result of ghoussoub and gui 21 proved for n 3 ams classification 35b05 35b40 35b50 35j60

a gradient bound and a liouville theorem for nonlinear poisson equations soit f c 2 r une fonction non negative et u c 3 r n une solution dans tout r n de l equation u f u ou f f est la derivee 1ere de f si u est borne sur r n et s il existe x 0 r n tel que f u x 0 0 alors u est constante

estimating the intensity of a random measure by histogram type estimators the purpose of this paper is to estimate the intensity of some random measure n on a set mathcal x by a piecewise constant function on a finite partition of mathcal x given a possibly large family mathcal m of candidate partitions we build a piecewise constant estimator histogram on each of them and then use the data to select one estimator in the family choosing the square of a hellinger type distance as our loss function we show that each estimator built on a given partition satisfies an analogue of the classical squared bias plus variance risk bound moreover the selection procedure leads to a final estimator satisfying some oracle type inequality with as usual a possible loss corresponding to the complexity of the family mathcal m when this complexity is not too high the selected estimator has a risk bounded up to a universal constant by the smallest risk bound obtained for the estimators in the family for suitable choices of the family of partitions we deduce uniform risk bounds over various classes of intensities our approach applies to the estimation of the intensity of an inhomogenous poisson process among other counting processes or the estimation of the mean of a random vector with nonnegative components