maximum likelihood estimation of functionals of discrete distributions we consider the problem of estimating functionals of discrete distributions and focus on a tight up to universal multiplicative constants for each specific functional nonasymptotic analysis of the worst case squared error risk of widely used estimators we apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional namely their bias we explicitly characterize the worst case squared error risk incurred by the maximum likelihood estimator mle in estimating the shannon entropy h p sum i 1 s p i ln p i and the power sum f alpha p sum i 1 s p i alpha alpha 0 up to universal multiplicative constants for each fixed functional for any alphabet size s leq infty and sample size n for which the risk may vanish as a corollary for shannon entropy estimation we show that it is necessary and sufficient to have n gg s observations for the mle to be consistent in addition we establish that it is necessary and sufficient to consider n gg s 1 alpha samples for the mle to consistently estimate f alpha p 0 the minimax rate optimal estimators for both problems require s ln s and s 1 alpha ln s samples which implies that the mle has a strictly sub optimal sample complexity when 1 we show that the worst case squared error rate of convergence for the mle is n 2 alpha 1 for infinite alphabet size while the minimax squared error rate is n ln n 2 alpha 1 when alpha geq 3 2 the mle achieves the minimax optimal rate n 1 regardless of the alphabet size as an application of the general theory we analyze the dirichlet prior smoothing techniques for shannon entropy estimation in this context one approach is to plug in the dirichlet prior smoothed distribution into the entropy functional while the other one is to calculate the bayes estimator for entropy under the dirichlet prior for squared error which is the conditional expectation we show that in general such estimators do not improve over the maximum likelihood estimator no matter how we tune the parameters in the dirichlet prior this approach cannot achieve the minimax rates in entropy estimation the performance of the minimax rate optimal estimator with n samples is essentially at least as good as that of dirichlet smoothed entropy estimators with n ln n samples

co registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization diffusion mri provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain echo planar imaging epi sequences which are frequently used for acquisition of diffusion images are sensitive to inhomogeneities in the primary magnetic b0 field that cause localized distortions in the reconstructed images we describe and evaluate a new method for correction of susceptibility induced distortion in diffusion images in the absence of an accurate b0 fieldmap in our method the distortion field is estimated using a constrained non rigid registration between an undistorted t1 weighted anatomical image and one of the distorted epi images from diffusion acquisition our registration framework is based on a new approach inversion inverse contrast normalization for very simple registration which exploits the inverted contrast relationship between t1 and t2 weighted brain images to define a simple and robust similarity measure we also describe how inversion can be used for rigid alignment of diffusion images and t1 weighted anatomical images our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters compared to other methods inversion shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non rigid distortion correction

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

using spanning graphs for efficient image registration we provide a detailed analysis of the use of minimal spanning graphs as an alignment method for registering multimodal images this yields an efficient graph theoretic algorithm that for the first time jointly estimates both an alignment measure and a viable descent direction with respect to a parameterized class of spatial transformations we also show how prior information about the interimage modality relationship from prealigned image pairs can be incorporated into the graph based algorithm a comparison of the graph theoretic alignment measure is provided with more traditional measures based on plug in entropy estimators this highlights previously unrecognized similarities between these two registration methods our analysis gives additional insight into the tradeoffs the graph based algorithm is making and how these will manifest themselves in the registration algorithm s performance

retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations we propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena whose diffusion exponent varies with time and which correspondingly cannot be viewed as self affine random processes possessing a unique hurst exponent we prove the positivity of the solutions of the proposed equations and establish their relation to the continuous time random walk theory we show that the distributed order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the wiener process and whose diffusion exponent decreases in time retarding subdiffusion this process may lead to superslow diffusion with the mean square displacement growing logarithmically in time we also demonstrate that the distributed order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time accelerating superdiffusion

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

the hp local discontinuous galerkin method for low frequency time harmonic maxwell equations the local discontinuous galerkin method for the numerical approximation of the time harmonic maxwell equations in a low frequency regime is introduced and analyzed topologically nontrivial domains and heterogeneous media are considered containing both conducting and insulating materials the presented method involves discontinuous galerkin discretizations of the curl curl and grad div operators derived by introducing suitable auxiliary variables and so called numerical fluxes an hp analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained

detecting inclusions in electrical impedance tomography without reference measurements we develop a new variant of the factorization method that can be used to detect inclusions in electrical impedance tomography from either absolute current to voltage measurements at a single nonzero frequency or from frequency difference measurements this eliminates the need for numerically simulated reference measurements at an inclusion free body and thus greatly improves the method s robustness against forward modeling errors e g in the assumed body s shape

a finite element method with lagrange multipliers for low frequency harmonic maxwell equations the aim of this paper is to analyze a finite element method to solve the low frequency harmonic maxwell equations in a bounded domain containing conductors and dielectrics this system of partial differential equations is a model for the so called eddy currents problem after writing this problem in terms of the magnetic field it is discretized by nedelec edge finite elements on a tetrahedral mesh error estimates are easily obtained if the curl free condition is imposed on the elements in the dielectric domain then the curl free condition is imposed at a discrete level by introducing a piecewise linear multivalued potential the resulting problem is shown to be a discrete version of other continuous formulation in which the magnetic field in the dielectric part of the domain has been replaced by a magnetic potential moreover this approach leads to an important saving in computational effort problems related to the topology are also considered in that the possibility of having a nonsimply connected dielectric domain is taken into account implementation issues are discussed including an amenable procedure to impose the boundary conditions by means of a lagrange multiplier finally the method is applied to solve a three dimensional model problem a cylindrical electrode surrounded by dielectric

efficient registration of nonrigid 3 d bodies we present a novel method to perform an accurate registration of 3 d nonrigid bodies by using phase shift properties of the dual tree complex wavelet transform dt bbcwt since the phases of dt bbcwt coefficients change approximately linearly with the amount of feature displacement in the spatial domain motion can be estimated using the phase information from these coefficients the motion estimation is performed iteratively first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field we use a parametric affine model to describe the motion where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations from the estimated affine parameters the motion field between the sensed and the reference data sets can be generated and the sensed data set then can be shifted and interpolated spatially to align with the reference datafeature displacement set

some solutions to the space fractional schrodinger equation using momentum representation method the space fractional schrodinger equation with linear potential delta function potential and coulomb potential is studied under momentum representation using fourier transformation by use of mellin transform and its inverse transform we obtain the energy levels and wave functions expressed in h function for a particle in linear potential field the wave function expressed also by the h function and the unique energy level of the bound state for the particle of even parity state in delta function potential well which is proved to have no action on the particle of odd parity state is also obtained the integral form of the wave functions for a particle in coulomb potential field is shown and the corresponding energy levels which have been discussed in laskin s paper phys rev e 66 056108 2002 are proved to satisfy an equality of infinite limit of the h function all of these results contain the ones of the standard quantum mechanics as their special cases

a frequency domain technique for range data registration this work introduces an original method for registering pairs of 3d views consisting of range data sets which operates in the frequency domain the fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters our algorithm exploits this well known property by suggesting a three step procedure the rotation parameters are estimated by the first two steps through convenient representations and projections of the fourier transforms magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation the performance of the algorithm which is well suited for unsupervised registration is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3d rigid motion are achievable our algorithm can be used as a prealignment tool for more accurate space domain registration techniques like the icp algorithm

audio visual group recognition using diffusion maps data fusion is a natural and common approach to recovering the state of physical systems but the dissimilar appearance of different sensors remains a fundamental obstacle we propose a unified embedding scheme for multisensory data based on the spectral diffusion framework which addresses this issue our scheme is purely data driven and assumes no a priori statistical or deterministic models of the data sources to extract the underlying structure we first embed separately each input channel the resultant structures are then combined in diffusion coordinates in particular as different sensors sample similar phenomena with different sampling densities we apply the density invariant laplace beltrami embedding this is a fundamental issue in multisensor acquisition and processing overlooked in prior approaches we extend previous work on group recognition and suggest a novel approach to the selection of diffusion coordinates to verify our approach we demonstrate performance improvements in audio visual speech recognition

exact solutions of fractional schrodinger like equation with a nonlocal term we study the time space fractional schrodinger equation with a nonlocal potential by the method of fourier transform and laplace transform the green function and hence the wave function is expressed in terms of h functions graphical analysis demonstrates that the influence of both the space fractal parameter and the nonlocal parameter on the fractional quantum system is strong indeed the nonlocal potential may act similar to a fractional spatial derivative as well as fractional time derivative

the coulomb gauged vector potential formulation for the eddy current problem in general geometry well posedness and numerical approximation in this paper we prove that in a general geometric situation the coulomb gauged vector potential formulation of the eddy current problem for the time harmonic maxwell equations is well posed i e its solution exists and is unique moreover a quasi optimal error estimate for its finite element approximation with nodal elements is proved to illustrate the performances of the finite element algorithm some numerical results are also presented

detecting interfaces in a parabolic elliptic problem from surface measurements assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic elliptic interface problem in this work we aim to detect these interfaces from thermal measurements on the surface of the body we deduce an equivalent variational formulation for the parabolic elliptic problem and give a new proof of the unique solvability based on lions s projection lemma for the case that the heat conductivity is higher inside the inclusions we develop an adaptation of the factorization method to this time dependent problem in particular this shows that the locations of the interfaces are uniquely determined by boundary measurements the method also yields to a numerical algorithm to recover the inclusions and thus the interfaces we demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method and finally we present some numerical results for the inverse problem

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

one dimensional mapping for estimating projective transformations in this paper the 1 d mapping is studied for estimating a general projective transformation between images first a ray model of image patches is proposed to convert a complex projective deformation of a patch in the cartesian space into two simple rigid shifts of radial lines in the log polar inverse polar space to capture these shifts via direct search two types of radial image line matching viz 1 d log polar mapping and 1 d inverse polar mapping are formally defined also the unique features of these shifts are analyzed then a novel two step mathematical framework is devised for transformation estimation in the first step the 1 d log polar mapping is applied to estimating four affine parameters via two alternative methods for simulated real images in the second step the 1 d inverse polar mapping is applied to estimating two projective parameters by a direct search combined with the two step line matching two translational parameters are also determined finally the performance of the framework is evaluated first in estimating a variety of projective transformations by comparing the estimates with their ground truths and between the two proposed methods and second in registering a wide range of challenging image pairs by comparing with a state of the art feature based method

image registration using the walsh transform this paper presents a new algorithm which can be used to register images of the same or different modalities e g images with multiple channels such as x rays temperature or elevation or simply images of different spectral bands in particular a correlation based scheme is used but instead of gray values it correlates numbers formulated by different combinations of the extracted local walsh coefficients of the images each image patch is expanded in terms of walsh basis functions each walsh basis function can be thought of as measuring a different aspect of local structure e g horizontal edge corner etc the coefficients of the expansion therefore can be thought of as dense local features estimating at each point the degree of presence of for example a horizontal edge a corner with contrast of a certain type etc these coefficients are normalized and used as digits in a chosen number system which allows one to create a unique number for each type of local structure the choice of the basis of the number system allows one to give different emphasis to different types of local feature e g corners versus edges and thus the method we present forms a unified framework in terms of which several feature matching methods may be interpreted the algorithm is compared with wavelet and contour based approaches using simulated and real images the two images are assumed to differ from each other by a rotation and a translation only

well posedness of two nonrigid multimodal image registration methods image registration methods may be designed as solutions of minimization problems on a set of geometric deformations in the nonrigid case solving these problems often means computing the steady state of a system of evolution equations involving the gradient of the error criterion defined from the euler lagrange equations of the corresponding minimization problem the well posedness of the registration methodrequires showing the existence of a solution to the minimization problem as well as that of a stable solution of the evolution equations derived from it we provide such proofs in the case where the error criterion is derived from two different statistical similarity measures global mutual information and local cross covariance we also describe our numerical implementation for solving the corresponding evolution equations and show examples of registrations of real 2d and 3d images achieved with these algorithms the proofs are quite general and can be applied to most of the known nonrigid image

multimodal image registration using a variational approach this paper presents an approach to obtain a deformation which matches two images acquired from different medical imaging modalities this problem arises in the investigation of human brains two distance functionals for the images are proposed with different pros and cons these functionals are to be minimized we add a smoothing term to the minimization problem which retains certain desired elastic features in the solution at each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration furthermore we use a multiresolution minimization approach to obtain a suitable initial guess finally we present some experimental results for registration problems of synthetic images and for a real computer tomography ct magnetic resonance imaging mri registration

a singular field method for the solution of maxwell s equations in polyhedral domains it is well known that in the case of a regular domain the solution of the time harmonic maxwell s equations allows a discretization by means of nodal finite elements this is achieved by solving a regularized problem similar to the vector helmholtz equation the present paper deals with the same problem in the case of a nonconvex polyhedron it is shown that a nodal finite element method does not approximate in general the solution to maxwell s equations but actually the solution to a neighboring variational problem involving a different function space indeed the solution to maxwell s equations presents singularities near the edges and corners of the domain that cannot be approximated by lagrange finite elements a new method is proposed involving the decomposition of the solution field into a regular part that can be treated numerically by nodal finite elements and a singular part that has to be taken into account explicitly this singular field method is presented in various situations such as electri

nonlinear registration using variational principle for mutual information we extend the multimodal image registration method described in alexander and summers fast registration algorithm using a variational principle for mutual information proc spie int soc opt eng 5032 2003 1053 1063 to nonlinear registration a variational principle maximizing mutual information leads to an euler lagrange el equation for the displacement field represented here in a basis of cubic b spline functions a cost function is constructed from the sum of squares of the residuals of the el equation at a subset of pixels where the magnitude of the spatial gradient of intensity exceeds a user chosen threshold the unknown coefficients in the displacement field representation are evaluated using a levenberg marquardt minimization procedure the proposed method was successfully applied to several image pairs of the same and different modalities and an artificially constructed series of images containing nonlinear distortions and noise

image registration by super curves we solve the 2 d affine image registration problem by curve matching and alignment our approach starts with a super curve which is formed by superimposing two affine related curves in one coordinate system we use b spline fusion technique to find a single b spline approximation of the super curve and a registration between the two curves simultaneously this approach achieves superior accuracy and efficiency in curve matching and alignment we then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps which are affine invariant the combination of edge detection and curve alignment lead to accurate image registration

motion estimation based on mutual information and adaptive multi scale thresholding this paper proposes a new method of calculating a matching metric for motion estimation the proposed method splits the information in the source images into multiple scale and orientation subbands reduces the subband values to a binary representation via an adaptive thresholding algorithm and uses mutual information to model the similarity of corresponding square windows in each image a moving window strategy is applied to recover a dense estimated motion field whose properties are explored the proposed matching metric is a sum of mutual information scores across space scale and orientation this facilitates the exploitation of information diversity in the source images experimental comparisons are performed amongst several related approaches revealing that the proposed matching metric is better able to exploit information diversity generating more accurate motion fields

coupling scalar and vector potentials on nonmatching grids for eddy currents in a moving conductor the t formulation of the magnetic field has been introduced in many papers for the approximation of the magnetic quantities modelled by the eddy current equations this decomposition allows to use a scalar function in the main part of the computational domain reducing the use of vector quantities to the conducting parts we propose to approximate these two quantities on nonmatching grids so as to be able to tackle a problem where the conducting part can move in the global domain the connection between the two grids is managed with mortar element techniques

image comparison by compound disjoint information with applications to perceptual visual quality assessment image registration and tracking in this paper we study normalized disjoint information as a metric for image comparison and its applications to perceptual image quality assessment image registration and video tracking disjoint information is the joint entropy of random variables excluding the mutual information this measure of statistical dependence and information redundancy satisfies more rigorous metric conditions than mutual information including self similarity minimality symmetry and triangle inequality it is applicable to two or more random variables and can be computed by vector histogramming vector parzen window density approximation and upper bound approximation involving fewer variables we show such a theoretic advantage does have implications in practice in the domain of digital image and video multiple visual features are extracted and normalized compound disjoint information is derived from a set of marginal densities of the image distributions thus enriching the vocabulary of content representation the proposed metric matching functions are applied to several domain applications to demonstrate their efficacy

shape from texture estimation isotropy and moments a theory is proposed for the interpretation of 3d textures with oriented elements it builds on two previous theories a statistical one due to witkin and kanatani s buffon transform we show that the statistical estimation of orientation of a textured plane is one of a general family of optimal backprojection problems which also includes maximal compactness general uniqueness and convergence results are obtained for an efficient algorithm employing second moment feedback this framework greatly enhances the usefulness of surface orientation estimation for texture in two ways first an error distribution is derived for the estimator and this is crucial for integration of shape information second hypotheses about intrinsic texture statistics can be verified by a 2 test which if failed warns that the orientation estimator is not to be believed finally it is argued that these results suggest a general moment tensor approach to analysis of 3d texture

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

a unified variational formulation for the parabolic elliptic eddy current equations transient excitation currents generate electromagnetic fields which in turn induce electric currents in proximal conductors for slowly varying fields this can be described by the eddy current equations which are obtained by neglecting the dielectric displacement currents in maxwell s equations the eddy current equations are of parabolic elliptic type in insulating regions the field instantaneously adapts to the excitation quasistationary elliptic behavior while in conducting regions this adaptation takes some time due to the induced eddy currents parabolic behavior for fixed conductivity the equations are well studied however little rigorous mathematical results are known for the solution s dependence on the conductivity in particular for the solution s sensitivity with respect to the equation changing from elliptic to parabolic type in this work we derive a new unified variational formulation for the eddy current equations that is uniformly coercive with respect to the conductivity

numerical solution of eddy current problems in bounded domains using realistic boundary conditions abstract the aim of this paper is to analyze a finite element method to solve the low frequency harmonic maxwell equations in a bounded domain containing conductors and dielectrics and using realistic boundary conditions in that they can be easily measured these equations provide a model for the so called eddy currents the problem is formulated in terms of the magnetic field this formulation is discretized by using nedelec edge finite elements on a tetrahedral mesh error estimates are easily obtained when the curl free condition is imposed explicitly on the elements in the dielectric domain a multivalued magnetic scalar potential is introduced then to impose this curl free condition the discrete counterpart of this formulation leads to an important saving in computational effort problems related to the topology are also considered more precisely the possibility of having a non simply connected dielectric domain is taken into account finally the method is applied to solve two three dimensional model problems a test with a known analytical solution and the computation of the electromagnetic field in a metallurgical arc furnace

time dependent schrodinger like equation with nonlocal term we investigate a time dependent schrodinger like equation in presence of a nonlocal term by using the method of variable separation and the green function approach we analyze the green function for different forms of the memory kernel and the nonlocal term results for delta potential energy function are presented distributed order memory kernels are also considered and the asymptotic behaviors of the green function are derived by using tauberian theorem the obtained results for the green function for the considered schrodinger like equation may be transformed to those for the probability distribution function of a diffusion like equation with memory kernel and can be used to explain various anomalous diffusive behaviors

the fractional finite hankel transform and its applications in fractal space in the present work a generalized finite hankel transform is derived which is useful in solving equations in fractal dimension df and involving a fractal diffusion coefficient d0r the corresponding inversion formula is established and some properties are given then the transform is successfully used to solve a class of time fractional diffusion equations in fractional spatial dimension with an absorbent term and schrodinger equation in fractional dimensional space green s functions and exact wave function of the above problems are found

time dependent solutions for a fractional schrodinger equation with delta potentials we investigate for an arbitrary initial condition the time dependent solutions for a fractional schrodinger equation in the presence of delta potentials by using the green function approach the solutions obtained show an anomalous spreading asymptotically characterized by a power law behavior which is governed by the order of the fractional spatial operator present in the schrodinger equation

fictitious domain methods for the numerical solution of two dimensional scattering problems fictitious domain methods for the numerical solution of two dimensional scattering problems are considered the original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary first order second order and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries the finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes and the discrete equations are solved with fictitious domain methods a special finite element method using nonmatching meshes is considered this method uses the macro hybrid formulation based on domain decomposition to couple polar and cartesian coordinate systems a special preconditioner based on fictitious domains is introduced for the arising algebraic saddle point system such that the subspace of constraints becomes invariant with respect to the preconditioned iterative procedure the performance of the new method is compared to the fictitious domain methods both with respect to accuracy and computational cost

rapid elastic image registration for 3 d ultrasound a subvolume based algorithm for elastic ultrasound registration sure was developed and evaluated designed primarily to improve spatial resolution in three dimensional compound imaging the algorithm registers individual image volumes nonlinearly before combination into compound volumes sure works in one or two stages optionally using miami fuse spl copy software first to determine a global affine registration before iteratively dividing the volume into subvolumes and computing local rigid registrations in the second stage connectivity of the entire volume is ensured by global interpolation using thin plate splines after each iteration the performance of sure was quantified in 20 synthetically deformed in vivo ultrasound volumes and in two phantom scans one of which was distorted at acquisition by placing an aberrating layer in the sound path the aberrating layer was designed to induce beam aberrations reported for the female breast synthetic deformations of 1 5 2 5 mm were reduced by over 85 when sure was applied to register the distorted image volumes with the original ones registration times were below 5 min on a 500 mhz cpu for an average data set size of 13mb in the aberrated phantom scans sure reduced the average deformation between the two volumes from 1 01 to 0 30mm this was a statistically significant p 0 01 improvement over rigid and affine registration transformations which produced reductions to 0 59 and 0 50 mm respectively

parameter estimation for the fractional schrodinger equation using bayesian method in this paper the fractional schrodinger equation is studied the bayesian method is put forward to estimate some relevant parameters of the equation results show that the estimated values can fit well with the exact solution the varying initial values and maximum iterations have little effect on the estimated results it indicates that the bayesian method is efficient for the multi parameter estimation for the fractional schrodinger equation this method can also be used to estimate parameters for the fractional schrodinger equation in other potential field

the time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems abstract in this paper a time fractional fourier law is obtained from fractional calculus according to the fractional fourier law a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built the fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases in addition we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized h function using integral transformation methods the fractional heat conduction equation in the case 0 1 interpolates the standard heat conduction equation 1 and the localized heat conduction equation 0 finally numerical results are presented graphically for various values of order of fractional derivative

multisensor image registration by feature consensus abstract this paper presents an approach for registering images obtained using different sensors viewpoints or lighting conditions this approach does not require feature correspondence or area correlation the geometric transformation between the images is reparametrized into a sequence of elementary stages at each stage a single transformation parameter is estimated using a feature consensus mechanism wherein the value of the parameter that is maximally consistent with all possible feature pairings is determined the concepts of parameter observability and separability are introduced to guide the choice of features attributes and transformation parameters experimental results on real data are provided

time fractional schrodinger equation the schrodinger equation is considered with the first order time derivative changed to a caputo fractional derivative the time fractional schrodinger equation the resulting hamiltonian is found to be non hermitian and nonlocal in time the resulting wave functions are thus not invariant under time reversal the time fractional schrodinger equation is solved for a free particle and for a potential well probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative new identities for the mittag leffler function are also found and presented in an appendix

a model based on local graphs for colour images and its application for gaussian noise smoothing in this paper a new model for processing colour images is presented a graph is built for each image pixel taking into account some constraints on links each pixel is characterized depending on the features of its related graph which allows to process it appropriately as an example we provide a characterization of each pixel based on the link cardinality of its connected component this feature enables us to properly distinguish flat image regions respect to edge and detail regions according to this we have designed a hybrid filter for colour image smoothing it combines a filter able to properly process flat image regions with another one that is more appropriate for details and texture experimental results show that our model performs appropriately we also see that our proposed filter is competitive with respect to state of the art methods it is close closer to the corresponding optimal switching filter respect to other analogous hybrid method

alignment using distributions of local geometric properties we describe a framework for aligning images without needing to establish explicit feature correspondences we assume that the geometry between the two images can be adequately described by an affine transformation and develop a framework that uses the statistical distribution of geometric properties of image contours to estimate the relevant transformation parameters the estimates obtained using the proposed method are robust to illumination conditions sensor characteristics etc since image contours are relatively invariant to these changes moreover the distributional nature of our method alleviates some of the common problems due to contour fragmentation occlusion clutter etc we provide empirical evidence of the accuracy and robustness of our algorithm finally we demonstrate our method on both real and synthetic images including multisensor image pairs

evaluation of optimization methods for nonrigid medical image registration using mutual information and b splines a popular technique for nonrigid registration of medical images is based on the maximization of their mutual information in combination with a deformation field parameterized by cubic b splines the coordinate mapping that relates the two images is found using an iterative optimization procedure this work compares the performance of eight optimization methods gradient descent with two different step size selection algorithms quasi newton nonlinear conjugate gradient kiefer wolfowitz simultaneous perturbation robbins monro and evolution strategy special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives the optimization methods are tested on manually deformed ct images of the heart on follow up ct chest scans and on mr scans of the prostate acquired using a bffe tl and t2 protocol registration accuracy is assessed by computing the overlap of segmented edges precision and convergence properties are studied by comparing deformation fields the results show that the robbins monro method is the best choice in most applications with this approach the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image randomly selected in every iteration to compute the derivative of the mutual information from the other methods the quasi newton and the nonlinear conjugate gradient method achieve a slightly higher precision at the price of larger computation times

matching by tone mapping photometric invariant template matching a fast pattern matching scheme termed matching by tone mapping mtm is introduced which allows matching under nonlinear tone mappings we show that when tone mapping is approximated by a piecewise constant linear function a fast computational scheme is possible requiring computational time similar to the fast implementation of normalized cross correlation ncc in fact the mtm measure can be viewed as a generalization of the ncc for nonlinear mappings and actually reduces to ncc when mappings are restricted to be linear we empirically show that the mtm is highly discriminative and robust to noise with comparable performance capability to that of the well performing mutual information but on par with ncc in terms of computation time

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

parametric estimation of affine deformations of planar shapes we consider the estimation of affine transformations aligning a known 2d shape and its distorted observation the classical way to solve this registration problem is to find correspondences between the shapes and then compute the transformation parameters from these landmarks here we propose a novel approach where the exact transformation is obtained as the solution of a polynomial system of equations the method has been tested on synthetic as well as on real images and its robustness in the presence of segmentation errors and additive geometric noise has also been demonstrated we have successfully applied the method for the registration of hip prosthesis x ray images the advantage of the proposed solution is that it is fast easy to implement has linear time complexity works without established correspondences and provides an exact solution regardless of the magnitude of transformation

information theoretic matching of two point sets this paper describes the theoretic roadmap of least relative entropy matching of two point sets the novel feature is to align two point sets without needing to establish explicit point correspondences the recovery of transformational geometry is achieved using a mixture of principal axes registrations whose parameters are estimated by minimizing the relative entropy between the two point distributions and using the expectation maximization algorithm we give evidence of the optimality of the method and we then evaluate the algorithm s performance in both rigid and nonrigid image registration cases

formulation of the eddy current problem in multiply connected regions in terms of h in this paper various formulations for the eddy current problem are presented the formulations are based on solving directly for the magnetic field h and they differ from each other mainly by how the field on the boundary is treated the electromagnetic problem is studied in connection with the fivefold decomposition of the space of square integrable vector fields within a bounded region this provides us with numerical approaches with clear signposts about how to solve the eddy current problem in multiply connected domains besides the fivefold decomposition another essential tool in our approach is whitney elements as they provide the structure needed to retain consistency between the continuous and discrete problems the paper demonstrates the usefulness of these mathematical tools in solving electromagnetic field problems 1998 john wiley sons ltd

fractional time quantum dynamics application of the fractional calculus to quantum processes is presented in particular the quantum dynamics is considered in the framework of the fractional time schr odinger equation se which differs from the standard se by the fractional time derivative ensuremath partial ensuremath partial t ensuremath rightarrow ensuremath partial ensuremath alpha ensuremath partial t ensuremath alpha it is shown that for ensuremath alpha 1 2 the fractional se is isospectral to a comb model an analytical expression for the green s functions of the systems are obtained the semiclassical limit is discussed

robust matching cost function for stereo correspondence using matching by tone mapping and adaptive orthogonal integral image real world stereo images are inevitably affected by radiometric differences including variations in exposure vignetting lighting and noise stereo images with severe radiometric distortion can have large radiometric differences and include locally nonlinear changes in this paper we first introduce an adaptive orthogonal integral image which is an improved version of an orthogonal integral image after that based on matching by tone mapping and the adaptive orthogonal integral image we propose a robust and accurate matching cost function that can tolerate locally nonlinear intensity distortion by using the adaptive orthogonal integral image the proposed matching cost function can adaptively construct different support regions of arbitrary shapes and sizes for different pixels in the reference image so it can operate robustly within object boundaries furthermore we develop techniques to automatically estimate the values of the parameters of our proposed function we conduct experiments using the proposed matching cost function and compare it with functions employing the census transform supporting local binary pattern and adaptive normalized cross correlation as well as a mutual information based matching cost function using different stereo data sets by using the adaptive orthogonal integral image the proposed matching cost function reduces the error from 21 51 to 15 73 in the middlebury data set and from 15 9 to 10 85 in the kitti data set as compared with using the orthogonal integral image the experimental results indicate that the proposed matching cost function is superior to the state of the art matching cost functions under radiometric variation

a linear discriminant analysis method based on mutual information maximization we present a new linear discriminant analysis method based on information theory where the mutual information between linearly transformed input data and the class labels is maximized first we introduce a kernel based estimate of mutual information with a variable kernel size furthermore we devise a learning algorithm that maximizes the mutual information w r t the linear transformation two experiments are conducted the first one uses a toy problem to visualize and compare the transformation vectors in the original input space the second one evaluates the performance of the method for classification by employing cross validation tests on four datasets from the uci repository various classifiers are investigated our results show that this method can significantly boost class separability over conventional methods especially for nonlinear classification

fractional schrodinger equation with noninteger dimensions the spatial and time dependent solutions of the schrodinger equation incorporating the fractional time derivative of distributed order and extending the spatial operator to noninteger dimensions are investigated they are obtained by using the green function approach in two situations the free case and in the presence of a harmonic potential the results obtained show an anomalous spreading of the wave packet which may be related to an anomalous diffusion process

time fractional schrodinger equation fox s h functions and the effective potential after introducing the formalism of the general space and time fractional schrodinger equation we concentrate on the time fractional schrodinger equation and present new results via the elegant language of fox s h functions we show that the general time dependent part of the wave function for the separable solutions of the time fractional schrodinger equation is the mittag leffler function with an imaginary argument by two different methods after separating the mittag leffler function into its real and imaginary parts in contrast to existing works we show that the total probability is 1 and decays with time introducing the effective potential approach we also write the mittag leffler function with an imaginary argument as the product of its purely decaying and purely oscillating parts in the light of these we reconsider the simple box problem

fox function representation of non debye relaxation processes applying the liouville riemann fractional calculus we derive and solve a fractional operator relaxation equation we demonstrate how the exponent of the asymptotic power law decay t relates to the order of the fractional operatordv dtv 0 1 continuous time random walk ctrw models offer a physical interpretation of fractional order equations and thus we point out a connection between a special type of ctrw and our fractional relaxation model exact analytical solutions of the fractional relaxation equation are obtained in terms of fox functions by using laplace and mellin transforms apart from fractional relaxation fox functions are further used to calculate fourier integrals of kohlrausch williams watts type relaxation functions because of its close connection to integral transforms the rich class of fox functions forms a suitable framework for discussing slow relaxation phenomena

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

a hyperelastic regularization energy for image registration image registration is one of the most challenging problems in image processing where ill posedness arises due to noisy data as well as nonuniqueness and hence the choice of regularization is crucial this paper presents hyperelasticity as a regularizer and introduces a new and stable numerical implementation on one hand hyperelastic registration is an appropriate model for large and highly nonlinear deformations for which a linear elastic model needs to fail on the other hand the hyperelastic regularizer yields very regular and diffeomorphic transformations while hyperelasticity might be considered as just an additional outstanding regularization option for some applications it becomes inevitable for applications involving higher order distance measures like mass preserving registration the paper gives a short introduction to image registration and hyperelasticity the hyperelastic image registration problem is phrased in a variational setting and an existence proof is provided the focus of th

nonparametric hypothesis tests for statistical dependency determining the structure of dependencies among a set of variables is a common task in many signal and image processing applications including multitarget tracking and computer vision in this paper we present an information theoretic machine learning approach to problems of this type we cast this problem as a hypothesis test between factorizations of variables into mutually independent subsets we show that the likelihood ratio can be written as sums of two sets of kullback leibler kl divergence terms the first set captures the structure of the statistical dependencies within each hypothesis whereas the second set measures the details of model differences between hypotheses we then consider the case when the signal prior models are unknown so that the distributions of interest must be estimated directly from data showing that the second set of terms is asymptotically negligible and quantifying the loss in hypothesis separability when the models are completely unknown we demonstrate the utility of nonparametric estimation methods for such problems providing a general framework for determining and distinguishing between dependency structures in highly uncertain environments additionally we develop a machine learning approach for estimating lower bounds on kl divergence and mutual information from samples of high dimensional random variables for which direct density estimation is infeasible we present empirical results in the context of three prototypical applications association of signals generated by sources possessing harmonic behavior scene correspondence using video imagery and detection of coherent behavior among sets of moving objects

solutions for a schrodinger equation with a nonlocal term we obtain time dependent solutions for a schrondiger equation in the presence of a nonlocal term by using the green function approach these solutions are compared with recent results obtained for the fractional schrodinger equation as well as for the usual one the nonlocal term incorporated in the schrodinger equation may also be related to the spatial and time fractional derivative and introduces different regimes of spreading of the solution with the time evolution

geodesics based image registration applications to biological and medical images depicting concentric ring patterns in many biological or medical applications images that contain sequences of shapes are common the existence of high inter individual variability makes their interpretation complex in this paper we address the computer assisted interpretation of such images and we investigate how we can remove or reduce these image variabilities the proposed approach relies on the development of an efficient image registration technique we first show the inadequacy of state of the art intensity based and feature based registration techniques for the considered image datasets then we propose a robust variational method which benefits from the geometrical information present in this type of images in the proposed non rigid geodesics based registration the successive shapes are represented by a level set representation which we rely on to carry out the registration the successive level sets are regarded as elements in a shape space and the corresponding matching is that of the optimal geodesic path the proposed registration scheme is tested on synthetic and real images the comparison against results of state of the art methods proves the relevance of the proposed method for this type of images

generalized fractional schrodinger equation with space time fractional derivatives in this paper the generalized fractional schrodinger equation with space and time fractional derivatives is constructed the equation is solved for free particle and for a square potential well by the method of integral transforms fourier transform and laplace transform and the solution can be expressed in terms of mittag leffler function the green function for free particle is also presented in this paper finally we discuss the relationship between the cases of the generalized fractional schrodinger equation and the ones in standard quantum

decay of a potential vortex in a generalized oldroyd b fluid the velocity field and the adequate shear stress corresponding to the decay of a potential vortex in a generalized oldroyd b fluid are determined by means of hankel and laplace transforms the exact solutions written in terms of the generalized g and r functions are presented as a sum of the newtonian solutions and the adequate non newtonian contributions these solutions can be easy specialized to give the solutions for generalized maxwell fluids and ordinary oldroyd b or maxwell fluids performing the same motion the influence of the fractional parameters as well as that of the material parameters on the decay of the vortex is emphasized by graphical illustrations

the factorization method for electrical impedance tomography in the half space we consider the inverse problem of electrical impedance tomography in a conducting half space given electrostatic measurements on its boundary i e a hyperplane we first provide a rigorous weak analysis of the corresponding forward problem and then develop a numerical algorithm to solve an associated inverse problem this inverse problem consists of the reconstruction of certain inclusions within the half space which have a different conductivity than the background to solve the inverse problem we employ the so called factorization method of kirsch which so far has only been considered for the impedance tomography problem in bounded domains our analysis of the forward problem makes use of a liouville type argument which says that a harmonic function in the entire two dimensional plane must be a constant if some weighted l 2 norm of this function is bounded

identification of small inhomogeneities asymptotic factorization we consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions we give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential the location of the inhomogeneities and their geometry as the size of the inhomogeneities tends to zero such asymptotic expansions have already been used to design direct i e noniterative reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary e g music type methods our derivation of the asymptotic formulas is based on integral equation methods it demonstrates the strong relation between factorization methods and music type methods for the solution of this inverse problem

class based feature matching across unrestricted transformations we develop a novel method for class based feature matching across large changes in viewing conditions the method is based on the property that when objects share a similar part the similarity is preserved across viewing conditions given a feature and a training set of object images we first identify the subset of objects that share this feature the transformation of the feature s appearance across viewing conditions is determined mainly by properties of the feature rather than of the object in which it is embedded therefore the transformed feature will be shared by approximately the same set of objects based on this consistency requirement corresponding features can be reliably identified from a set of candidate matches unlike previous approaches the proposed scheme compares feature appearances only in similar viewing conditions rather than across different viewing conditions as a result the scheme is not restricted to locally planar objects or affine transformations the approach also does not require examples of correct matches we show that by using the proposed method a dense set of accurate correspondences can be obtained experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes finally we show that the scheme can be successfully used for invariant object recognition

computing accurate correspondences across groups of images groupwise image registration algorithms seek to establish dense correspondences between sets of images typically they involve iteratively improving the registration between each image and an evolving mean a variety of methods have been proposed which differ in their choice of objective function representation of deformation field and optimization methods given the complexity of the task the final accuracy is significantly affected by the choices made for each component here we present a groupwise registration algorithm which can take advantage of the statistics of both the image intensities and the range of shapes across the group to achieve accurate matching by testing on large sets of images in both 2d and 3d we explore the effects of using different image representations and different statistical shape constraints we demonstrate that careful choice of such representations can lead to significant improvements in overall performance

variational geometric and statistical methods for modeling brain anatomy and function we survey the recent activities of the odyssee laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function we start with the problem of reconstructing sources in meg and eeg and discuss the variational approach we have developed for solving these inverse problems this motivates the need for geometric models of the head we present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance mr images anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but in the current state of the technology it must be preceded by a robust estimation and regularization stage we discuss our work based on variational principles and show how the results can be used to track fibers in the white matter wm as geodesics in some riemannian space we then go to the statistical modeling of functional magnetic resonance imaging fmri signals from the viewpoint of their decomposition in a pseudo deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory multimodal image matching is discussed next in the framework of image statistics and partial differential equations pdes with an eye on registering fmri to the anatomy the paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases

hybrid electric magnetic methods in eddy current problems we discuss a method of approximation of eddy current equations in bounded space that relies on the use of the electric field as primary variable in the conductive parts and of the magnetic field in the air theoretical issues about this hybrid approach are addressed is the problem well posed and one shows that edge elements offer a straightforward way to discretize such formulations the now popular a v method is then shown to come as a variant of this formulation in such a way that it allows the use of standard nodal elements however attention is called on the fact that the numerical convergence of the latter method may be in question

maximum likelihood image matching image matching applications such as tracking and stereo commonly use the sum of squared difference ssd measure to determine the best match however this measure is sensitive to outliers and is not robust to template variations alternative measures have also been proposed that are more robust to these issues we improve upon these using a probabilistic formulation for image matching in terms of maximum likelihood estimation that can be used for both edge template matching and gray level image matching this formulation generalizes previous edge matching methods based on distance transforms we apply the techniques to stereo matching and feature tracking uncertainty estimation techniques allow feature selection to be performed by choosing features that minimize the localization uncertainty

the dual bootstrap iterative closest point algorithm with application to retinal image registration motivated by the problem of retinal image registration this paper introduces and analyzes a new registration algorithm called dual bootstrap iterative closest point dual bootstrap icp the approach is to start from one or more initial low order estimates that are only accurate in small image regions called bootstrap regions in each bootstrap region the algorithm iteratively 1 refines the transformation estimate using constraints only from within the bootstrap region 2 expands the bootstrap region and 3 tests to see if a higher order transformation model can be used stopping when the region expands to cover the overlap between images steps 1 and 3 the bootstrap steps are governed by the covariance matrix of the estimated transformation estimation refinement step 2 uses a novel robust version of the icp algorithm in registering retinal image pairs dual bootstrap icp is initialized by automatically matching individual vascular landmarks and it aligns images based on detected blood vessel centerlines the resulting quadratic transformations are accurate to less than a pixel on tests involving approximately 6000 image pairs it successfully registered 99 5 of the pairs containing at least one common landmark and 100 of the pairs containing at least one common landmark and at least 35 image overlap

a direct impedance tomography algorithm for locating small inhomogeneities impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface in its most general form impedance tomography is quite ill posed but when additional a priori information is admitted the situation changes dramatically in this paper we consider the case where the goal is to find a number of small objects inhomogeneities inside an otherwise known conductor taking advantage of the smallness of the inhomogeneities we can use asymptotic analysis to design a direct i e non iterative reconstruction algorithm for the determination of their locations the viability of this direct approach is documented by numerical examples

space time fractional schrodinger equation with time independent potentials abstract we develop a space time fractional schrodinger equation containing caputo fractional derivative and the quantum riesz fractional operator from a space fractional schrodinger equation in this paper by use of the new equation we study the time evolution behaviors of the space time fractional quantum system in the time independent potential fields and two cases that the order of the time fractional derivative is between zero and one and between one and two are discussed respectively the space time fractional schrodinger equation with time independent potentials is divided into a space equation and a time one a general solution which is composed of oscillatory terms and decay ones is obtained we investigate the time limits of the total probability and the energy levels of particles when time goes to infinity and find that the limit values not only depend on the order of the time derivative but also on the sign positive or negative of the eigenvalues of the space equation we also find that the limit value of the total probability can be greater or less than one which means the space time fractional schrodinger equation describes the quantum system where the probability is not conservative and particles may be extracted from or absorbed by the potentials additionally the non markovian time evolution laws of the space time fractional quantum system are discussed the formula of the time evolution of the mechanical quantities is derived and we prove that there is no conservative quantities in the space time fractional quantum system we also get a mittag leffler type of time evolution operator of wave functions and then establish a heisenberg equation containing fractional operators

high dimensional statistical measure for region of interest tracking this paper deals with region of interest roi tracking in video sequences the goal is to determine in successive frames the region which best matches in terms of a similarity measure a roi defined in a reference frame some tracking methods define similarity measures which efficiently combine several visual features into a probability density function pdf representation thus building a discriminative model of the roi this approach implies dealing with pdfs with domains of definition of high dimension to overcome this obstacle a standard solution is to assume independence between the different features in order to bring out low dimension marginal laws and or to make some parametric assumptions on the pdfs at the cost of generality we discard these assumptions by proposing to compute the kullback leibler divergence between high dimensional pdfs using the k th nearest neighbor framework in consequence the divergence is expressed directly from the samples i e without explicit estimation of the underlying pdfs as an application we defined 5 7 and 13 dimensional feature vectors containing color information including pixel based gradient based and patch based and spatial layout the proposed procedure performs tracking allowing for translation and scaling of the roi experiments show its efficiency on a movie excerpt and standard test sequences selected for the specific conditions they exhibit partial occlusions variations of luminance noise and complex motion

mutual information aspects of scale space images in image registration mutual information is a well performing measure based on principles of uncertainty similarly in image analysis the gaussian scale space based on minimal assumptions of the image is used to derive intrinsic properties of an image this paper starts an investigation of a combination of both methods this combination results in a double parameterized mutual information measure using local information of the image for single modality matching best response is found for coinciding parameters then critical values are found for which the parameterized mutual information has extrema first results on multi modality matching show that different parameter values instead of coinciding values yield the best response for the parameterized mutual information

generalized time dependent schrodinger equation in two dimensions under constraints we investigate a generalized two dimensional time dependent schrodinger equation on a comb with a memory kernel a dirac delta term is introduced in the schrodinger equation so that the quantum motion along the x direction is constrained at y 0 the wave function is analyzed by using green s function approach for several forms of the memory kernel which are of particular interest closed form solutions for the cases of dirac delta and power law memory kernels in terms of fox h function as well as for a distributed order memory kernel are obtained further a nonlocal term is also introduced and investigated analytically it is shown that the solution for such a case can be represented in terms of infinite series in fox h functions green s functions for each of the considered cases are analyzed and plotted for the most representative ones anomalous diffusion signatures are evident from the presence of the power law tails the normalized green s functions obtained in this work are of broader interest

point matching under large image deformations and illumination changes to solve the general point correspondence problem in which the underlying transformation between image patches is represented by a homography a solution based on extensive use of first order differential techniques is proposed we integrate in a single robust m estimation framework the traditional optical flow method and matching of local color distributions these distributions are computed with spatially oriented kernels in the 5d joint spatial color space the estimation process is initiated at the third level of a gaussian pyramid uses only local information and the illumination changes between the two images are also taken into account subpixel matching accuracy is achieved under large projective distortions significantly exceeding the performance of any of the two components alone as an application the correspondence algorithm is employed in oriented tracking of objects

computation of image spatial entropy using quadrilateral markov random field shannon entropy is a powerful tool in image analysis but its reliable computation from image data faces an inherent dimensionality problem that calls for a low dimensional and closed form model for the pixel value distributions the most promising such models are markovian however the conventional markov random field is hampered by noncausality and its causal versions are also not free of difficulties for example the markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system a new model named quadrilateral markov random field qmrf is introduced in this paper in order to overcome these limitations a property of qmrf with neighboring size of 2 is then used to decompose an image prior into a product of 2 d joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption in addition the paper includes an extension of the introduced method to the computation of image spatial mutual information comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones

solution of a modified fractional diffusion equation abstract recently a modified fractional diffusion equation has been proposed i sokolov j klafter from diffusion to anomalous diffusion a century after einstein s brownian motion chaos 15 2005 026103 a v chechkin r gorenflo i m sokolov v yu gonchar distributed order time fractional diffusion equation frac calc appl anal 6 3 2003 259279 i m sokolov a v checkin j klafter distributed order fractional kinetics acta phys pol b 35 2004 1323 for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term in this letter we give the solution of the modified equation on an infinite domain in contrast to the solution of the traditional fractional diffusion equation the solution of the modified equation requires an infinite series of fox functions instead of a single fox function

decoupled linear estimation of affine geometric deformations and nonlinear intensity transformations of images we consider the problem of registering two observations on an arbitrary object where the two are related by a geometric affine transformation of their coordinate systems and by a nonlinear mapping of their intensities more generally the framework is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object we show that the original high dimensional nonlinear and nonconvex search problem of simultaneously recovering the geometric and radiometric deformations can be represented by an equivalent sequence of two linear systems a solution of this sequence yields an exact explicit and efficient solution to the joint estimation problem

rigid shape matching by segmentation averaging we use segmentations to match images by shape the new matching technique does not require point to point edge correspondence and is robust to small shape variations and spatial shifts to address the unreliability of segmentations computed bottom up we give a closed form approximation to an average over all segmentations our method has many extension yielding new algorithms for tracking object detection segmentation and edge preserving smoothing for segmentation instead of a maximum a posteriori approach we compute the central segmentation minimizing the average distance to all segmentations of an image for smoothing instead of smoothing images based on local structures we smooth based on the global optimal image structures our methods for segmentation smoothing and object detection perform competitively and we also show promising results in shape based tracking