point process principal components analysis via geometric optimization there has been a fast growing demand for analysis tools for multivariate point process data driven by work in neural coding and more recently high frequency finance here we develop a true or exact as opposed to one based on time binning principal components analysis for preliminary processing of multivariate point processes we provide a maximum likelihood estimator an algorithm for maximization involving steepest ascent on two stiefel manifolds and novel constrained asymptotic analysis the method is illustrated with a simulation and compared with a binning approach

symmetry detection by generalized complex gc moments a close form solution this paper presents a unified method for detecting both reflection symmetry and rotation symmetry of 2d images based on an identical set of features i e the first three nonzero generalized complex gc moments this method is theoretically guaranteed to detect all the axes of symmetries of every 2d image if more nonzero gc moments are used in the feature set furthermore we establish the relationship between reflectional symmetry and rotational symmetry in an image which can be used to check the correctness of symmetry detection this method has been demonstrated experimentally using more than 200 images

finding imaging patterns of structural covariance via non negative matrix factorization in this paper we investigate the use of non negative matrix factorization nnmf for the analysis of structural neuroimaging data the goal is to identify the brain regions that co vary across individuals in a consistent way hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies nnmf offers a directly data driven way of extracting relatively localized co varying structural regions thereby transcending limitations of principal component analysis pca independent component analysis ica and other related methods that tend to produce dispersed components of positive and negative loadings in particular leveraging upon the well known ability of nnmf to produce parts based representations of image data we derive decompositions that partition the brain into regions that vary in consistent ways across individuals importantly these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split sample experiments we empirically validate nnmf in two data sets i a diffusion tensor dt mouse brain development study and ii a structural magnetic resonance smr study of human brain aging we demonstrate the ability of nnmf to produce sparse parts based representations of the data at various resolutions these representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes moreover we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like pca and ica

generalized affine invariant image normalization we provide a generalized image normalization technique which basically solves all problems in image normalization the orientation of any image can be uniquely defined by at most three non zero generalized complex moments the correctness of our method is demonstrated theoretically as well as in practice by applying them to a number of degenerate images which have failed other previously reported techniques for image normalization

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

f timer fast tensor image morphing for elastic registration we propose a novel diffusion tensor imaging dti registration algorithm called fast tensor image morphing for elastic registration f timer f timer leverages multiscale tensor regional distributions and local boundaries for hierarchically driving deformable matching of tensor image volumes registration is achieved by utilizing a set of automatically determined structural landmarks via solving a soft correspondence problem based on the estimated correspondences thin plate splines are employed to generate a smooth topology preserving and dense transformation and to avoid arbitrary mapping of nonlandmark voxels to mitigate the problem of local minima which is common in the estimation of high dimensional transformations we employ a hierarchical strategy where a small subset of voxels with more distinctive attribute vectors are first deployed as landmarks to estimate a relatively robust low degrees of freedom transformation as the registration progresses an increasing number of voxels are permitted to participate in refining the correspondence matching a scheme as such allows less conservative progression of the correspondence matching towards the optimal solution and hence results in a faster matching speed compared with its predecessor timer which has been shown to outperform state of the art algorithms experimental results indicate that f timer is capable of achieving comparable accuracy at only a fraction of the computation cost

exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification in this paper two supervised methods for enhancing the classification accuracy of the nonnegative matrix factorization nmf algorithm are presented the idea is to extend the nmf algorithm in order to extract features that enforce not only the spatial locality but also the separability between classes in a discriminant manner the first method employs discriminant analysis in the features derived from nmf in this way a two phase discriminant feature extraction procedure is implemented namely nmf plus linear discriminant analysis lda the second method incorporates the discriminant constraints inside the nmf decomposition thus a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived the introduced methods have been applied to the problem of frontal face verification using the well known xm2vts database both methods greatly enhance the performance of nmf for frontal face verification

a high order non conforming discontinuous galerkin method for time domain electromagnetics in this paper we discuss the formulation stability and validation of a high order non dissipative discontinuous galerkin dg method for solving maxwell s equations on non conforming simplex meshes the proposed method combines a centered approximation for the numerical fluxes at inter element boundaries with either a second order or a fourth order leap frog time integration scheme moreover the interpolation degree is defined at the element level and the mesh is refined locally in a non conforming way resulting in arbitrary level hanging nodes the method is proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities numerical experiments with high order elements show the potential of the method

brief paper state feedback stabilization of linear impulsive systems we address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily spaced impulse times and possibly singular state transition matrices specifically we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed loop system the approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well known results for time varying linear systems for both continuous and discrete time cases

plurality and resemblance in fmri data analysis abstract we apply nine analytic methods employed currently in imaging neuroscience to simulated and actual bold fmri signals and compare their performances under each signal type starting with baseline time series generated by a resting subject during a null hypothesis study we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple convolved with spatially varying hemodynamic responses and highly spatially interactive we then apply these same nine methods to bold fmri time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study paired comparisons of results across methods include a voxel specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces receiver operating characteristic curves show considerable model differences in ranges less than 10 significance level false positives and greater than 80 power true positives concordance and resemblance measures reveal significant differences between activity surfaces in both data sets these measures can assist researchers by identifying groups of models producing similar and dissimilar results and thereby help to validate consolidate and simplify reports of statistical findings a pluralistic strategy for fmri data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain behavior relationships that may remain hidden if only a single method is employed

margin maximizing feature elimination methods for linear and nonlinear kernel based discriminant functions feature selection for classification in high dimensional spaces can improve generalization reduce classifier complexity and identify important discriminating feature markers for support vector machine svm classification a widely used technique is recursive feature elimination rfe we demonstrate that rfe is not consistent with margin maximization central to the svm learning approach we thus propose explicit margin based feature elimination mfe for svms and demonstrate both improved margin and improved generalization compared with rfe moreover for the case of a nonlinear kernel we show that rfe assumes that the squared weight vector 2 norm is strictly decreasing as features are eliminated we demonstrate this is not true for the gaussian kernel and consequently rfe may give poor results in this case mfe for nonlinear kernels gives better margin and generalization we also present an extension which achieves further margin gains by optimizing only two degrees of freedom the hyperplane s intercept and its squared 2 norm with the weight vector orientation fixed we finally introduce an extension that allows margin slackness we compare against several alternatives including rfe and a linear programming method that embeds feature selection within the classifier design on high dimensional gene microarray data sets university of california at irvine uci repository data sets and alzheimer s disease brain image data mfe methods give promising results

an asynchronous spacetime discontinuous galerkin finite element method for time domain electromagnetics abstract we present an asynchronous spacetime discontinuous galerkin asdg method for time domain electromagnetics in which space and time are directly discretized by using differential forms we express maxwell s equations and consequently their discontinuous galerkin discretization for arbitrary domains in spacetime the elements are discretized with electric and magnetic basis functions that are discontinuous across all inter element boundaries and can have arbitrary high and per element spacetime orders when restricted to unstructured grids that satisfy a specific causality constraint the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements we numerically investigate the convergence properties of the method for 1d to 3d uniform grids for energy dissipation an error relative to the exact solution and von neumann dissipation and dispersion errors two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts

linear and nonlinear projective nonnegative matrix factorization a variant of nonnegative matrix factorization nmf which was proposed earlier is analyzed here it is called projective nonnegative matrix factorization pnmf the new method approximately factorizes a projection matrix minimizing the reconstruction error into a positive low rank matrix and its transpose the dissimilarity between the original data matrix and its approximation can be measured by the frobenius matrix norm or the modified kullback leibler divergence both measures are minimized by multiplicative update rules whose convergence is proven for the first time enforcing orthonormality to the basic objective is shown to lead to an even more efficient update rule which is also readily extended to nonlinear cases the formulation of the pnmf objective is shown to be connected to a variety of existing nmf methods and clustering approaches in addition the derivation using lagrangian multipliers reveals the relation between reconstruction and sparseness for kernel principal component analysis pca with the binary constraint useful in graph partitioning problems the nonlinear kernel pnmf provides a good approximation which outperforms an existing discretization approach empirical study on three real world databases shows that pnmf can achieve the best or close to the best in clustering the proposed algorithm runs more efficiently than the compared nmf methods especially for high dimensional data moreover contrary to the basic nmf the trained projection matrix can be readily used for newly coming samples and demonstrates good generalization

a hybridizable discontinuous galerkin method combined to a schwarz algorithm for the solution of 3d time harmonic maxwell s equation a schwarz type domain decomposition method is presented for the solution of the system of 3d time harmonic maxwell s equations we introduce a hybridizable discontinuous galerkin hdg scheme for the discretization of the problem based on a tetrahedrization of the computational domain the discrete system of the hdg method on each subdomain is solved by an optimized sparse direct lu factorization solver the solution of the interface system in the domain decomposition framework is accelerated by a krylov subspace method the formulation and the implementation of the resulting dd hdg domain decomposed hybridizable discontinuous galerkin method are detailed numerical results show that the resulting dd hdg solution strategy has an optimal convergence rate and can save both cpu time and memory cost compared to a classical upwind flux based dd dg domain decomposed discontinuous galerkin approach

evaluation of spatio temporal decomposition techniques for group analysis of fmri resting state data sets the existing functional connectivity assessment techniques rely on different mathematical and neuro physiological models they may consequently provide different sets of spatial connectivity maps and associated temporal responses within their significant spatiotemporal sets of components note that the word component is used to generically refer to spatio temporal pairs of maps and associated time courses such differences may confound the application of functional connectivity measurements in neuroscientific and clinical applications using several performance metrics we evaluated six fmri resting state connectivity measurement techniques including three fully exploratory techniques 1 melodic independent component analysis ica 2 agnostic canonical variates analysis acva and 3 generalized canonical correlation analysis gcca and three seed based techniques 1 seed gcca sgcca and 2 3 seed partial least squares spls with a posterior cingulate seed and two different time series normalizations we separately assessed the temporal and spatial domains for 1 technique stability as a function of sample size using rv coefficients and 2 subspace component similarity between pairs of techniques using cca overall gcca was the only technique that displayed high temporal and spatial stabilities together with high spatial and temporal subspace similarities with multiple other techniques ica acva and sgcca tended to be the most stable spatially and produced similar spatial subspaces all techniques produced relatively unstable and dissimilar temporal subspaces except spls that produced relatively high temporal and lower spatial subspace stabilities but with unique power spectral hurst coefficients 1 our results indicate that spatial maps from resting state data sets are much less dependent on the analysis technique used than are the associated time series such temporal variability is coupled with individual spatial component maps which may be quite dissimilar across techniques even with similar spatial subspaces therefore we suggest that consensus estimation approaches i e a 2nd level gcca would have great utility to produce and aid interpretation of stable results from bold fmri resting state data analysis

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

finite time observer design for nonlinear impulsive systems with impact perturbation this paper investigates the observer design problem of nonlinear impulsive systems with impact perturbation by using the concept of normal form this paper proposes a full order finite time observer which guarantees the finite time convergence independent of the impact perturbation reduced order observer is additionally developed for the proposed normal form an illustrative example is given in order to illustrate the capability of the proposed method

model sparsity and brain pattern interpretation of classification models in neuroimaging interest is increasing in applying discriminative multivariate analysis techniques to the analysis of functional neuroimaging data model interpretation is of great importance in the neuroimaging context and is conventionally based on a brain map derived from the classification model in this study we focus on the relative influence of model regularization parameter choices on both the model generalization the reliability of the spatial patterns extracted from the classification model and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment for a support vector machine logistic regression and fisher s discriminant analysis we demonstrate that selection of model regularization parameters has a strong but consistent impact on the generalizability and both the reproducibility and interpretable sparsity of the models for both 2 and 1 regularization importantly we illustrate a trade off between model spatial reproducibility and prediction accuracy we show that known parts of brain networks can be overlooked in pursuing maximization of classification accuracy alone with either 2 and or 1 regularization this supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy our results instead suggest that model regularization parameters must be carefully selected so that the model and its visualization enhance our ability to interpret the brain

discriminative wavelet shape descriptors for recognition of 2 d patterns in this paper we present a set of wavelet moment invariants together with a discriminative feature selection method for the classification of seemingly similar objects with subtle di erences these invariant features are selected automatically based on the discrimination measures defined for the invariant features using a minimum distance classifier our wavelet moment invariants achieved the highest classification rate for all four di erent sets tested compared with zernike s moment invariants and li s moment invariants for a test set consisting of 26 upper cased english letters wavelet moment invariants could obtain 100 classification rate when applied to 26 30 randomly generated noisy and scaled letters whereas zernike s moment invariants and li s moment invariants obtained only 98 7 and 75 3 respectively the theoretical and experimental analyses in this paper prove that the proposed method has the ability to classify many types of image objects and is particularly suitable for classifying seemingly similar objects with subtle di erences 1999 pattern recognition society published by elsevier science ltd all rights reserved

nonnegative decomposition of functional count data we present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization our decomposition which we refer to as narfd nonnegative and regularized function decomposition enables the study of patterns in variation across subjects in a highly interpretable manner prototypic modes of variation are estimated directly on the observed scale of the data are local and are transparently added together to reconstruct observed functions this contrasts with generalized functional principal component analysis an alternative approach that estimates functional principal components on a transformed scale produces components that typically vary across the entire functional domain and reconstructs observations using complex patterns of cancellation and multiplication of functional principal components narfd is implemented using an alternating minimization algorithm and we evaluate our approach in simulations we apply narfd to an accelerometer dataset comprising observations of physical activity for healthy older americans

application of principal component analysis to distinguish patients with schizophrenia from healthy controls based on fractional anisotropy measurements principal component analysis pca is often used to reduce the dimension of data before applying more sophisticated data analysis methods such as non linear classification algorithms or independent component analysis this practice is based on selecting components corresponding to the largest eigenvalues if the ultimate goal is separation of data in two groups then these set of components need not have the most discriminatory power we measured the distance between two such populations using mahalanobis distance and chose the eigenvectors to maximize it a modified pca method which we call the discriminant pca dpca dpca was applied to diffusion tensor based fractional anisotropy images to distinguish age matched schizophrenia subjects from healthy controls the performance of the proposed method was evaluated by the one leave out method we show that for this fractional anisotropy data set the classification error with 60 components was close to the minimum error and that the mahalanobis distance was twice as large with dpca than with pca finally by masking the discriminant function with the white matter tracts of the johns hopkins university atlas we identified left superior longitudinal fasciculus as the tract which gave the least classification error in addition with six optimally chosen tracts the classification error was zero

a reduced order discontinuous galerkin method based on pod for electromagnetic simulation this paper is concerned with the design of a reduced order discontinuous galerkin dg method based on the proper orthogonal decomposition pod method for electromagnetic simulation a centered flux approximation for surface integral and a second order leap frog scheme for advancing in time are applied in the classical dg method the pod basis is created by the eigensystem of the correlation matrix which is generated by the snapshot matrix whose columns are the snapshot vectors extracted from the high fidelity dg simulation the pod discontinuous galerkin time domain formulation with lower dimension and sufficiently high accuracy is established by applying a galerkin projection for the semidiscrete dg scheme the overall goal is to reduce the computational cost while maintaining an acceptable level of accuracy numerical experiments for electromagnetic problems illustrate the performance of the proposed reduction method

remarks on the time varying h riccati equations in this paper we establish some useful properties of three riccati equations appearing in the standard h control problems for continuous and discrete time time varying systems we then give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent riccati equations with a coupling inequality

hammer hierarchical attribute matching mechanism for elastic registration a new approach is presented for elastic registration of medical images and is applied to magnetic resonance images of the brain experimental results demonstrate very high accuracy in superposition of images from different subjects there are two major novelties in the proposed algorithm first it uses an attribute vector i e a set of geometric moment invariants gmis that are defined on each voxel in an image and are calculated from the tissue maps to reflect the underlying anatomy at different scales the attribute vector if rich enough can distinguish between different parts of an image which helps establish anatomical correspondences in the deformation procedure it also helps reduce local minima by reducing ambiguity in potential matches this is a fundamental deviation of our method referred to as the hierarchical attribute matching mechanism for elastic registration hammer from other volumetric deformation methods which are typically based on maximizing image similarity second in order to avoid being trapped by local minima i e suboptimal poor matches hammer uses a successive approximation of the energy function being optimized by lower dimensional smooth energy functions which are constructed to have significantly fewer local minima this is achieved by hierarchically selecting the driving features that have distinct attribute vectors thus drastically reducing ambiguity in finding correspondence a number of experiments demonstrate that the proposed algorithm results in accurate superposition of image data from individuals with significant anatomical differences

measuring size and shape of the hippocampus in mr images using a deformable shape model a method for segmentation and quantification of the shape and size of the hippocampus is proposed based on an automated image analysis algorithm the algorithm uses a deformable shape model to locate the hippocampus in magnetic resonance images and to determine a geometric representation of its boundary the deformable model combines three types of information first it employs information about the geometric properties of the hippocampal boundary from a local and relatively finer scale to a more global and relatively coarser scale second the model includes a statistical characterization of normal shape variation across individuals serving as prior knowledge to the algorithm third the algorithm utilizes a number of manually defined boundary points which can help guide the model deformation to the appropriate boundaries wherever these boundaries are weak or not clearly defined in mr images excellent agreement is demonstrated between the algorithm and manual segmentations by well trained raters with a correlation coefficient equal to 0 97 and algorithm rater differences statistically equivalent to interrater differences for manual definitions

characterizing the response of pet and fmri data using multivariate linear models this paper presents a new method for characterizing brain responses in both pet and fmri data the aim is to capture the correlations between the scans of an experiment and a set of external predictor variables that are thought to affect the scans such as type intensity or shape of stimulus response its main feature is a canonical variates analysis cva of the estimated effects of the predictors from a multivariate linear model mlm the advantage of this over current methods is that temporal correlations can be incorporated into the model making the mlm method suitable for fmri as well as pet data moreover tests for the presence of any correlation and inference about the number of canonical variates needed to capture that correlation can be based on standard multivariate statistics rather than simulations when applied to an fmri data set previously analyzed by another cva method the mlm method reveals a pattern of responses that is closer to that detected in an earlier non cva analysis

estimation of the intrinsic dimensionality of fmri data a new method based on an autoregressive noise model of order 1 is introduced to the problem of detecting the number of components in fmri data unlike current information theoretic criteria like aic mdl and related ppca which do not incorporate autocorrelations in the noise the new method leads to more consistent estimates of the model order as illustrated in simulated and real fmri resting state data

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

hierarchical unbiased graph shrinkage hugs a novel groupwise registration for large data set normalizing all images in a large data set into a common space is a key step in many clinical and research studies e g for brain development maturation and aging recently groupwise registration has been developed for simultaneous alignment of all images without selecting a particular image as template thus potentially avoiding bias in the registration however most conventional groupwise registration methods do not explore the data distribution during the image registration thus their performance could be affected by large inter subject variations in the data set under registration to solve this potential issue we propose to use a graph to model the distribution of all image data sitting on the image manifold with each node representing an image and each edge representing the geodesic pathway between two nodes or images then the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other thus the topology of image distribution on the image manifold is always preserved during the groupwise registration more importantly by modeling the distribution of all images via a graph we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph we have evaluated our proposed groupwise registration method on both infant and adult data sets by also comparing with the conventional group mean based registration and the absorb methods all experimental results show that our proposed method can achieve better performance in terms of registration accuracy and robustness

a staggered fourth order accurate explicit finite difference scheme for the time domain maxwell s equations abstract we consider a model explicit fourth order staggered finite difference method for the hyperbolic maxwell s equations appropriate fourth order accurate extrapolation and one sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces an eigenvalue analysis of the overall scheme provides a necessary but not sufficient stability condition and indicates long time stability numerical results verify both the stability analysis and the scheme s fourth order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces for a fixed error level we find the fourth order scheme is computationally cheaper in comparison to the yee scheme by more than an order of magnitude some open problems encountered in the application of such high order schemes are also discussed

conservative space time mesh refinement methods for the fdtd solution of maxwell s equations a new variational space time mesh refinement method is proposed for the fdtd solution of maxwell s equations the main advantage of this method is to guarantee the conservation of a discrete energy that implies that the scheme remains l 2 stable under the usual cfl condition the only additional cost induced by the mesh refinement is the inversion at each time step of a sparse symmetric positive definite linear system restricted to the unknowns located on the interface between coarse and fine grid the method is presented in a rather general way and its stability is analyzed an implementation is proposed for the yee scheme in this case various numerical results in 3 d are presented in order to validate the approach and illustrate the practical interest of space time mesh refinement methods

collective sparse symmetric non negative matrix factorization for identifying overlapping communities in resting state brain functional networks resting state functional magnetic resonance imaging rs fmri provides a valuable tool to study spontaneous brain activity using rs fmri researchers have extensively studied the organization of the brain functional network and found several consistent communities consisting of functionally connected but spatially separated brain regions across subjects however increasing evidence in many disciplines has shown that most realistic complex networks have overlapping community structure only recently has the overlapping community structure drawn increasing interest in the domain of brain network studies another issue is that the inter subject variability is often not directly reflected in the process of community detection at the group level in this paper we propose a novel method called collective sparse symmetric non negative matrix factorization cssnmf to address these issues the cssnmf approach identifies the group level overlapping communities across subjects and in the meantime preserves the information of individual variation in brain functional network organization to comprehensively validate cssnmf a simulated fmri dataset with ground truth a real rs fmri dataset with two repeated sessions and another different real rs fmri dataset have been used for performance comparison in the experiment experimental results show that the proposed cssnmf method accurately and stably identifies group level overlapping communities across subjects as well as individual differences in network organization with neurophysiologically meaningful interpretations this research extends our understanding of the common underlying community structures and individual differences in community strengths in brain functional network organization

boundary finding with prior shape and smoothness models we propose a unified framework for boundary finding where a bayesian formulation based on prior knowledge and the edge information of the input image likelihood is employed the prior knowledge in our framework is based on principal component analysis of four different covariance matrices corresponding to independence smoothness statistical shape and combined models respectively indeed snakes modal analysis fourier descriptors and point distribution models can be derived from or linked to our approaches of different prior models when the true training set does not contain enough variability to express the full range of deformations a mixed covariance matrix uses a combined prior of the smoothness and statistical variation modes it adapts gradually to use more statistical modes of variation as larger data sets are available

svd based initialization a head start for nonnegative matrix factorization we describe nonnegative double singular value decomposition nndsvd a new method designed to enhance the initialization stage of nonnegative matrix factorization nmf nndsvd can readily be combined with existing nmf algorithms the basic algorithm contains no randomization and is based on two svd processes one approximating the data matrix the other approximating positive sections of the resulting partial svd factors utilizing an algebraic property of unit rank matrices simple practical variants for nmf with dense factors are described nndsvd is also well suited to initialize nmf algorithms with sparse factors many numerical examples suggest that nndsvd leads to rapid reduction of the approximation error of many nmf algorithms

h control of multirate sampled data systems a state space approach a state space solution of the h control problem for periodic multirate sampled data systems is presented the solution is characterized in terms of a pair of discrete algebraic riccati equations with a set of associated matrix positive definiteness conditions and coupling criteria the solution is derived using two different approaches in the first approach the solution is obtained by discretizing two coupled periodic riccati equations with jumps which characterize the h optimal controller the second approach is based on the lifting technique the h optimal controller for a lifted representation of the multirate system is characterized by a two riccati equation solution in which the so called causality constraint is represented by a set of positive definiteness conditions and coupling criteria

nonlinear denoising and analysis of neuroimages with kernel principal component analysis and pre image estimation we investigate the use of kernel principal component analysis pca and the inverse problem known as pre image estimation in neuroimaging i we explore kernel pca and pre image estimation as a means for image denoising as part of the image preprocessing pipeline evaluation of the denoising procedure is performed within a data driven split half evaluation framework ii we introduce manifold navigation for exploration of a nonlinear data manifold and illustrate how pre image estimation can be used to generate brain maps in the continuum between experimentally defined brain states classes we base these illustrations on two fmri bold data sets one from a simple finger tapping experiment and the other from an experiment on object recognition in the ventral temporal lobe

adaptive normalization of handwritten characters using global local affine transformation this paper introduces an adaptive or category dependent normalization method that normalizes an input pattern against each reference pattern using global local affine transformation gat lat in a hierarchical manner as a general deformation model also the normalization criterion is clearly defined as minimization of the mean of nearest neighbor interpoint distances between each reference pattern and a normalized input pattern optimal gat lat is determined by iterative application of weighted least squares fitting techniques experiments using input patterns of 3 171 character categories including kanji kana and alphanumerics written by 36 people in the cursive style against square style reference patterns show that the proposed method not only can absorb a fairly large amount of handwriting fluctuation within the same category but the discrimination ability is greatly improved by the suppression of excessive normalization against similarly shaped but different categories furthermore comparative results obtained by the conventional shape normalization method for preprocessing are presented

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

a framework for callosal fiber distribution analysis this paper presents a framework for analyzing the spatial distribution of neural fibers in the brain with emphasis on interhemispheric fiber bundles crossing through the corpus callosum the proposed approach combines methodologies for fiber tracking and spatial normalization and is applied on diffusion tensor images and standard magnetic resonance images

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

multirate observers for nonlinear sampled data systems using input to state stability and discrete time approximation this paper is devoted to the problem of nonlinear state estimation under multirate sampling in presence of disturbance inputs considering a general description of a nonlinear sampled data system we establish a prescriptive framework for multirate observer design via an approximate discrete time model of the plant this framework is shown to be input to state stable in a semiglobal practical sense with respect to the estimation error for the unknown exact discrete time model a numerical example of an aerospace vehicle with input and output channels of various sampling rates demonstrates how the multirate observer can drastically improve performance compared with the single rate observer

a parallel non conforming multi element dgtd method for the simulation of electromagnetic wave interaction with metallic nanoparticles the present work is about the development of a parallel non conforming multi element discontinuous galerkin time domain dgtd method for the simulation of the scattering of electromagnetic waves by metallic nanoparticles such nanoparticles most often have curvilinear shapes therefore we propose a numerical modeling strategy which combines the use of an unstructured tetrahedral mesh for the discretization of the scattering structures with a structured uniform cartesian mesh for treating efficiently the rest of the domain the overall goal is to increase the flexibility in the meshing process while decreasing the needs in computational resources for the target applications the latter are here modeled by the system of 3d time domain maxwell equations coupled to a drude dispersion model for taking into account the material properties of nanoparticles at optical frequencies we propose an auxiliary differential equation ade based dgtd method for solving the resulting system and present numerical results demonstrating the benefits of using non conforming multi element meshes in this particular application context

probabilistic independent component analysis for functional magnetic resonance imaging we present an integrated approach to probabilistic independent component analysis ica for functional mri fmri data that allows for nonsquare mixing in the presence of gaussian noise in order to avoid overfitting we employ objective estimation of the amount of gaussian noise through bayesian analysis of the true dimensionality of the data i e the number of activation and non gaussian noise sources this enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data it reduces problems of interpretation as each final independent component is now much more likely to be due to only one physical or physiological process we also describe other improvements to standard ica such as temporal prewhitening and variance normalization of timeseries the latter being particularly useful in the context of dimensionality reduction when weak activation is present we discuss the use of prior information about the spatiotemporal nature of the source processes and an alternative hypothesis testing approach for inference using gaussian mixture models the performance of our approach is illustrated and evaluated on real and artificial fmri data and compared to the spatio temporal accuracy of results obtained from classical ica and glm analyses

nonrigid image registration with crystal dislocation energy the goal of nonrigid image registration is to find a suitable transformation such that the transformed moving image becomes similar to the reference image the image registration problem can also be treated as an optimization problem which tries to minimize an objective energy function that measures the differences between two involved images in this paper we consider image matching as the process of aligning object boundaries in two different images the registration energy function can be defined based on the total energy associated with the object boundaries the optimal transformation is obtained by finding the equilibrium state when the total energy is minimized which indicates the object boundaries find their correspondences and stop deforming we make an analogy between the above processes with the dislocation system in physics the object boundaries are viewed as dislocations line defects in crystal then the well developed dislocation energy is used to derive the energy assigned to object boundaries in images the newly derived registration energy function takes the global gradient information of the entire image into consideration and produces an orientation dependent and long range interaction between two images to drive the registration process this property of interaction endows the new registration framework with both fast convergence rate and high registration accuracy moreover the new energy function can be adapted to realize symmetric diffeomorphic transformation so as to ensure one to one matching between subjects in this paper the superiority of the new method is theoretically proven experimentally tested and compared with the state of the art syn method experimental results with 3 d magnetic resonance brain images demonstrate that the proposed method outperforms the compared methods in terms of both registration accuracy and computation time

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

composition methods maxwell s equations and source terms this paper is devoted to high order numerical time integration of first order wave equation systems originating from spatial discretization of maxwell s equations the focus lies on the accuracy of high order composition in the presence of source functions source functions are known to generate order reduction and this is most severe for high order methods for two methods based on two well known fourth order symmetric compositions convergence results are given assuming simultaneous space time grid refinement herewith physical sources and source functions emanating from dirichlet boundary conditions are distinguished among other things it is shown that the reduction can cost two orders on the other hand when a certain perturbation of a source function is used the reduction is generally diminished by one order in that case reduction is absent for physical sources and for dirichlet sources the order is equal to at least three under stable simultaneous space time grid refinement

penalized discriminant analysis of sup 15 o water pet brain images with prediction error selection of smoothness and regularization hyperparameters the authors propose a flexible comprehensive approach for analysis of sup 15 o water positron emission tomography pet brain images using a penalized version of linear discriminant analysis pda they applied it to scans from 20 subjects eight scans subject performing a finger movement task and analyzed 1 two classes to obtain a covariance normalized baseline activation image and 2 eight classes for the mean within subject temporal structure which contained baseline activation and time dependent changes in a two dimensional canonical subspace the authors imposed spatial smoothness on the resulting image s by expanding it in five tensor product b spline tps bases of varying smoothness and further regularized with a ridge type penalty on the noise covariance matrix the discrimination approach of pda provides a probabilistic framework within which prediction error pe estimates are derived the authors used these to optimize over tps bases and a ridge hyperparameter expressed as equivalent degrees of freedom edf they obtained unbiased low variance pe estimates using modern resampling tools 632 bootstrap and cross validation and compared pda of 1 tps projected mean normalized and unnormalized scans and 2 mean normalized scans with and without additional presmoothing by examining the tradeoffs between pe and edf as a function of basis selection and image smoothing the authors demonstrate the utility of pda the pe framework and the relationship between singular value decomposition and smooth tps bases in the analysis of functional neuroimages

on the constants in hp finite element trace inverse inequalities we derive inverse trace inequalities for hp finite elements utilizing orthogonal polynomials we show how to derive explicit expressions for the constants when considering triangular and tetrahedral elements we also discuss how to generalize this technique to the general d simplex

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

group analysis in functional neuroimaging selecting subjects using similarity measures standard group analyses of fmri data rely on spatial and temporal averaging of individuals this averaging operation is only sensible when the mean is a good representation of the group this is not the case if subjects are not homogeneous and it is therefore a major concern in fmri studies to assess this group homogeneity we present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects the method allows a multivariate comparison between data sets of several subjects in the time or in the space domain these analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects at the population level we adapt the rv coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject s position with respect to other subjects in the group we also provide a measure for detecting subjects that may be outliers results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns and that despite the apparent loss of information restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fmri analyses

using a deformable surface model to obtain a shape representation of the cortex this paper examines the problem of obtaining a mathematical representation of the outer cortex of the human brain which is a key problem in several applications including morphological analysis of the brain and spatial normalization and registration of brain images a parameterization of the outer cortex is first obtained using a deformable surface algorithm which motivated by the structure of the cortex is constructed to find the central layer of thick surfaces based on this parameterization a hierarchical representation of the outer cortical structure is proposed through its depth map and its curvature maps at various scales various experiments on magnetic resonance data are presented

structure seeking multilinear methods for the analysis of fmri data in comprehensive fmri studies of brain function the data structures often contain higher order ways such as trial task condition subject and group in addition to the intrinsic dimensions of time and space while multivariate bilinear methods such as principal component analysis pca have been used successfully for extracting information about spatial and temporal features in data from a single fmri run the need to unfold higher order data sets into bilinear arrays has led to decompositions that are nonunique and to the loss of multiway linkages and interactions present in the data these additional dimensions or ways can be retained in multilinear models to produce structures that are unique and which admit interpretations that are neurophysiologically meaningful multiway analysis of fmri data from multiple runs of a bilateral finger tapping paradigm was performed using the parallel factor parafac model a trilinear model was fitted to a data cube of dimensions voxels by time by run similarly a quadrilinear model was fitted to a higher way structure of dimensions voxels by time by trial by run the spatial and temporal response components were extracted and validated by comparison to results from traditional svd pca analyses based on scenarios of unfolding into lower order bilinear structures

dimensionality estimation for optimal detection of functional networks in bold fmri data estimation of the intrinsic dimensionality of fmri data is an important part of data analysis that helps to separate the signal of interest from noise we have studied multiple methods of dimensionality estimation proposed in the literature and used these estimates to select a subset of principal components that was subsequently processed by linear discriminant analysis lda using simulated multivariate gaussian data we show that the dimensionality that optimizes signal detection in terms of the receiver operating characteristic roc metric goes through a transition from many dimensions to a single dimension as a function of the signal to noise ratio this transition happens when the loci of activation are organized into a spatial network and the variance of the networked task related signals is high enough for the signal to be easily detected in the data we show that reproducibility of activation maps is a metric that captures this switch in intrinsic dimensionality except for reproducibility all of the methods of dimensionality estimation we considered failed to capture this transition optimization of bayesian evidence minimum description length supervised and unsupervised lda prediction and stein s unbiased risk estimator this failure results in sub optimal roc performance of lda in the presence of a spatially distributed network and may have caused lda to underperform in many of the reported comparisons in the literature using real fmri data sets including multi subject group and within subject longitudinal analysis we demonstrate the existence of these dimensionality transitions in real data

dimension estimation in noisy pca with sure and random matrix theory principal component analysis pca is one of the best known methods for dimensionality reduction perhaps the most important problem in using pca is to determine the number of principal components pcs or equivalently choose the rank of the loading matrix many methods have been proposed to deal with this problem but almost all of them fail in the important practical case when the number of observation is comparable to the number of variables i e the realm of random matrix theory rmt in this paper we propose to use stein s unbiased risk estimator sure to estimate with some assistance from rmt the number of principal components the method is applied both on simulated and real functional magnetic resonance imaging fmri data and compared to bic and the laplace method

model selection for gaussian kernel pca denoising we propose kernel parallel analysis kpa for automatic kernel scale and model order selection in gaussian kernel principal component analysis kpca parallel analysis is based on a permutation test for covariance and has previously been applied for model order selection in linear pca we here augment the procedure to also tune the gaussian kernel scale of radial basis function based kpca we evaluate kpa for denoising of simulated data and the u s postal data set of handwritten digits we find that kpa outperforms other heuristics to choose the model order and kernel scale in terms of signal to noise ratio of the denoised data

an lmi solution to the robust synthesis problem for multi rate sampled data systems in this paper we address the asynchronous multi rate sampled data h synthesis problem necessary and sufficient conditions are given for the existence of a controller achieving the desired performance and the problem is shown to be equivalent to a convex optimization problem expressed in the form of linear operator inequalities in the case where the sample and hold rates are synchronous these operator inequalities reduce to linear matrix inequalities for which standard numerical software is available

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

a reduced order dg formulation based on pod method for the time domain maxwell s equations in dispersive media abstract in this work a proper orthogonal decomposition pod method is applied to time domain maxwell s equations coupled to a drude dispersion model which are discretized in space by a discontinuous galerkin dg method an auxiliary differential equation ade method is used to represent the constitutive relation for the dispersive medium a pod dgtd formulation with lower dimension and sufficiently high accuracy is established together with the description of the pod reduced order basis its construction from a snapshot set and its application to the solution of the time domain maxwell s equations the overall goal is to reduce the computational time while maintaining an acceptable level of accuracy in order to obtain an efficient time domain solver to be used as a starting point for an optimization strategy we provide results from numerical experiments for two dimensional problems that illustrate the capabilities of the proposed pod dgtd formulation and assess its efficiency

a staggered upwind embedded boundary sueb method to eliminate the fdtd staircasing error in spite of its flexibility and second order accuracy in a homogeneous medium yee s finite difference time domain fdtd method suffers from serious degradation when treating material interfaces greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors indeed such so called staircasing approximation may lead to local zeroth order and global first order errors in this work an embedded fdtd scheme the staggered upwind embedded boundary sueb method is developed for the solution of oneand two dimensional maxwell s equations this simple embedded technique uses upwind conditions in the fdtd method to correctly represent the location and physical conditions of material and metallic boundaries hence eliminating problems caused by the staircasing approximation accuracy analysis has been made to show that the sueb method maintains a second order accuracy globally since the entire problem has been embedded into the simple staggered grid similar to that employed by the yee s scheme extra effort is only needed when treating the grid points close to the interfaces therefore little additional computational cost is needed over yee s scheme the sueb method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the tm wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder

rism single modal image registration via rank induced similarity measure similarity measure is an important block in image registration most traditional intensity based similarity measures e g sum of squared difference correlation coefficient and mutual information assume a stationary image and pixel by pixel independence these similarity measures ignore the correlation between pixel intensities hence perfect image registration cannot be achieved especially in the presence of spatially varying intensity distortions here we assume that spatially varying intensity distortion such as bias field is a low rank matrix based on this assumption we formulate the image registration problem as a nonlinear and low rank matrix decomposition nllrmd therefore image registration and correction of spatially varying intensity distortion are simultaneously achieved we illustrate the uniqueness of nllrmd and therefore we propose the rank of difference image as a robust similarity in the presence of spatially varying intensity distortion finally by incorporating the gaussian noise we introduce rank induced similarity measure based on the singular values of the difference image this measure produces clinically acceptable registration results on both simulated and real world problems examined in this paper and outperforms other state of the art measures such as the residual complexity approach

gyral folding pattern analysis via surface profiling folding is an essential shape characteristic of the human cerebral cortex descriptors of cortical folding patterns have been studied for decades however many previous studies are either based on local shape descriptors such as curvature or based on global descriptors such as gyrification index or spherical wavelets this paper proposes a gyrus scale folding pattern analysis technique via cortical surface profiling firstly we sample the cortical surface into 2d profiles and model them using a power function this step provides both the flexibility of representing arbitrary shape by profiling and the compactness of representing shape by parametric modeling secondly based on the estimated model parameters we extract affine invariant features on the cortical surface and apply the affinity propagation clustering algorithm to parcellate the cortex into cortical regions with strict hierarchy and smooth transitions among them finally a second round surface profiling is performed on the parcellated cortical surface and the number of hinges is detected to describe the gyral folding pattern we have applied the surface profiling method to two normal brain datasets and a schizophrenia patient dataset the experimental results demonstrate that the proposed method can accurately classify human gyri into 2 hinge 3 hinge and 4 hinge patterns the distribution of these folding patterns on brain lobes and the relationship between fiber density and gyral folding patterns are further investigated results from the schizophrenia dataset are consistent with commonly found abnormality in former studies by others which demonstrates the potential clinical applications of the proposed technique

a spatial high order hexahedral discontinuous galerkin method to solve maxwell s equations in time domain in this paper we present a non dissipative spatial high order discontinuous galerkin method to solve the maxwell equations in the time domain the non intuitive choice of the space of approximation and the basis functions induce an important gain for mass stiffness and jump matrices in terms of memory this spatial approximation combined with a leapfrog scheme in time leads also to a fast explicit and accurate method a study of the dispersive error is carried out and a stability condition for the proposed scheme is established some comparisons with other schemes are presented to validate the new scheme and to point out its advantages finally in order to improve the efficiency of the method in terms of cpu time on general unstructured meshes a strategy of local time stepping is proposed

generalizable patterns in neuroimaging how many principal components generalization can be defined quantitatively and can be used to assess the performance of principal component analysis pca the generalizability of pca depends on the number of principal components retained in the analysis we provide analytic and test set estimates of generalization we show how the generalization error can be used to select the number of principal components in two analyses of functional magnetic resonance imaging activation sets

high order non conforming multi element discontinuous galerkin method for time domain electromagnetics we study a high order discontinuous galerkin time domain dgtd method for solving the system of maxwell equations this method is formulated on a non conforming multi element mesh mixing an unstructured triangulation for the discretization of irregularly shaped objects with a structured cartesian quadrangulation for the rest of the computational domain within each element the electromagnetic field components are approximated by a high order nodal polynomial the dg method proposed here makes use of a centered scheme for the definition of the numerical traces of the electric and magnetic fields at element interfaces associated to a second order or fourth order leap frog scheme for the time integration of the associated semi discrete equations we formulate this dgtd method in 3d and study its theoretical properties in particular an a priori convergence estimation is elaborated finally we present numerical results for the application of the method to 2d test problems

orthogonal moment features for use with parametric and non parametric classifiers this research examines a variety of approaches for using two dimensional orthogonal polynomials for the recognition of handwritten arabic numerals it also makes use of parametric and non parametric statistical and neural network classifiers polynomials including legendre zernike and pseudo zernike are used to generate moment based features which are invariant to location size and optionally rotation an efficient method for computing the moments via geometric moments is presented a side effect of this method also yields scale invariance a new approach to location invariance using a minimum bounding circle is presented and a detailed analysis of the rotational properties of the moments is given data partitioning tests are performed to evaluate the various feature types and classifiers for rotational invariant character recognition the highest percentage of correctly classified characters was 91 7 and for non rotational invariant recognition it was 97 6 this compares with a previous effort using the same data and test conditions of 94 8 the techniques developed here should also be applicable to other areas of shape recognition

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

intermediate templates guided groupwise registration of diffusion tensor images registration of a population of diffusion tensor images dtis is one of the key steps in medical image analysis and it plays an important role in the statistical analysis of white matter related neurological diseases however pairwise registration with respect to a pre selected template may not give precise results if the selected template deviates significantly from the distribution of images to cater for more accurate and consistent registration a novel framework is proposed for groupwise registration with the guidance from one or more intermediate templates determined from the population of images specifically we first use a euclidean distance defined as a combinative measure based on the fa map and adc map for gauging the similarity of each pair of dtis a fully connected graph is then built with each node denoting an image and each edge denoting the distance between a pair of images the root template image is determined automatically as the image with the overall shortest path length to all other images on the minimum spanning tree mst of the graph finally a sequence of registration steps is applied to progressively warping each image towards the root template image with the help of intermediate templates distributed along its path to the root node on the mst extensive experimental results using diffusion tensor images of real subjects indicate that registration accuracy and fiber tract alignment are significantly improved compared with the direct registration from each image to the root template image

a meshless local petrov galerkin method for the time dependent maxwell equations abstract in this paper the meshless local petrov galerkin mlpg method is employed to solve the 2 d time dependent maxwell equations the mlpg method is a truly meshless method in which the trial and test functions are chosen from totally different functional spaces in the current work the moving least square reproducing kernel mlsrk scheme is chosen to be the trial function the method is applied for the unsteady maxwell equations in different media in the local weak form by employing the difference operator for evolution in time and simultaneously in time and space the semi discrete and fully discrete schemes are obtained respectively the error estimation is discussed for both the semi discrete and fully discrete numerical schemes for modelling the time dependent maxwell equations we show that provided that the time step size is sufficiently small the proposed scheme yields an error of o 2 m 1 2 in the l 2 norm for the square of error the new scheme is implemented and the numerical results are provided to justify our theoretical analysis

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data

morphological appearance manifolds in computational anatomy groupwise registration and morphological analysis abstract existing approaches to computational anatomy assume that a perfectly conforming diffeomorphism applied to an anatomy of interest captures its morphological characteristics relative to a template however the amount of biological variability in a groupwise analysis renders this task practically impossible due to the nonexistence of a single template that matches all anatomies in an ensemble even if such a template is constructed by group averaging procedures consequently anatomical characteristics not captured by the transformation and which are left out in the residual image are lost permanently from subsequent analysis if only properties of the transformation are examined this paper extends our recent work makrogiannis s verma r davatzikos c 2007 anatomical equivalence class a computational anatomy framework using a lossless shape descriptor ieee trans biomed imag 26 4 619 631 on characterizing subtle morphological variations via a lossless morphological descriptor that takes the residual into account along with the transformation since there are infinitely many transformation residual pairs that reconstruct a given anatomy we treat them as members of an anatomical equivalence class aec thereby forming a manifold embedded in the space spanned by transformation residual this paper develops a unique and optimal representation of each anatomy that is estimated from the corresponding aecs by solving a global optimization problem this effectively determines the optimal template and transformation parameters for each individual anatomy and eliminates respective confounding variation in the data it therefore constitutes the second novelty in that it represents a group wise optimal registration strategy that individually adjusts the template and the smoothness of the transformation according to each anatomy experimental results support the superiority of our morphological analysis framework over conventional analysis and demonstrate better diagnostic accuracy