multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

free energy and correlations of the number theoretical spin chain we analyze the number theoretical spin chain with partition function z 1 using the polymer model technique the finite grand canonical chains give bounds for the limit free energy and internal energy the correlation functions for inverse temperature 1 are products of two point functions a combinatorial result for general interval graphs is derived

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

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

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

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

maximum likelihood wavelet density estimation with applications to image and shape matching density estimation for observational data plays an integral role in a broad spectrum of applications e g statistical data analysis and information theoretic image registration of late wavelet based density estimators have gained in popularity due to their ability to approximate a large class of functions adapting well to difficult situations such as when densities exhibit abrupt changes the decision to work with wavelet density estimators brings along with it theoretical considerations e g non negativity integrability and empirical issues e g computation of basis coefficients that must be addressed in order to obtain a bona fide density in this paper we present a new method to accurately estimate a non negative density which directly addresses many of the problems in practical wavelet density estimation we cast the estimation procedure in a maximum likelihood framework which estimates the square root of the density allowing us to obtain the natural non negative density representation analysis of this method will bring to light a remarkable theoretical connection with the fisher information of the density and consequently lead to an efficient constrained optimization procedure to estimate the wavelet coefficients we illustrate the effectiveness of the algorithm by evaluating its performance on mutual information based image registration shape point set alignment and empirical comparisons to known densities the present method is also compared to fixed and variable bandwidth kernel density estimators

image registration based on autocorrelation of local structure registration of images in the presence of intra image signal fluctuations is a challenging task the definition of an appropriate objective function measuring the similarity between the images is crucial for accurate registration this paper introduces an objective function that embeds local phase features derived from the monogenic signal in the modality independent neighborhood descriptor mind the image similarity relies on the autocorrelation of local structure alost which has two important properties 1 low sensitivity to space variant intensity distortions e g differences in contrast enhancement in mri 2 high distinctiveness for salient image features such as edges the alost method is quantitatively compared to the mind approach based on three different datasets thoracic ct images synthetic and real abdominal mr images the proposed method outperformed the nmi and mind similarity measures on these three datasets the registration of dynamic contrast enhanced and post contrast mr images of patients with crohn s disease led to relative contrast enhancement measures with the highest correlation rm r 0 56 to the crohn s disease endoscopic index of severity

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

smo based pruning methods for sparse least squares support vector machines solutions of least squares support vector machines ls svms are typically nonsparse the sparseness is imposed by subsequently omitting data that introduce the smallest training errors and retraining the remaining data iterative retraining requires more intensive computations than training a single nonsparse ls svm in this paper we propose a new pruning algorithm for sparse ls svms the sequential minimal optimization smo method is introduced into pruning process in addition instead of determining the pruning points by errors we omit the data points that will introduce minimum changes to a dual objective function this new criterion is computationally efficient the effectiveness of the proposed method in terms of computational cost and classification accuracy is demonstrated by numerical experiments

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

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

on a ferromagnetic spin chain the quotient s 1 s of riemann zeta functions is shown to be the partition function of a ferromagnetic spin chain for inverse temperatures

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

a pruning method of refining recursive reduced least squares support vector regression in this paper a pruning method is proposed to refine the recursive reduced least squares support vector regression rrlssvr and its improved version irrlssvr and thus two novel algorithms prurrlssvr and pruirrlssvr are yielded this pruning method ranks support vectors by defining a contribution function to the objective function and then the support vector with the least contribution is pruned unless it is the most recently selected support vector consequently prurrlssvr and pruirrlssvr outperform rrlssvr and irrlssvr respectively in terms of the number of support vectors while not impairing the generalization performance in addition a speedup scheme is presented that reduces the computational burden of computing the contribution function to show the effectiveness and feasibility of the proposed prurrlssvr and pruirrlssvr experiments are performed on ten benchmark data sets and a gas furnace instance

pruning error minimization in least squares support vector machines the support vector machine svm is a method for classification and for function approximation this method commonly makes use of an spl epsi insensitive cost function meaning that errors smaller than spl epsi remain unpunished as an alternative a least squares support vector machine lssvm uses a quadratic cost function when the lssvm method is used for function approximation a nonsparse solution is obtained the sparseness is imposed by pruning i e recursively solving the approximation problem and subsequently omitting data that has a small error in the previous pass however omitting data with a small approximation error in the previous pass does not reliably predict what the error will be after the sample has been omitted in this paper a procedure is introduced that selects from a data set the training sample that will introduce the smallest approximation error when it will be omitted it is shown that this pruning scheme outperforms the standard one

gradient based manipulation of nonparametric entropy estimates this paper derives a family of differential learning rules that optimize the shannon entropy at the output of an adaptive system via kernel density estimation in contrast to parametric formulations of entropy this nonparametric approach assumes no particular functional form of the output density we address problems associated with quantized data and finite sample size and implement efficient maximum likelihood techniques for optimizing the regularizer we also develop a normalized entropy estimate that is invariant with respect to affine transformations facilitating optimization of the shape rather than the scale of the output density kernel density estimates are smooth and differentiable this makes the derived entropy estimates amenable to manipulation by gradient descent the resulting weight updates are surprisingly simple and efficient learning rules that operate on pairs of input samples they can be tuned for data limited or memory limited situations or modified to give a fully online implementation

automatic registration of images to untextured geometry using average shading gradients many existing approaches for image to geometry registration assume that either a textured 3d model or a good initial guess of the 3d pose is available to bootstrap the registration process in this paper we consider the registration of photographs to 3d models even when no texture information is available this is very challenging as we cannot rely on texture gradients and even shading gradients are hard to estimate since the lighting conditions are unknown to that end we propose average shading gradients a rendering technique that estimates the average gradient magnitude over all lighting directions under lambertian shading we use this gradient representation as the building block of a registration pipeline based on matching sparse features to cope with inevitable false matches due to the missing texture information and to increase robustness the pose of the 3d model is estimated in two stages coarse pose hypotheses are first obtained from a single correct match each subsequently refined using sift flow and finally verified we apply our algorithm to registering images of real world objects to untextured 3d meshes of limited accuracy moreover we show that registration can be performed even for paintings despite lacking photo realism

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

maps of intervals with indifferent fixed points thermodynamic formalism and phase transitions we develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points for such systems the formalism yields onedimensional systems with many body infinite range interactions for which the thermodynamics is well defined but gibbs states are not piecewise linear systems of this kind yield the soluble in a sense fisher models we prove that such systems exhibit phase transitions the order of which depends on the behavior at the indifferent fixed points we obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable expanding induced version the technique allows one also to obtain a version of the bowen ruelle formula for the hausdorff dimension of repellers for maps with indifferent fixed points and to generalize fisher results to some nonsoluble models

a statistical analysis of brain morphology using wild bootstrapping methods for the analysis of brain morphology including voxel based morphology and surface based morphometries have been used to detect associations between brain structure and covariates of interest such as diagnosis severity of disease age iq and genotype the statistical analysis of morphometric measures usually involves two statistical procedures 1 invoking a statistical model at each voxel or point on the surface of the brain or brain subregion followed by mapping test statistics e g t test or their associated p values at each of those voxels 2 correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation we propose the use of new statistical methods for each of these procedures we first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion e g cortical or subcortical surfaces and the covariates of interest moreover we develop a robust test procedure that is based on a resampling method called wild bootstrapping this procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest the value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data including data from both anatomical and functional magnetic resonance imaging fmri simulation studies demonstrate that this robust test procedure can accurately control the family wise error rate we demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects

multi view stereo reconstruction and scene flow estimation with a global image based matching score we present a new variational method for multi view stereovision and non rigid three dimensional motion estimation from multiple video sequences our method minimizes the prediction error of the shape and motion estimates both problems then translate into a generic image registration task the latter is entrusted to a global measure of image similarity chosen depending on imaging conditions and scene properties rather than integrating a matching measure computed independently at each surface point our approach computes a global image based matching score between the input images and the predicted images the matching process fully handles projective distortion and partial occlusions neighborhood as well as global intensity information can be exploited to improve the robustness to appearance changes due to non lambertian materials and illumination changes without any approximation of shape motion or visibility moreover our approach results in a simpler more flexible and more efficient implementation than in existing methods the computation time on large datasets does not exceed thirty minutes on a standard workstation finally our method is compliant with a hardware implementation with graphics processor units our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency we have successfully tested our motion estimation algorithm on a very challenging multi view video sequence of a non rigid scene

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

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

kernel recursive least squares tracker for time varying regression in this paper we introduce a kernel recursive least squares krls algorithm that is able to track nonlinear time varying relationships in data to this purpose we first derive the standard krls equations from a bayesian perspective including a sensible approach to pruning and then take advantage of this framework to incorporate forgetting in a consistent way thus enabling the algorithm to perform tracking in nonstationary scenarios the resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner in addition to its tracking ability it has a number of appealing properties it is online requires a fixed amount of memory and computation per time step incorporates regularization in a natural manner and provides confidence intervals along with each prediction we include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm

a unified approach to fast image registration and a new curvature based registration technique abstract image registration is central to many challenges in medical imaging today it has a vast range of applications the purpose of this note is twofold first we review some of the most promising non linear registration strategies currently used in medical imaging we show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment second we introduce within the variational framework a new non linear registration model based on a curvature type smoother we show that affine linear transformations belong to the kernel of this regularizer as a result the approach becomes more robust against poor initializations of a pre registration step furthermore we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation we demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering mr mammography images

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

comments on pruning error minimization in least squares support vector machines in this letter we comment on pruning error minimization in least squares support vector machines by b j de kruif and t j a de vries the original paper proposes a way of pruning training examples for least squares support vector machines ls svm using no regularization gamma infin this causes a problem as the derivation involves inverting a matrix that is often singular we discuss a modification of this algorithm that prunes with regularization gamma finite and nonzero and is also computationally more efficient

the minkowski question mark function explicit series for the dyadic period function and moments previously several natural integral transforms of the minkowski question mark function f x were introduced by the author each of them is uniquely characterized by certain regularity conditions and the functional equation thus encoding intrinsic information about f x one of them the dyadic period function g z was defined as a stieltjes transform in this paper we introduce a family of distributions f p x for rp 1 such that f 1 x is the question mark function and f 2 x is a discrete distribution with support on x 1 we prove that the generating function of moments of f p x satisfies the three term functional equation this has an independent interest though our main concern is the information it provides about f x this approach yields the following main result we prove that the dyadic period function is a sum of infinite series of rational functions with rational coefficients

a farey fraction spin chain we introduce a new number theoretic spin chain and explore its thermodynamics and connections with number theory the energy of each spin configuration is defined in a translation invariant manner in terms of the farey fractions and is also expressed using pauli matrices we prove that the free energy exists and a phase transition occurs for positive inverse temperature 2 the free energy is the same as that of related non translation invariant number theoretic spin chain using a number theoretic argument the low temperature 3 state is shown to be completely magnetized for long chains the number of states of energy e log n summed over chain length is expressed in terms of a restricted divisor problem we conjecture that its asymptotic form is n log n consistent with the phase transition at 2 and suggesting a possible connection with the riemann function the spin interaction coefficients include all even many body terms and are translation invariant computer results indicate that all the interaction coefficients except the constant term are ferromagnetic

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

generalized farey trees transfer operators and phase transitions we consider a family of markov maps on the unit interval interpolating between the tent map and the farey map the latter is not uniformly expanding each map being composed of two fractional linear transformations the family generalizes many particular properties which for the case of the farey map have been successfully exploited in number theory we analyze the dynamics through the spectral properties of the generalized transfer operator application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function

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

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

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

generalization to novel views universal class based andmodel based processing a major problem in object recognition is that a novel image of a given object can be different from all previously seen images images can vary considerably due to changes in viewing conditions such as viewing position and illumination in this paper we distinguish between three types of recognition schemes by the level at which generalization to novel images takes place universal class and model based the first is applicable equally to all objects the second to a class of objects and the third uses known properties of individual objects we derive theoretical limitations on each of the three generalization levels for the universal level previous results have shown that no invariance can be obtained here we show that this limitation holds even when the assumptions made on the objects and the recognition functions are relaxed we also extend the results to changes of illumination direction for the class level previous studies presented specific examples of classes of objects for which functions invariant to viewpoint exist here we distinguish between classes that admit such invariance and classes that do not we demonstrate that there is a tradeoff between the set of objects that can be discriminated by a given recognition function and the set of images from which the recognition function can recognize these objects furthermore we demonstrate that although functions that are invariant to illumination direction do not exist at the universal level when the objects are restricted to belong to a given class an invariant function to illumination direction can be defined a general conclusion of this study is that class based processing that has not been used extensively in the past is often advantageous for dealing with variations due to viewpoint and illuminant changes

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

stereo processing by semiglobal matching and mutual information this paper describes the semiglobal matching sgm stereo method it uses a pixelwise mutual information ml based matching cost for compensating radiometric differences of input images pixelwise matching is supported by a smoothness constraint that is usually expressed as a global cost function sgm performs a fast approximation by pathwise optimizations from all directions the discussion also addresses occlusion detection subpixel refinement and multibaseline matching additionally postprocessing steps for removing outliers recovering from specific problems of structured environments and the interpolation of gaps are presented finally strategies for processing almost arbitrarily large images and fusion of disparity images using orthographic projection are proposed a comparison on standard stereo images shows that sgm is among the currently top ranked algorithms and is best if subpixel accuracy is considered the complexity is linear to the number of pixels and disparity range which results in a runtime of just 1 2 seconds on typical test images an in depth evaluation of the ml based matching cost demonstrates a tolerance against a wide range of radiometric transformations finally examples of reconstructions from huge aerial frame and pushbroom images demonstrate that the presented ideas are working well on practical problems

image registration using markov random coefficient and geometric transformation fields image registration is central to different applications such as medical analysis biomedical systems and image guidance in this paper we propose a new algorithm for multimodal image registration a bayesian formulation is presented in which a likelihood term is defined using an observation model based on coefficient and geometric fields these coefficients which represent the local intensity polynomial transformations as the local geometric transformations are modeled as prior information by means of markov random fields this probabilistic approach allows one to find optimal estimators by minimizing an energy function in terms of both fields making the registration between the images possible

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

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

a variational approach to nonrigid morphological image registration a variational method for nonrigid registration of multimodal image data is presented a suitable deformation will be determined via the minimization of a morphological i e contrast invariant matching functional along with an appropriate regularization energy the aim is to correlate the morphologies of a template and a reference image under the deformation mathematically the morphology of images can be described by the entity of level sets of the image and hence by its gauss map a class of morphological matching functionals is presented which measure the defect of the template gauss map in the deformed state with respect to the deformed gauss map of the reference image the problem is regularized by considering a nonlinear elastic regularization energy existence of homeomorphic minimizing deformation is proved under assumptions on the class of admissible deformations with respect to actual medical applications suitable generalizations of the matching energies and the boundary conditions are pre

recursive reduced least squares support vector regression combining reduced technique with iterative strategy we propose a recursive reduced least squares support vector regression the proposed algorithm chooses the data which make more contribution to target function as support vectors and it considers all the constraints generated by the whole training set thus it acquires less support vectors the number of which can be arbitrarily predefined to construct the model with the similar generalization performance in comparison with other methods our algorithm also gains excellent parsimoniousness numerical experiments on benchmark data sets confirm the validity and feasibility of the presented algorithm in addition this algorithm can be extended to classification

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

the number theoretical spin chain and the riemann zeroes it is an empirical observation that the riemann zeta function can be well approximated in its critical strip using the number theoretical spin chain a proof of this would imply the riemann hypothesis here we relate that question to the one of spectral radii of a family of markov chains this in turn leads to the question whether certain graphs are ramanujan

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

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

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

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

correction to gradient based manipulation of nonparametric entropy estimates jul 04 828 837 in the above titled paper ibid vol 15 no 4 pp 828 837 jul 04 the m step 22 was incorrect the corrected m step is presented here

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

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 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

generalizing inverse compositional and esm image alignment inverse compositional ic image alignment baker and matthews in int j comput vis 56 3 221 255 2004 uses the symmetry between the roles of the fixed and moving images for faster processing however it requires implementation of compositional optimizer update steps the ic approach can be viewed as an efficient way of computing the similarity measure derivative relative to the fixed image warp parameters since the mapping between the fixed and moving warp parameters is continuous and differentiable this derivative can be converted into the moving warp space using the chain rule this avoids the need for compositional update steps our generalization also allows the efficient second order method esm malis in proceedings of the 2004 ieee international conference on robotics and automation icra04 pp 1843 1848 2004 benhimane and malis in ieee rsj international conference on intelligent robots and systems 2004 malis and benhimane in robot auton syst 52 1 39 52 2005 to be applied to general parameterizations of the transformation experiments using multiple similarity measures and optimizers show that our generalized ic method equals or exceeds the performance of the original ic approach the generalized esm approach is more reliable than the classic approach as it increases the capture radius of the optimization

towards a complete determination of the spectrum of a transfer operator associated with intermittency the physical phenomenon of intermittency can be investigated via the spectral analysis of a transfer operator associated with the dynamics of an interval map with indifferent fixed point for an example of such an intermittent map the farey map we give a simple proof that the transfer operator is self adjoint on a suitably defined hilbert space and characterize its spectrum using a suitable first return map we present a highly efficient numerical method for the determination of all the eigenvalues including those embedded in the continuous spectrum

geodesic active fields a geometric framework for image registration in this paper we present a novel geometric framework called geodesic active fields for general image registration in image registration one looks for the underlying deformation field that best maps one image onto another this is a classic ill posed inverse problem which is usually solved by adding a regularization term here we propose a multiplicative coupling between the registration term and the regularization term which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem then the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem this proposed approach for registration shares close similarities with the well known geodesic active contours model in image segmentation where the segmentation term the edge detector function is coupled with the regularization term the length functional via multiplication as well as a matter of fact our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by caselles kimmel sapiro the energy of the deformation field is measured with the polyakov energy weighted by a suitable image distance borrowed from standard registration models we investigate three different weighting functions the squared error and the approximated absolute error for monomodal images and the local joint entropy for multimodal images as compared to specialized state of the art methods tailored for specific applications our geometric framework involves important contributions firstly our general formulation for registration works on any parametrizable smooth and differentiable surface including nonflat and multiscale images in the latter case multiscale images are registered at all scales simultaneously and the relations between space and scale are intrinsically being accounted for second this method is to the best of our knowledge the first reparametrization invariant registration method introduced in the literature thirdly the multiplicative coupling between the registration term i e local image discrepancy and the regularization term naturally results in a data dependent tuning of the regularization strength finally by choosing the metric on the deformation field one can freely interpolate between classic gaussian and more interesting anisotropic tv like regularization

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

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

an image morphing technique based on optimal mass preserving mapping image morphing or image interpolation in the time domain deals with the metamorphosis of one image into another in this paper a new class of image morphing algorithms is proposed based on the theory of optimal mass transport the l2 mass moving energy functional is modified by adding an intensity penalizing term in order to reduce the undesired double exposure effect it is an intensity based approach and thus is parameter free the optimal warping function is computed using an iterative gradient descent approach this proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique along with finite element methods

contrast invariant snr and isotonic regressions we design an image quality measure independent of contrast changes which are defined as a set of transformations preserving an order between the level lines of an image this problem can be expressed as an isotonic regression problem depending on the definition of a level line the partial order between adjacent regions can be defined through chains polytrees or directed acyclic graphs we provide a few analytic properties of the minimizers and design original optimization procedures together with a full complexity analysis the methods worst case complexities range from o n for chains to o n log n for polytrees and o frac n 2 sqrt epsilon for directed acyclic graphs where n is the number of pixels and epsilon is a relative precision the proposed algorithms have potential applications in change detection stereo vision image registration color image processing or image fusion a c implementation with matlab headers is available at https github com pierre weiss contrast invariant snr

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

geometric transformations of multidimensional color images based on nass we present quantum algorithms to realize geometric transformations two point swappings symmetric flips local flips orthogonal rotations and translations based on an n qubit normal arbitrary superposition state nass these transformations are implemented using quantum circuits consisting of basic quantum gates which are constructed with polynomial numbers of single qubit and two qubit gates complexity analysis shows that the global operators symmetric flips local flips orthogonal rotations can be implemented with o n gates the proposed geometric transformations are used to facilitate applications of quantum images with low complexity

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

an improved conjugate gradient scheme to the solution of least squares svm the least square support vector machines ls svm formulation corresponds to the solution of a linear system of equations several approaches to its numerical solutions have been proposed in the literature in this letter we propose an improved method to the numerical solution of ls svm and show that the problem can be solved using one reduced system of linear equations compared with the existing algorithm for ls svm the approach used in this letter is about twice as efficient numerical results using the proposed method are provided for comparisons with other existing algorithms

on a ferromagnetic spin chain ii thermodynamic limit the existence of the thermodynamic limit of the free energy for the ferromagnetic spin chain connected with the riemann zeta function is proven

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

intermittency and regularized fredholm determinants we consider real analytic maps of the interval i 0 1 which are expanding everywhere except for a neutral fixed point at 0 we show that on a certain function space the associated perron frobenius operator has a continuous and residual spectrum contained in the line segment c 0 1 and a point spectrum p which has no points of accumulation outside 0 and 1 furthermore points in p 0 1 are eigenvalues of finite multiplicity we construct a regularized fredholm determinant d which has a holomorphic extension to c and can be analytically continued from each side of c to an open neighborhood of c 0 1 on different riemann sheets in c the zero set of d is in one to one correspondence with the point spectrum of through the conformal transformation the function d z extends to a holomorphic function in a domain which contains the unit disc

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

registration of cervical mri using multifeature mutual information radiation therapy for cervical cancer can benefit from image registration in several ways for example by studying the motion of organs or by partially automating the delineation of the target volume and other structures of interest in this paper the registration of cervical data is addressed using mutual information mi of not only image intensity but also features that describe local image structure three aspects of the registration are addressed to make this approach feasible first instead of relying on a histogram based estimation of mutual information which poses problems for a larger number of features a graph based implementation of alpha mutual information alpha mi is employed second the analytical derivative of alpha mi is derived this makes it possible to use a stochastic gradient descent method to solve the registration problem which is substantially faster than non derivative based methods third the feature space is reduced by means of a principal component analysis which also decreases the registration time the proposed technique is compared to a standard approach based on the mutual information of image intensity only experiments are performed on 93 t2 weighted mr clinical data sets acquired from 19 patients with cervical cancer several characteristics of the proposed algorithm are studied on a subset of 19 image pairs one pair per patient on the remaining data 36 image pairs one or two pairs per patient the median overlap is shown to improve significantly compared to standard mi from 0 85 to 0 86 for the clinical target volume ctv p 2 ldr10 2 from 0 75 to 0 81 for the bladder p 8 ldr 10 6 and from 0 76 to 0 77 for the rectum p 2 ldr 10 4 the registration error is improved at important tissue interfaces such as that of the bladder with the ctv and the interface of the rectum with the uterus and cervix

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

sparse lssvm in primal using cholesky factorization for large scale problems for support vector machine svm learning least squares svm lssvm derived by duality lssvm d lssvm is a widely used model because it has an explicit solution one obvious limitation of the model is that the solution lacks sparseness which limits it from training large scale problems efficiently in this paper we derive an equivalent lssvm model in primal space lssvm p lssvm by the representer theorem and prove that p lssvm can be solved exactly at some sparse solutions for problems with low rank kernel matrices two algorithms are proposed for finding the sparse approximate solution of p lssvm by cholesky factorization one is based on the decomposition of the kernel matrix k as p p top with the best low rank matrix p approximately by pivoting cholesky factorization the other is based on solving p lssvm by approximating the cholesky factorization of the hessian matrix with rank one update scheme for linear learning problems theoretical analysis and experimental results support that p lssvm can give the sparsest solutions in all svm learners experimental results on some large scale nonlinear training problems show that our algorithms based on p lssvm can converge to acceptable test accuracies at very sparse solutions with a sparsity level 1 and even as little as 0 01 hence our algorithms are a better choice for large scale training problems