positive solutions for a class of multiparameter ordinary elliptic systems abstract using a fixed point theorem due to m a krasnosel skii the upper lower solutions method and fixed point index theory we study existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations we give a new notion of superlinearity for nonlinearities observe that the nonlinearities may even be in some sense singular as an application we show multiplicity results for a class of semilinear elliptic systems in both bounded annular domains and exterior domains in addition we apply our results to fourth order boundary value problems

positive solutions for higher order multi point boundary value problems with nonhomogeneous boundary conditions abstract we study nth order boundary value problems with a nonlinear term f t x subject to nonhomogeneous multi point boundary conditions criteria for the existence of positive solutions of such problems are established conditions are determined by the relationship between the behavior of f t x x near 0 and when compared with the smallest positive characteristic value of an associated linear integral operator this work improves and extends some recent results in the literature for the second order problems the results are illustrated with examples

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

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

higher order boundary value problems with nonhomogeneous boundary conditions abstract we study the following nonlinear boundary value problem with nonhomogeneous multi point boundary condition u 2 n g t f t u t 0 1 u 2 i 0 j 1 m a j u 2 i t j 1 i 2 i u 2 i 1 j 1 m b j u 2 i t j 1 i 2 i 1 i 0 n 1 sufficient conditions are obtained for the problem to have at least one positive solution and to have no solution respectively moreover under certain conditions we prove that there exists a bounded and continuous surface separating r 2 n 0 0 into two disjoint subsets e and n with e such that the problem has at least two positive solutions for each 0 2 n 1 e one positive solution for each 0 2 n 1 and no positive solution for any 0 2 n 1 n

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

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

local superlinearity for elliptic systems involving parameters abstract we study the existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations using the fixed point theorem of cone expansion compression type the upper lower solutions method and degree arguments we apply our abstract results to study semilinear elliptic systems in bounded annular domains with non homogeneous boundary conditions here the nonlinearities satisfy local superlinear assumptions

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

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

geodesic estimation for large deformation anatomical shape averaging and interpolation the goal of this research is to promote variational methods for anatomical averaging that operate within the space of the underlying image registration problem this approach is effective when using the large deformation viscous framework where linear averaging is not valid or in the elastic case the theory behind this novel atlas building algorithm is similar to the traditional pairwise registration problem but with single image forces replaced by average forces these group forces drive an average transport ordinary differential equation allowing one to estimate the geodesic that moves an image toward the mean shape configuration this model gives large deformation atlases that are optimal with respect to the shape manifold as defined by the data and the image registration assumptions we use the techniques in the large deformation context here but they also pertain to small deformation atlas construction furthermore a natural inherently inverse consistent image registration is gained for free as is a tool for constant arc length geodesic shape interpolation the geodesic atlas creation algorithm is quantitatively compared to the euclidean anatomical average to elucidate the need for optimized atlases the procedures generate improved average representations of highly variable anatomy from distinct populations

seamless warping of diffusion tensor fields to warp diffusion tensor fields accurately tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers forward mapping however can also create ldquoseamsrdquo or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large e g jacobian 1 backward mapping in contrast defines voxels in the template space by mapping them back to locations in the original imaging space backward mapping allows every voxel in the template space to be defined without the creation of seams including voxels in which the deformation is extensive backward mapping however cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original unwarped imaging space only and backward mapping alone cannot transfer that information to the template space to combine the advantages of forward and backward mapping we propose a novel method for the spatial normalization of diffusion tensor dt fields that uses a bijection a bidirectional mapping with one to one correspondences between image spaces to warp dt datasets seamlessly from one imaging space to another once the bijection has been achieved and tensors have been correctly relocated to the template space we can appropriately reorient tensors in the template space using a warping method based on procrustean estimation

diffeomorphic brain registration under exhaustive sulcal constraints the alignment and normalization of individual brain structures is a prerequisite for group level analyses of structural and functional neuroimaging data the techniques currently available are either based on volume and or surface attributes with limited insight regarding the consistent alignment of anatomical landmarks across individuals this article details a global geometric approach that performs the alignment of the exhaustive sulcal imprints cortical folding patterns across individuals this diffeomorphic sulcal based cortical disco technique proceeds to the automatic extraction identification and simplification of sulcal features from t1 weighted magnetic resonance image mri series these features are then used as control measures for fully 3 d diffeomorphic deformations quantitative and qualitative evaluations show that disco correctly aligns the sulcal folds and gray and white matter volumes across individuals the comparison with a recent iconic diffeomorphic approach dartel highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci we also feature disco in the automatic design of an empirical sulcal template from group data we also demonstrate how disco can efficiently be combined with an image based deformation dartel to further improve the consistency and accuracy of alignment performances finally we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group level analysis of neuroimaging data

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

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

maxsolver an efficient exact algorithm for weighted maximum satisfiability maximum boolean satisfiability max sat is the optimization counterpart of boolean satisfiability sat in which a variable assignment is sought to satisfy the maximum number of clauses in a boolean formula a branch and bound algorithm based on the davis putnam logemann loveland procedure dpll is one of the most competitive exact algorithms for solving max sat in this paper we propose and investigate a number of strategies for max sat the first strategy is a set of unit propagation or unit resolution rules for max sat we summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max sat the second strategy is an effective lower bound based on linear programming lp we show that the lp lower bound can be made effective as the number of clauses increases the third strategy consists of a binary clause first rule and a dynamic weighting variable ordering rule which are motivated by a thorough analysis of two existing well known variable orderings based on the analysis of these strategies we develop an exact solver for both max sat and weighted max sat our experimental results on random problem instances and many instances from the max sat libraries show that our new solver outperforms most of the existing exact max sat solvers with orders of magnitude of improvement in many cases

efficient branch and bound algorithms for weighted max 2 sat max 2 sat is one of the representative combinatorial problems and is known to be np hard given a set of m clauses on n propositional variables where each clause contains at most two literals and is weighted by a positive real max 2 sat asks to find a truth assignment that maximizes the total weight of satisfied clauses in this paper we propose branch and bound exact algorithms for max 2 sat utilizing three kinds of lower bounds all lower bounds are based on a directed graph that represents conflicts among clauses and two of them use a set covering representation of max 2 sat computational comparisons on benchmark instances disclose that these algorithms are highly effective in reducing the number of search tree nodes as well as the computation time

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

second order boundary value problems with nonhomogeneous boundary conditions ii sufficient conditions are given for the existence of solutions of the following nonlinear boundary value problem with nonhomogeneous multi point boundary condition u f t u u 0 t 0 1 u 0 i 1maiu ti 1 u 1 i 1mbiu ti 2 we prove that the whole plane r2 is divided by a continuous decreasing curve into two disjoint connected regions e and n such that the above problem has at least one solution for 1 2 has at least two solutions for 1 2 e and has no solution for 1 2 n we also find explicit subregions of e where the above problem has at least two solutions and two positive solutions respectively

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

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

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

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

registration of longitudinal brain image sequences with implicit template and spatial temporal heuristics abstract accurate measurement of longitudinal changes of brain structures and functions is very important but challenging in many clinical studies also across subject comparison of longitudinal changes is critical in identifying disease related changes in this paper we propose a novel method to meet these two requirements by simultaneously registering sets of longitudinal image sequences of different subjects to the common space without assuming any explicit template specifically our goal is to 1 consistently measure the longitudinal changes from a longitudinal image sequence of each subject and 2 jointly align all image sequences of different subjects to a hidden common space to achieve these two goals we first introduce a set of temporal fiber bundles to explore the spatial temporal behavior of anatomical changes in each longitudinal image sequence then a probabilistic model is built upon the temporal fibers to characterize both spatial smoothness and temporal continuity finally the transformation fields that connect each time point image of each subject to the common space are simultaneously estimated by the expectation maximization em approach via the maximum a posterior map estimation of the probabilistic models promising results have been obtained in quantitative measurement of longitudinal brain changes i e hippocampus volume changes showing better performance than those obtained by either the pairwise or the groupwise only registration methods

adaptive memory tabu search for binary quadratic programs recent studies have demonstrated the effectiveness of applying adaptive memory tabu search procedures to combinatorial optimization problems in this paper we describe the development and use of such an approach to solve binary quadratic programs computational experience is reported showing that the approach optimally solves the most difficult problems reported in the literature for challenging problems of limited size which are capable of being approached by exact procedures we find optimal solutions considerably faster than the best reported exact method moreover we demonstrate that our approach is significantly more efficient and yields better solutions than the best heuristic method reported to date finally we give outcomes for larger problems that are considerably more challenging than any currently reported in the literature

anatomical equivalence class a morphological analysis framework using a lossless shape descriptor methods of computational anatomy are typically based on a spatial transformation that maps a template to an individual anatomy and vice versa however important morphological characteristics are frequently not captured by this transformation thereby leading to lossy representations we extend this formulation by incorporating residual anatomical information i e information that is not captured by the shape transformation but is necessary in order to fully and exactly reconstruct the anatomy under measurement we therefore arrive at a lossless morphological representation by virtue of being lossless this representation allows us to represent the same anatomy by an infinite number of pairs transformation residual since different residuals correspond to different transformations we treat these pairs as members of an anatomical equivalence class aec which we approximate using principal component analysis we show that projection onto the orthogonal to the aec subspace produces measurements that allow us to better detect morphological abnormalities by eliminating variation in the data that is irrelevant and confounds underlying subtle morphological characteristics finally we show that higher classification rates between a group of normal brains and a group of brains with localized atrophy are obtained if we use nonmetric distances between aecs instead of conventional euclidean distances between individual morphological measurements the results confirm that this representation can improve the results compared to conventional analysis but also highlight limitations of the current approach and point to directions of further development of this general morphological analysis framework

one pass heuristics for large scale unconstrained binary quadratic problems abstract many significant advances have been made in recent years for solving unconstrained binary quadratic programs uqp as a result the size of problem instances that can be efficiently solved has grown from a hundred or so variables a few years ago to 2000 or 3000 variables today these advances have motivated new applications of the model which in turn have created the need to solve even larger problems in response to this need we introduce several new one pass heuristics for solving very large versions of this problem our computational experience on problems of up to 9000 variables indicates that these methods are both efficient and effective for very large problems the significance of problems of this size is that they not only open the door to solving a much wider array of real world problems but also that the standard linear mixed integer formulations of the nonlinear models involve over 40 000 000 variables and three times that many constraints our approaches can be used as stand alone solution methods or they can serve as procedures for quickly generating high quality starting points for other more sophisticated methods

volumetric image registration from invariant keypoints we present a method for image registration based on 3d scale and rotation invariant keypoints the method extends the scale invariant feature transform sift to arbitrary dimensions by making key modifications to orientation assignment and gradient histograms rotation invariance is proven mathematically additional modifications are made to extrema detection and keypoint matching based on the demands of image registration our experiments suggest that the choice of neighborhood in discrete extrema detection has a strong impact on image registration accuracy in head mr images the brain is registered to a labeled atlas with an average dice coefficient of 92 outperforming registration from mutual information as well as an existing 3d sift implementation in abdominal ct images the spine is registered with an average error of 4 82 mm furthermore keypoints are matched with high precision in simulated head mr images exhibiting lesions from multiple sclerosis these results were achieved using only affine transforms and with no change in parameters across a wide variety of medical images this paper is freely available as a cross platform software library

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

the geometric median on riemannian manifolds with application to robust atlas estimation one of the primary goals of computational anatomy is the statistical analysis of anatomical variability in large populations of images the study of anatomical shape is inherently related to the construction of transformations of the underlying coordinate space which map one anatomy to another it is now well established that representing the geometry of shapes or images in euclidian spaces undermines our ability to represent natural variability in populations in our previous work we have extended classical statistical analysis techniques such as averaging principal components analysis and regression to riemannian manifolds which are more appropriate representations for describing anatomical variability in this paper we extend the notion of robust estimation a well established and powerful tool in traditional statistical analysis of euclidian data to manifold valued representations of anatomical variability in particular we extend the geometric median a classic robust estimator of centrality for data in euclidean spaces we formulate the geometric median of data on a riemannian manifold as the minimizer of the sum of geodesic distances to the data points we prove existence and uniqueness of the geometric median on manifolds with non positive sectional curvature and give sufficient conditions for uniqueness on positively curved manifolds generalizing the weiszfeld procedure for finding the geometric median of euclidean data we present an algorithm for computing the geometric median on an arbitrary manifold we show that this algorithm converges to the unique solution when it exists in this paper we exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images using this approach we also present a robust brain atlas estimation technique based on the geometric median in the space of deformable images

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

nonrigid brain mr image registration using uniform spherical region descriptor there are two main issues that make nonrigid image registration a challenging task first voxel intensity similarity may not be necessarily equivalent to anatomical similarity in the image correspondence searching process second during the imaging process some interferences such as unexpected rotations of input volumes and monotonic gray level bias fields can adversely affect the registration quality in this paper a new feature based nonrigid image registration method is proposed the proposed method is based on a new type of image feature namely uniform spherical region descriptor usrd as signatures for each voxel the usrd is rotation and monotonic gray level transformation invariant and can be efficiently calculated the registration process is therefore formulated as a feature matching problem the usrd feature is integrated with the markov random field labeling framework in which energy function is defined for registration the energy function is then optimized by the expansion algorithm the proposed method has been compared with five state of the art registration approaches on both the simulated and real 3 d databases obtained from the brainweb and internet brain segmentation repository respectively experimental results demonstrate that the proposed method can achieve high registration accuracy and reliable robustness behavior

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

attribute vector guided groupwise registration abstract groupwise registration has been recently introduced to simultaneously register a group of images by avoiding the selection of a particular template to achieve this several methods have been proposed to take advantage of information theoretic entropy measures based on image intensity however simplistic utilization of voxelwise image intensity is not sufficient to establish reliable correspondences since it lacks important contextual information therefore we explore the notion of attribute vector as the voxel signature instead of image intensity to guide the correspondence detection in groupwise registration in particular for each voxel the attribute vector is computed from its multi scale neighborhoods in order to capture the geometric information at different scales the probability density function pdf of each element in the attribute vector is then estimated from the local neighborhood providing a statistical summary of the underlying anatomical structure in that local pattern eventually with the help of jensen shannon js divergence a group of subjects can be aligned simultaneously by minimizing the sum of js divergences across the image domain and all attributes we have employed our groupwise registration algorithm on both real nirep na0 data set and simulated data 12 pairs of normal control and simulated atrophic data set the experimental results demonstrate that our method yields better registration accuracy compared with a popular groupwise registration method

registration atlas estimation and variability analysis of white matter fiber bundles modeled as currents this paper proposes a generic framework for the registration the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images this framework is based on the metric on currents for the comparison of fiber bundles this metric measures anatomical differences between fiber bundles seen as global homologous structures across subjects it avoids the need to establish correspondences between points or between individual fibers of different bundles it can measure differences both in terms of the geometry of the bundles like its boundaries and in terms of the density of fibers within the bundle it is robust to fiber interruptions and reconnections in addition a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents first we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects a dense deformation of the underlying white matter is estimated which is constrained by the bundles seen as global anatomical landmarks by contrast the alignment obtained from image registration is driven only by the local gradient of the image second we propose a generative statistical model for the analysis of a collection of homologous bundles this model consistently estimates prototype fiber bundles called template which capture the anatomical invariants in the population a set of deformations which align the geometry of the template to that of each subject and a set of residual perturbations the statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry stretching torque etc and texture fiber density etc third this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability this gives a way to interpret the anatomical features that the model detects consistently across the subjects this may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles

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

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

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

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

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

sharpmean groupwise registration guided by sharp mean image and tree based registration groupwise registration has become more and more popular due to its attractiveness for unbiased analysis of population data one of the most popular approaches for groupwise registration is to iteratively calculate the group mean image and then register all subject images towards the latest estimated group mean image however its performance might be undermined by the fuzzy mean image estimated in the very beginning of groupwise registration procedure because all subject images are far from being well aligned at that moment in this paper we first point out the significance of always keeping the group mean image sharp and clear throughout the entire groupwise registration procedure which is intuitively important but has not been explored in the literature yet to achieve this we resort to developing the robust mean image estimator by the adaptive weighting strategy where the weights are adaptive across not only the individual subject images but also all spatial locations in the image domain on the other hand we notice that some subjects might have large anatomical variations from the group mean image which challenges most of the state of the art registration algorithms to ensure good registration results in each iteration we explore the manifold of subject images and build a minimal spanning tree mst with the group mean image as the root of the mst therefore each subject image is only registered to its parent node often with similar shapes and its overall transformation to the group mean image space is obtained by concatenating all deformations along the paths connecting itself to the root of the mst the group mean image as a result all the subjects will be well aligned to the group mean image adaptively our method has been evaluated in both real and simulated datasets in all experiments our method outperforms the conventional algorithm which generally produces a fuzzy group mean image throughout the entire groupwise registration

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

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

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

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

sphere spherical harmonic elastic registration of hardi data abstract in contrast to the more common diffusion tensor imaging dti high angular resolution diffusion imaging hardi allows superior delineation of angular microstructures of brain white matter and makes possible multiple fiber modeling of each voxel for better characterization of brain connectivity however the complex orientation information afforded by hardi makes registration of hardi images more complicated than scalar images in particular the question of how much orientation information is needed for satisfactory alignment has not been sufficiently addressed low order orientation representation is generally more robust than high order representation although the latter provides more information for correct alignment of fiber pathways however high order representation when naively utilized might not necessarily be conducive to improving registration accuracy since similar structures with significant orientation differences prior to proper alignment might be mistakenly taken as non matching structures we present in this paper a hardi registration algorithm called spherical harmonic elastic registration sphere which in a principled means hierarchically extracts orientation information from hardi data for structural alignment the image volumes are first registered using robust relatively direction invariant features derived from the orientation distribution function odf and the alignment is then further refined using spherical harmonic sh representation with gradually increasing orders this progression from non directional single directional to multi directional representation provides a systematic means of extracting directional information given by diffusion weighted imaging coupled with a template subject consistent soft correspondence matching scheme this approach allows robust and accurate alignment of hardi data experimental results show marked increase in accuracy over a state of the art dti registration algorithm

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