symmetric capacity of the gaussian interference channel with an out of band relay to within 1 15 bits this paper studies the gaussian interference channel ic with a relay which transmits and receives in a band that is orthogonal to the ic the channel associated with the relay is thus an out of band relay channel obrc the focus is on a symmetric channel model in order to assess the fundamental impact of the obrc on the signal interaction of the ic in the simplest possible setting first the linear deterministic model is investigated and the sum capacity of this channel is established for all possible channel parameters in particular it is observed that the impact of obrc as its links get stronger is similar to that of output feedback for the ic the insights obtained from the deterministic model are then used to design achievable schemes for the gaussian model the interference links are classified as extremely strong very strong strong moderate weak and very weak for strong and moderate interference separate encoding is near optimal for very strong and extremely strong interference the interference links provide side information to the destinations which can help the transmission through the obrc for weak or very weak interference an extension of the han kobayashi scheme for the ic is utilized where the messages are split into common and private to achieve higher rates it is beneficial to further split the common message into two parts and the obrc plays an important role in decoding the common message it is shown that our strategy achieves the symmetric capacity to within 1 14625 bits per channel use with duplexing factor 0 5 and 1 27125 bits per channel use for arbitrary duplexing factors for all channel parameters an important observation from the constant gap result is that strong interference can be beneficial with the presence of an obr

duality between channel capacity and rate distortion with two sided state information we show that the duality between channel capacity and data compression is retained when state information is available to the sender to the receiver to both or to neither we present a unified theory for eight special cases of channel capacity and rate distortion with state information which also extends existing results to arbitrary pairs of independent and identically distributed i i d correlated state information s sub 1 s sub 2 available at the sender and at the receiver respectively in particular the resulting general formula for channel capacity c max sub p u x s sub 1 i u s sub 2 y i u s sub 1 assumes the same form as the generalized wyner ziv 1976 rate distortion function r d min sub p u x s sub 1 p x spl i cap u s sub 2 i u s sub 1 x 1 u s sub 2

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

geometric coupling thresholds in a two dimensional strip we consider the laplacian in a strip r 0 d with the boundary condition which is dirichlet except at the segment of a length 2a of one of the boundaries where it is switched to neumann this operator is known to have a non empty and simple discrete spectrum for any a 0 there is a sequence 0 a1 a2 of critical values at which new eigenvalues emerge from the continuum when the neumann window expands we find the asymptotic behavior of these eigenvalues around the thresholds showing that the gap is in the leading order proportional to a an 2 with an explicit coefficient expressed in terms of the corresponding threshold energy resonance eigenfunction

structural image restoration through deformable templates abstract prior knowledge on the space of possible images is given in the form of a function or template in some domain the set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself a prior gaussian distribution is given on the set of continuous mappings the observed image is assumed to be a degradation of the true image with additive noise given the observed image a posterior distribution is then obtained and has the form of a nonlinear perturbation of the gaussian measure on the space of mappings we present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image as well as to spot pathologies in it moreover we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive

a penalized likelihood approach to image warping discussion a warping is a function that deforms images by mapping between image domains the choice of function is formulated statistically as maximum penalized likelihood where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping the paper addresses two issues simultaneously of how to choose the warping function and how to assess the alignment a new fourier von mises image model is identified with phase differences between fourier transformed images having von mises distributions also new null set distortion criteria are proposed with each criterion uniquely minimized by a particular set of polynomial functions a conjugate gradient algorithm is used to estimate the warping function which is numerically approximated by a piecewise bilinear function the method is motivated by and used to solve three applied problems to register a remotely sensed image with a map to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images

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

learning to match deriving optimal template matching algorithms from probabilistic image models finding correspondences between images by template matching is a common problem in image understanding although a variety of solutions have been proposed most of them rely on the arbitrary choice of a template and a matching function often different cost functions lead to different results and the choice of a good cost for a specific application remains an art statistical models on the other hand allow us to derive optimal learning and matching algorithms from modeling assumptions using likelihood maximization principles the key contribution of this paper is the development of a statistical framework for learning what function to optimize from training examples we present a family of statistical models for grayscale images which allow us to derive optimal template matching algorithms the intensity at each pixel is described by a random variable whose distribution is encoded by a deformable template firstly we assume the intensity distribution to be gaussian and derive an intensity matching algorithm which is a generalization of the classical sum of squared differences then we introduce a hidden segmentation variable in the probabilistic model and derive a segmentation matching algorithm that can handle photometric variations both models are exemplified on the automatic detection of anatomical landmarks in brain magnetic resonance images

hermitian boundary conditions at a dirichlet singularity the marletta rozenblum model in domains b with smoothly varying boundary conditions points where wavefunctions are required to vanish were recently identified as dirichlet singularities d points where the hamiltonian h does not define discrete eigenvalues and a scattering phase is undetermined berry and dennis 2008 j phys a math theor 41 135203 this is explained marletta and rozenblum 2009 j phys a math theor 42 125204 by the observation illustrated with an exactly solvable separable model that a d point requires the specification of an additional parameter defining a family of self adjoint extensions of h here the underlying theory is presented in an elementary way and a d point is identified as a leak through which current can flow into or out of b hermiticity seals the leak ensuring that no current flows though the d point as well as across the boundary of b the solvable model is examined in detail for bound states where b is a semidisk and for wave reflections where b is a half plane the quantization condition for a nonseparable billiard is obtained explicitly

theory of a curved planar waveguide with robin boundary conditions a model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative robin boundary condition is analyzed theoretically within the framework of the linear schrodinger equation and is applied to the study of the processes in the bent magnetic multilayers superconducting films and metallic ferrite filled waveguides in particular subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the robin parameter 1 lambda with lambda being an extrapolation length entering robin boundary condition for the arbitrary robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest mode energy of the continuously curved duct is always smaller than its straight counterpart accordingly the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend in terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart localized level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius conditions of the bound state existence for the different robin parameters on the opposite edges are analyzed too in particular it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one in the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode for example for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths lambda at the opposite interfaces various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the dirichlet to the neumann case as the extrapolation length lambda sweeps the positive axis

domain perturbation for elliptic equations subject to robin boundary conditions abstract we prove domain perturbation theorems for linear and nonlinear elliptic equations under robin boundary conditions the theory allows very singular perturbation of domains in particular it includes cutting holes parts degenerating to a set of measure zero such as the dumbbell problem or wildly oscillating boundaries in the last case we show that the limiting problem is the dirichlet problem

a mathematical motivation for complex valued convolutional networks a complex valued convolutional network convnet implements the repeated application of the following composition of three operations recursively applying the composition to an input vector of nonnegative real numbers 1 convolution with complex valued vectors followed by 2 taking the absolute value of every entry of the resulting vectors followed by 3 local averaging for processing real valued random vectors complex valued convnets can be viewed as data driven multiscale windowed power spectra data driven multiscale windowed absolute spectra data driven multiwavelet absolute values or in their most general configuration data driven nonlinear multiwavelet packets indeed complex valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex valued exponentials standard real valued convnets using rectified linear units relus sigmoidal e g logistic or tanh nonlinearities or max pooling for example do not obviously exhibit the same exact correspondence with data driven wavelets whereas for complex valued convnets the correspondence is much more than just a vague analogy courtesy of the exact correspondence the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to complex valued convnets

a laplace operator with boundary conditions singular at one point we discuss a recent paper of berry and dennis j phys a math theor 2008 41 135203 concerning a laplace operator on a smooth domain with singular boundary condition we explain a paradox in the article j phys a math theor 2008 41 135203 and show that if a certain additional condition is imposed the result is a spectral problem for a self adjoint operator having only eigenvalues and no continuous spectrum the eigenvalues accumulate at only and we obtain the asymptotic behaviours of the counting functions n and n for positive and negative eigenvalues the physical meaning of the additional boundary condition is not yet clear

unsupervised learning of invariant representations the present phase of machine learning is characterized by supervised learning algorithms relying on large sets of labeled examples n the next phase is likely to focus on algorithms capable of learning from very few labeled examples n 1 like humans seem able to do we propose an approach to this problem and describe the underlying theory based on the unsupervised automatic learning of a good representation for supervised learning characterized by small sample complexity we consider the case of visual object recognition though the theory also applies to other domains like speech the starting point is the conjecture proved in specific cases that image representations which are invariant to translation scaling and other transformations can considerably reduce the sample complexity of learning we prove that an invariant and selective signature can be computed for each image or image patch the invariance can be exact in the case of group transformations and approximate under non group transformations a module performing filtering and pooling like the simple and complex cells described by hubel and wiesel can compute such signature the theory offers novel unsupervised learning algorithms for deep architectures for image and speech recognition we conjecture that the main computational goal of the ventral stream of visual cortex is to provide a hierarchical representation of new objects images which is invariant to transformations stable and selective for recognition and show how this representation may be continuously learned in an unsupervised way during development and visual experience

a coarse to fine strategy for multiclass shape detection multiclass shape detection in the sense of recognizing and localizing instances from multiple shape classes is formulated as a two step process in which local indexing primes global interpretation during indexing a list of instantiations shape identities and poses is compiled constrained only by no missed detections at the expense of false positives global information such as expected relationships among poses is incorporated afterward to remove ambiguities this division is motivated by computational efficiency in addition indexing itself is organized as a coarse to fine search simultaneously in class and pose this search can be interpreted as successive approximations to likelihood ratio tests arising from a simple naive bayes statistical model for the edge maps extracted from the original images the key to constructing efficient hypothesis tests for multiple classes and poses is local oring in particular spread edges provide imprecise but common and locally invariant features natural tradeoffs then emerge between discrimination and the pattern of spreading these are analyzed mathematically within the model based framework and the whole procedure is illustrated by experiments in reading license plates

towards a coherent statistical framework for dense deformable template estimation summary the problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge we provide a careful definition and analysis of a well defined statistical model based on dense deformable templates for grey level images of deformable objects we propose a rigorous bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting the model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class we illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood

on the equivalence between kernel quadrature rules and random feature expansions we show that kernel based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels for a particular decomposition that always exists for such kernels we provide a theoretical analysis of the number of required samples for a given approximation error leading to both upper and lower bounds that are based solely on the eigenvalues of the associated integral operator and match up to logarithmic terms in particular we show that the upper bound may be obtained from independent and identically distributed samples from a specific non uniform distribution while the lower bound if valid for any set of points applying our results to kernel based quadrature while our results are fairly general we recover known upper and lower bounds for the special cases of sobolev spaces moreover our results extend to the more general problem of full function approximations beyond simply computing an integral with results in l2 and l norm that match known results for special cases applying our results to random features we show an improvement of the number of random features needed to preserve the generalization guarantees for learning with lipshitz continuous losses

derf distinctive efficient robust features from the biological modeling of the p ganglion cells studies in neuroscience and biological vision have shown that the human retina has strong computational power and its information representation supports vision tasks on both ventral and dorsal pathways in this paper a new local image descriptor termed distinctive efficient robust features derf is derived by modeling the response and distribution properties of the parvocellular projecting ganglion cells in the primate retina derf features exponential scale distribution exponential grid structure and circularly symmetric function difference of gaussian dog used as a convolution kernel all of which are consistent with the characteristics of the ganglion cell array found in neurophysiology anatomy and biophysics in addition a new explanation for local descriptor design is presented from the perspective of wavelet tight frames dog is naturally a wavelet and the structure of the grid points array in our descriptor is closely related to the spatial sampling of wavelets the dog wavelet itself forms a frame and when we modulate the parameters of our descriptor to make the frame tighter the performance of the derf descriptor improves accordingly this is verified by designing a tight frame dog which leads to much better performance extensive experiments conducted in the image matching task on the multiview stereo correspondence data set demonstrate that derf outperforms state of the art methods for both hand crafted and learned descriptors while remaining robust and being much faster to compute

capacity bounds for the gaussian interference channel the capacity region of the two user gaussian interference channel ic is studied three classes of channels are considered weak one sided and mixed gaussian ics for the weak gaussian ic a new outer bound on the capacity region is obtained that outperforms previously known outer bounds the sum capacity for a certain range of channel parameters is derived for this range it is proved that using gaussian codebooks and treating interference as noise are optimal it is shown that when gaussian codebooks are used the full han kobayashi achievable rate region can be obtained by using the naive han kobayashi achievable scheme over three frequency bands equivalently three subspaces for the one sided gaussian ic an alternative proof for the sato s outer bound is presented we derive the full han kobayashi achievable rate region when gaussian codebooks are utilized for the mixed gaussian ic a new outer bound is obtained that outperforms previously known outer bounds for this case the sum capacity for the entire range of channel parameters is derived it is proved that the full han kobayashi achievable rate region using gaussian codebooks is equivalent to that of the one sided gaussian ic for a particular range of channel parameters

invariant scattering convolution networks a wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high frequency information for classification it cascades wavelet transform convolutions with nonlinear modulus and averaging operators the first network layer outputs sift type descriptors whereas the next layers provide complementary invariant information that improves classification the mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification a scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same fourier power spectrum state of the art classification results are obtained for handwritten digits and texture discrimination with a gaussian kernel svm and a generative pca classifier

a straight quantum wave guide with mixed dirichlet and neumann boundary conditions in uniform magnetic fields a straight quasi one dimensional dirichlet wave guide with a neumann window of length l on one or two confining surfaces is considered theoretically with and without perpendicular homogeneous magnetic field it is shown that for the field free case a bound state in the continuum bic for one neumann window exists for some critical lengths only while for the two neumann segments symmetrically located on the opposite walls due to the restored transverse symmetry of the system bics exist for the arbitrary l bound states lying below the fundamental propagation threshold of the dirichlet strip survive any strength of the uniform magnetic field and do not depend on its direction moreover an increasing field induces new bound states regularly arranged with the levels present at b 0 for two neumann windows strong magnetic fields lead to the degeneracy of the adjacent odd and even bound states with their energies almost equal to each other and to their corresponding counterpart for one neumann segment which is explained by mapping the problem onto the field free one or two purely attractive one dimensional quantum wells with field dependent depth miscellaneous magnetotransport characteristics of the structures are also considered in particular it is demonstrated that small fields applied to the channel with two neumann windows destroy bics by coupling them to the continuum states this is manifested in the conductance fermi energy dependence by fano resonances currents flowing in the wave guide are investigated too and it is shown that current density patterns near the resonances form vortices which change their chirality as energy sweeps through the resonant region generalizations to any other arbitrary combination of the boundary conditions are provided comparison with other structures such as window coupled dirichlet wave guides a bent strip or straight dirichlet channel with electrostatic impurity inside is performed

two birds and one stone gaussian interference channel with a shared out of band relay of limited rate the two user gaussian interference channel with a shared out of band relay is considered the relay observes a linear combination of the source signals and broadcasts a common message to the two destinations through a perfect link of fixed limited rate r0 bits per channel use the out of band nature of the relay is reflected by the fact that the common relay message does not interfere with the received signal at the two destinations a general achievable rate is established along with upper bounds on the capacity region for the gaussian case for r0 values below a certain threshold which depends on channel parameters in achievable rates asymptotically in regimes where joint a two for one gain is achievable by the capacity region of this channel is determined in this paper to within a constant gap of 1 95 bits we identify interference regimes where a two for one gain in achievable rates is possible for every bit relayed up to a constant approximation error instrumental to these results is a carefully designed quantize and forward type of relay strategy along with a joint decoding scheme employed at destination ends further we also study successive decoding strategies with optimal decoding order corresponding to the order at which common private and relay messages are decoded and identify interference regimes where with an optimal decoding order successive decoding may also achieve two for one gains similar to joint decoding yet in general successive decoding produces unbounded loss asymptotically when compared to joint decoding

group invariance stability to deformations and complexity of deep convolutional representations the success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals however a precise study of these properties and how they affect learning guarantees is still missing in this paper we consider deep convolutional representations of signals we study their invariance to translations and to more general groups of transformations their stability to the action of diffeomorphisms and their ability to preserve signal information this analysis is carried by introducing a multilayer kernel based on convolutional kernel networks and by studying the geometry induced by the kernel mapping we then characterize the corresponding reproducing kernel hilbert space rkhs showing that it contains a large class of convolutional neural networks with homogeneous activation functions this analysis allows us to separate data representation from learning and to provide a canonical measure of model complexity the rkhs norm which controls both stability and generalization of any learned model in addition to models in the constructed rkhs our stability analysis also applies to convolutional networks with generic activations such as rectified linear units and we discuss its relationship with recent generalization bounds based on spectral norms

computing large deformation metric mappings via geodesic flows of diffeomorphisms this paper examine the euler lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in dupuis et al 1998 and trouve 1995 in which two images i 0 i 1 are given and connected via the diffeomorphic change of coordinates i 0 1 i 1 where 1 is the end point at t 1 of curve t t 0 1 satisfying t v t t t 0 1 with 0 id the variational problem takes the form mathop arg text m in limits upsilon dot phi t upsilon t left dot phi right left int 0 1 left upsilon t right 2 text d t left i 0 circ phi 1 1 i 1 right l 2 2 right where v t v is an appropriate sobolev norm on the velocity field v t and the second term enforces matching of the images with l 2 representing the squared error norm in this paper we derive the euler lagrange equations characterizing the minimizing vector fields v t t 0 1 assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms we describe the implementation of the euler equations using semi lagrangian method of computing particle flows and show the solutions for various examples as well we compute the metric distance on several anatomical configurations as measured by 0 1 v t v dt on the geodesic shortest paths

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

local canonical correlation analysis for nonlinear common variables discovery in this paper we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high dimensional observations we present a metric based on local applications of canonical correlation analysis cca and incorporate it in a kernel based manifold learning technique we show that this metric discovers the hidden common variables underlying the multimodal observations by estimating the euclidean distance between them our approach can be viewed both as an extension of cca to a nonlinear setting as well as an extension of manifold learning to multiple data sets experimental results show that our method indeed discovers the common variables underlying high dimensional nonlinear observations without assuming prior rigid model assumptions

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

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

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

sound propagation in rigid bends a multimodal approach the sound propagation in a waveguide with bend of finite constant curvature is analyzed using multimodal decomposition two infinite first order differential equations are constructed for the pressure and velocity in the bend projected on the local transverse modes a riccati equation for the impedance matrix is then derived which can be numerically integrated after truncation at a sufficient number of modes an example of validation is considered and results show the accuracy of the method and its suitability for the formulation of radiation conditions reflection and transmission coefficients are also computed showing the importance of higher order mode generation at the junction between the bend and the straight ducts the case of varying cross section curved ducts is also considered using multimodal decomposition

gaussian z interference channel with a relay link achievability region and asymptotic sum capacity this paper studies a gaussian z interference channel with a rate limited digital relay link from one receiver to another achievable rate regions are derived based on a combination of a han kobayashi common private power splitting technique and either a compress and forward relay strategy or a decode and forward strategy for interference subtraction at the other end for the gaussian z interference channel with a digital link from the interference free receiver to the interfered receiver the capacity region is established in the strong interference regime an achievable rate region is established in the weak interference regime in the weak interference regime the decode and forward strategy is shown to be asymptotically sum capacity achieving in the high signal to noise ratio and high interference to noise ratio limit in this case each relay bit asymptotically improves the sum capacity by one bit for the gaussian z interference channel with a digital link from the interfered receiver to the interference free receiver the capacity region is established in the strong interference regime achievable rate regions are established in the moderately strong and weak interference regimes in addition the asymptotic sum capacity is established in the limit of a large relay link rate in this case the sum capacity improvement due to the digital link is bounded by half a bit when the interference link is weaker than a certain threshold but the sum capacity improvement becomes unbounded when the interference link is strong

boundary condition varying circle billiards and gratings the dirichlet singularity waves in a two dimensional domain with robin mixed boundary conditions that vary smoothly along the boundary exhibit unexpected phenomena if the variation includes a d point where the boundary condition is dirichlet vanishing wavefunction a variety of arguments indicate that the system is singular for a circle billiard the boundary condition fails to determine a discrete set of levels so the spectrum is continuous for a diffraction grating defined by periodically varying boundary conditions on the edge of a half plane the phase of a diffracted beam amplitude remains undetermined in both cases the wavefunction on the boundary has a singularity at a d point described by the polylogarithm function

feature learning via partial differential equation with applications to face recognition a novel partial differential equation method is proposed for feature learning the feature is discriminative and invariant under rotation translation and illumination the method is efficient in low resolution images and when the samples are few to our best knowledge this is the first work that applies pde to feature learning feature learning is a critical step in pattern recognition such as image classification however most of the existing methods cannot extract features that are discriminative and at the same time invariant under some transforms this limits the classification performance especially in the case of small training sets to address this issue in this paper we propose a novel partial differential equation pde based method for feature learning the feature learned by our pde is discriminative also translationally and rotationally invariant and robust to illumination variation to our best knowledge this is the first work that applies pde to feature learning and image recognition tasks specifically we model feature learning as an evolution process governed by a pde which is designed to be translationally and rotationally invariant and is learned via minimizing the training error hence extracts discriminative information from data after feature extraction we apply a linear classifier for classification we also propose an efficient algorithm that optimizes the whole framework our method is very effective when the training samples are few the experimental results of face recognition on the four benchmark face datasets show that the proposed method outperforms the state of the art feature learning methods in the case of low resolution images and when the training samples are limited

robin boundary value problems on arbitrary domains we develop a theory of generalised solutions for elliptic boundary value problems subject to robin boundary conditions on arbitrary domains which resembles in many ways that of the dirichlet problem in particular we establish lp lq estimates which turn out to be the best possible in that framework we also discuss consequences to the spectrum of robin boundary value problems finally we apply the theory to parabolic equations

deep scattering spectrum a scattering transform defines a locally translation invariant representation which is stable to time warping deformation it extends mfcc representations by computing modulation spectrum coefficients of multiple orders through cascades of wavelet convolutions and modulus operators second order scattering coefficients characterize transient phenomena such as attacks and amplitude modulation a frequency transposition invariant representation is obtained by applying a scattering transform along log frequency state the of art classification results are obtained for musical genre and phone classification on gtzan and timit databases respectively

riemannian curvature of deep neural networks we analyze deep neural networks using the theory of riemannian geometry and curvature the objective is to gain insight into how riemannian geometry can characterize and predict the trained behavior of neural networks we define a method for calculating riemann and ricci curvature tensors and ricci scalar curvature values for a trained neural net in such a way that the output classifier softmax values are related to the input transformations through the curvature equations we also measure these curvature tensors experimentally for different networks which are pretrained with stochastic gradient descent and offer a way of visualizing and understanding the measurements to gain insight into the effect curvature has on behavior the neural networks locally and possibly predict their behavior for different transformations of the test data we also analyze the effect of variation in depth of the neural networks as well as how it behaves for different choices of data set

manifold learning for latent variable inference in dynamical systems we study the inference of latent intrinsic variables of dynamical systems from output signal measurements the primary focus is the construction of an intrinsic distance between signal measurements which is independent of the measurement device this distance enables us to infer the latent intrinsic variables through the solution of an eigenvector problem with a laplace operator based on a kernel the signal geometry and its dynamics are represented with nonlinear observers an analysis of the properties of the observers that allow for accurate recovery of the latent variables is given and a way to test whether these properties are satisfied from the measurements is proposed scattering and window fourier transform observers are compared applications are shown on simulated data and on real intracranial electroencephalography eeg signals of epileptic patients recorded prior to seizures

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

feature based lucas kanade and active appearance models lucas kanade and active appearance models are among the most commonly used methods for image alignment and facial fitting respectively they both utilize nonlinear gradient descent which is usually applied on intensity values in this paper we propose the employment of highly descriptive densely sampled image features for both problems we show that the strategy of warping the multichannel dense feature image at each iteration is more beneficial than extracting features after warping the intensity image at each iteration motivated by this observation we demonstrate robust and accurate alignment and fitting performance using a variety of powerful feature descriptors especially with the employment of histograms of oriented gradient and scale invariant feature transform features our method significantly outperforms the current state of the art results on in the wild databases

localized mode evolution in a curved planar waveguide with combined dirichlet and neumann boundary conditions we present a theoretical study of a planar waveguide with a uniformly curved section opposite sides of the channel satisfy different boundary conditions it is shown that if the dirichlet condition is applied to the inner side of the strip and the neumann one to the outer wall then properties of such a system in many respects resemble those with the dirichlet requirements on both surfaces namely in both cases a propagation threshold for the curved section is smaller than its counterpart for the straight channel as a consequence a localized mode exists with its energy below the propagation threshold of the straight waveguide analysis of such states is presented as a function of the bend parameters for the transport in the fundamental mode an interaction of a quasibound level split off from the higher lying threshold with its degenerate continuum counterpart causes a dip in the transmission such a resonance is characterized by a location of its zero minimum e min and the half width gamma changing the bend angle and radius one varies e min and gamma in particular for some critical parameters of the bend it is possible to turn the half width to zero i e to eliminate the dip in the transmission this corresponds to the absence of the interaction between the split off level and the continuum and consequently to the formation of the true bound state in the continuum vortex structure of the currents flowing in the waveguide near the resonance is also shown to strongly resemble the analogous results for the dirichlet case it is pointed out that the properties of the waveguide with the neumann inner condition and the dirichlet outer one mimic the duct with the neumann requirements on the two sides since for both these cases the propagation threshold in the curved section is greater than in the straight channel

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

on lipschitz bounds of general convolutional neural networks many convolutional neural networks cnn s have a feed forward structure in this paper we model a general framework for analyzing the lipschitz bounds of cnn s and propose a linear program that estimates these bounds several cnn s including the scattering networks the alexnet and the googlenet are studied numerically in these practical numerical examples estimations of local lipschitz bounds are compared to these theoretical bounds based on the lipschitz bounds we next establish concentration inequalities for the output distribution with respect to a stationary random input signal the lipschitz bound is further used to perform nonlinear discriminant analysis that measures the separation between features of different classes

using basic image features for texture classification representing texture images statistically as histograms over a discrete vocabulary of local features has proven widely effective for texture classification tasks images are described locally by vectors of for example responses to some filter bank and a visual vocabulary is defined as a partition of this descriptor response space typically based on clustering in this paper we investigate the performance of an approach which represents textures as histograms over a visual vocabulary which is defined geometrically based on the basic image features of griffin and lillholm proc spie 6492 09 1 11 2007 rather than by clustering bifs provide a natural mathematical quantisation of a filter response space into qualitatively distinct types of local image structure we also extend our approach to deal with intra class variations in scale our algorithm is simple there is no need for a pre training step to learn a visual dictionary as in methods based on clustering and no tuning of parameters is required to deal with different datasets we have tested our implementation on three popular and challenging texture datasets and find that it produces consistently good classification results on each including what we believe to be the best reported for the kth tips and equal best reported for the uiuctex databases

an inverse eigenvalue problem for a general convex domain the underlying problem is to deduce the precise shape of a membrane from the complete knowledge of the eigenvalues i for the lapace operator a cf a ax in the x1x2 plane let d g r be a simply connected bounded domain with a smooth boundary ad let us suppose that the a are the eigenvalues of the impedance problem au k o in d

probabilistic inference of regularisation in non rigid registration a long standing issue in non rigid image registration is the choice of the level of regularisation regularisation is necessary to preserve the smoothness of the registration and penalise against unnecessary complexity the vast majority of existing registration methods use a fixed level of regularisation which is typically hand tuned by a user to provide nice results however the optimal level of regularisation will depend on the data which is being processed lower signal to noise ratios require higher regularisation to avoid registering image noise as well as features and different pairs of images require registrations of varying complexity depending on their anatomical similarity in this paper we present a probabilistic registration framework that infers the level of regularisation from the data an additional benefit of this proposed probabilistic framework is that estimates of the registration uncertainty are obtained this framework has been implemented using a free form deformation transformation model although it would be generically applicable to a range of transformation models we demonstrate our registration framework on the application of inter subject brain registration of healthy control subjects from the nirep database in our results we show that our framework appropriately adapts the level of regularisation in the presence of noise and that inferring regularisation on an individual basis leads to a reduction in model over fitting as measured by image folding while providing a similar level of overlap

random action of compact lie groups and minimax estimation of a mean pattern this paper considers the problem of estimating a mean pattern in the setting of grenander s pattern theory shape variability in a dataset of curves or images is modeled by the random action of elements in a compact lie group on an infinite dimensional space in the case of observations contaminated by an additive gaussian white noise it is shown that estimating a reference template in the setting of grenanders pattern theory falls into the category of deconvolution problems over lie groups to obtain this result we build an estimator of a mean pattern by using fourier deconvolution and harmonic analysis on compact lie groups in an asymptotic setting where the number of observed curves or images tends to infinity we derive upper and lower bounds for the minimax quadratic risk over sobolev balls this rate depends on the smoothness of the density of the random lie group elements representing shape variability in the data which makes a connection between estimating a mean pattern and standard deconvolution problems in nonparametric statistics

efficient svm training using low rank kernel representations svm training is a convex optimization problem which scales with the training set size rather than the feature space dimension while this is usually considered to be a desired quality in large scale problems it may cause training to be impractical the common techniques to handle this difficulty basically build a solution by solving a sequence of small scale subproblems our current effort is concentrated on the rank of the kernel matrix as a source for further enhancement of the training procedure we first show that for a low rank kernel matrix it is possible to design a better interior point method ipm in terms of storage requirements as well as computational complexity we then suggest an efficient use of a known factorization technique to approximate a given kernel matrix by a low rank matrix which in turn will be used to feed the optimizer finally we derive an upper bound on the change in the objective function value based on the approximation error and the number of active constraints support vectors this bound is general in the sense that it holds regardless of the approximation method

an inverse problem for the three dimensional multi connected vibrating membrane with robin boundary conditions this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t n 1exp t m n where m n n 1 are the eigenvalues of the negative laplacian 2 3 b 1 x b 2 in the x 1 x 2 x 3 space is studied for a general multiply connected bounded domain w in r 3 surrounded by simply connected bounded domains w j with smooth bounding surfaces s j j 1 n where a finite number of piecewise smooth robin boundary conditions on the piecewise smooth components s i i 1 k j 1 k j of the bounding surfaces s j are considered such that s j k j i 1 k j 1s i where k 0 0 some applications of q t for an ideal gas enclosed in the multiply connected bounded container w with robin boundary conditions are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the finite container w on the thermodynamic quantities of an ideal gas

sparse adaptive parameterization of variability in image ensembles this paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a hamiltonian flow of self interacting particles the proposed approach estimates a template image representative of a given image set an optimal set of control points that focuses on the most variable parts of the image and template to image registrations that quantify the variability within the image set the method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain the optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent the selection of the control points is done by adding a l 1 prior to the objective function which is optimized using the fista algorithm

intermittent process analysis with scattering moments scattering moments provide nonparametric models of random processes with stationary increments they are expected values of random variables computed with a nonexpansive operator obtained by iteratively applying wavelet transforms and modulus nonlinearities which preserves the variance first and second order scattering moments are shown to characterize intermittency and self similarity properties of multiscale processes scattering moments of poisson processes fractional brownian motions levy processes and multifractal random walks are shown to have characteristic decay the generalized method of simulated moments is applied to scattering moments to estimate data generating models numerical applications are shown on financial time series and on energy dissipation of turbulent flows

data representation using the weyl transform the weyl transform is introduced as a rich framework for data representation transform coefficients are connected to the walsh hadamard transform of multiscale autocorrelations and different forms of dyadic periodicity in a signal are shown to appear as different features in its weyl coefficients the weyl transform has a high degree of symmetry with respect to a large group of multiscale transformations which allows compact yet discriminative representations to be obtained by pooling coefficients the effectiveness of the weyl transform is demonstrated through the example of textured image classification

phase recovery maxcut and complex semidefinite programming phase retrieval seeks to recover a signal x in mathbb c p x c p from the amplitude a x a x of linear measurements ax in mathbb c n a x c n we cast the phase retrieval problem as a non convex quadratic program over a complex phase vector and formulate a tractable relaxation called phasecut similar to the classical maxcut semidefinite program we solve this problem using a provably convergent block coordinate descent algorithm whose structure is similar to that of the original greedy algorithm in gerchberg and saxton optik 35 237 246 1972 where each iteration is a matrix vector product numerical results show the performance of this approach over three different phase retrieval problems in comparison with greedy phase retrieval algorithms and matrix completion formulations

analysis of planar shapes using geodesic paths on shape spaces for analyzing shapes of planar closed curves we propose differential geometric representations of curves using their direction functions and curvature functions shapes are represented as elements of infinite dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces we use a fourier basis to represent tangents to the shape spaces and then use a gradient based shooting method to solve for the tangent that connects any two shapes via a geodesic using the surrey fish database we demonstrate some applications of this approach 1 interpolation and extrapolations of shape changes 2 clustering of objects according to their shapes 3 statistics on shape spaces and 4 bayesian extraction of shapes in low quality images

curved planar quantum wires with dirichlet and neumann boundary conditions we investigate the discrete spectrum of the hamiltonian describing a quantum particle living in the two dimensional curved strip we impose the dirichlet and neumann boundary conditions on opposite sides of the strip the existence of the discrete eigenvalue below the essential spectrum threshold depends on the sign of the total bending angle for the asymptotically straight strips

bound states in straight quantum waveguides with combined boundary conditions we investigate the discrete spectrum of the hamiltonian describing a quantum particle living in the two dimensional straight strip we impose the combined dirichlet and neumann boundary conditions on different parts of the boundary several statements on the existence or the absence of the discrete spectrum are compared for two models with combined boundary conditions examples of eigenfunctions and eigenvalues are computed numerically

a learning framework for age rank estimation based on face images with scattering transform this paper presents a cost sensitive ordinal hyperplanes ranking algorithm for human age estimation based on face images the proposed approach exploits relative order information among the age labels for rank prediction in our approach the age rank is obtained by aggregating a series of binary classification results where cost sensitivities among the labels are introduced to improve the aggregating performance in addition we give a theoretical analysis on designing the cost of individual binary classifier so that the misranking cost can be bounded by the total misclassification costs an efficient descriptor scattering transform which scatters the gabor coefficients and pooled with gaussian smoothing in multiple layers is evaluated for facial feature extraction we show that this descriptor is a generalization of conventional bioinspired features and is more effective for face based age inference experimental results demonstrate that our method outperforms the state of the art age estimation approaches

the radon cumulative distribution transform and its application to image classification invertible image representation methods transforms are routinely employed as low level image processing operations based on which feature extraction and recognition algorithms are developed most transforms in current use e g fourier wavelet and so on are linear transforms and by themselves are unable to substantially simplify the representation of image classes for classification here we describe a nonlinear invertible low level image processing transform based on combining the well known radon transform for image data and the 1d cumulative distribution transform proposed earlier we describe a few of the properties of this new transform and with both theoretical and experimental results show that it can often render certain problems linearly separable in a transform space

constructing diffeomorphic representations for the groupwise analysis of nonrigid registrations of medical images groupwise nonrigid registrations of medical images define dense correspondences across a set of images defined by a continuous deformation field that relates each target image in the group to some reference image these registrations can be automatic or based on the interpolation of a set of user defined landmarks but in both cases quantifying the normal and abnormal structural variation across the group of imaged structures implies analysis of the set of deformation fields we contend that the choice of representation of the deformation fields is an integral part of this analysis this paper presents methods for constructing a general class of multi dimensional diffeomorphic representations of deformations we demonstrate for the particular case of the polyharmonic clamped plate splines that these representations are suitable for the description of deformations of medical images in both two and three dimensions using a set of two dimensional annotated mri brain slices and a set of three dimensional segmented hippocampi with optimized correspondences the class of diffeomorphic representations also defines a non euclidean metric on the space of patterns and for the case of compactly supported deformations on the corresponding diffeomorphism group in an experimental study we show that this non euclidean metric is superior to the usual ad hoc euclidean metrics in that it enables more accurate classification of legal and illegal variations

computing average shaped tissue probability templates this note presents a framework for generating tissue probability maps that represent the average shape of a number of subjects brain images the procedure is formulated as finding maximum a posteriori estimates within a probabilistic generative model estimating the parameters involves alternating between estimating the deformations that match tissue class images of individual subjects to template and updating the template according to the latest estimates of the deformations a multinomial matching criterion is used such that multiple tissue class images e g grey and white matter are registered simultaneously with the current template estimate in order to generalise the resulting template to a broader range of subjects a template blurriness prior is included within the model

group invariant scattering this paper constructs translation invariant operators on l 2 r d which are lipschitz continuous to the action of diffeomorphisms a scattering propagator is a path ordered product of nonlinear and noncommuting operators each of which computes the modulus of a wavelet transform a local integration defines a windowed scattering transform which is proved to be lipschitz continuous to the action of c 2 diffeomorphisms as the window size increases it converges to a wavelet scattering transform that is translation invariant scattering coefficients also provide representations of stationary processes expected values depend upon high order moments and can discriminate processes having the same power spectrum scattering operators are extended on l 2 g where g is a compact lie group and are invariant under the action of g combining a scattering on l 2 r d and on l 2 so d defines a translation and rotation invariant scattering on l 2 r d 2012 wiley periodicals inc

template matching via densities on the roto translation group we propose a template matching method for the detection of 2d image objects that are characterized by orientation patterns our method is based on data representations via orientation scores which are functions on the space of positions and orientations and which are obtained via a wavelet type transform this new representation allows us to detect orientation patterns in an intuitive and direct way namely via cross correlations additionally we propose a generalized linear regression framework for the construction of suitable templates using smoothing splines here it is important to recognize a curved geometry on the position orientation domain which we identify with the lie group se 2 the roto translation group templates are then optimized in a b spline basis and smoothness is defined with respect to the curved geometry we achieve state of the art results on three different applications detection of the optic nerve head in the retina 99 83 percent success rate on 1 737 images of the fovea in the retina 99 32 percent success rate on 1 616 images and of the pupil in regular camera images 95 86 percent on 1 521 images the high performance is due to inclusion of both intensity and orientation features with effective geometric priors in the template matching moreover our method is fast due to a cross correlation based matching approach

bound states in curved quantum waveguides a free quantum particle living on a curved planar strip of a fixed width d with dirichlet boundary conditions is studied it can serve as a model for electrons in thin films on a cylinder type substrate or in a curved quantum wire assuming that the boundary of is infinitely smooth and its curvature decays fast enough at infinity it is proved that a bound state with energy below the first transversal mode exists for all sufficiently small d a lower bound on the critical width is obtained using the birman schwinger technique

semiclassical quantization of billiards with mixed boundary conditions the semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived the parametric dependence of the spectrum on the boundary condition is shown to be a very useful diagnostic tool in the semiclassical analysis of the spectrum of billiards it is also used to check in detail some recently proposed parametric spectral statistics the methods are illustrated in the analysis of the spectrum of the sinai billiard and its parametric dependence on the boundary condition on the dispersing arc