stable solutions with zeros to the ginzburg landau equation with neumann boundary condition abstract this paper is devoted to the ginzburg landau equation 1 2 0 u1 iu2in a bounded domain r nwith the homogeneous neumann boundary condition the previous works 12 14 showed that for large there exist stable non constant solutions with no zeros in domains which are topologically non trivial in a certain sense in this aritcle it is proved that for a domain containing a non trivial domaindas a subset there exist stable solutions with zeros provided that the volume of dis sufficiently small

a characterization of the finite simple groups abstract in this paper we obtain a quantitative characterization of all finite simple groups let t g denote the set of indices of maximal subgroups of group g and let p g be the smallest number in t g we have the following theorems theorem 2 let n and g be finite simple groups if n divides g p n p g and t n t g then or and 2 11 or 2 and 3 theorem 3 let n be a finite simple and let g be a finite group if g n and t g t n then g n

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

broueʼs abelian defect group conjecture for the sporadic simple janko group j4 revisited abstract we show that the 3 block of the sporadic simple janko group j 4 with defect group c 3 c 3 and the principal 3 block of the alternating group a 8 are puig equivalent answering a question posed in our previous paper to accomplish this we apply computational techniques in particular an explicit version of the brauer construction

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

a robust hybrid method for nonrigid image registration a nonrigid registration method is proposed to automatically align two images by registering two sets of sparse features extracted from the images motivated by the paradigm of robust point matching rpm algorithms 1 2 which were originally proposed for shape registration we develop robust hybrid image matching rhim algorithm by alternatively optimizing feature correspondence and spatial transformation for image registration our rhim algorithm is built to be robust to feature extraction errors a novel dynamic outlier rejection approach is described for removing outliers and a local refinement technique is applied to correct non exactly matched correspondences arising from image noise and deformations experimental results demonstrate the robustness and accuracy of our method

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

feature based nonrigid brain mr image registration with symmetric alpha stable filters a new feature based nonrigid image registration method for magnetic resonance mr brain images is presented in this paper each image voxel is represented by a rotation invariant feature vector which is computed by passing the input image volumes through a new bank of symmetric alpha stable s s filters there are three main contributions presented in this paper first this work is motivated by the fact that the frequency spectrums of the brain mr images often exhibit non gaussian heavy tail behavior which cannot be satisfactorily modeled by the conventional gabor filters to this end we propose the use of s s filters to model such behavior and show that the gabor filter is a special case of the s s filter second the maximum response orientation mro selection criterion is designed to extract rotation invariant features for registration tasks the mro selection criterion also significantly reduces the number of dimensions of feature vectors and therefore lowers the computation time third in case the segmentations of the input image volumes are available the fisher s separation criterion fsc is introduced such that the discriminating power of different feature types can be directly compared with each other before performing the registration process using fsc weights can also be assigned automatically to different voxels in the brain mr images the weight of each voxel determined by fsc reflects how distinctive and salient the voxel is using the most distinctive and salient voxels at the initial stage to drive the registration can reduce the risk of being trapped in the local optimum during image registration process the larger the weight the more important the voxel with the extracted feature vectors and the associated weights the proposed method registers the source and the target images in a hierarchical multiresolution manner the proposed method has been intensively evaluated on both simulated and real 3 d datasets obtained from brainweb and internet brain segmentation repository ibsr respectively and compared with hammer an extended version of hammer based on local histograms lhf ffd demons and the gabor filter based registration method it is shown that the proposed method achieves the highest registration accuracy among the five widely used image registration methods

computer construction of matrix representations of the covering group of the higman sims group in this paper we will describe how to use the meat axe of r parker 9 to construct two 28 dimensional matrix representations of the covering group of the higman sims group denoted by 2 hs over the finite field gf of order 5 these techniques have been developed in cambridge over a number of years the first use of them was the construction by norton and parker see s of the 112 dimensional representation of the sporadic simple group j4 over the field of order 2 these matrices have been used for example in determining the maximal subgroups of j4 see s there are also other examples involving sporadic groups such as the 11 l dimensional representation of the lyons group ly over the field of order 5 see 11 i the 45 dimensional representation of the triple cover 3 o n of the o nan group over the field of order 7 see 12 and the 248 dimensional representation of the thompson group th over the field of order 3 see is at the end of this paper we will write down two 28 x 28 matrices over gf which generate 2 hs

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

broue s abelian defect group conjecture holds for the harada norton sporadic simple group hn abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent rickard equivalent this conjecture is called broue s abelian defect group conjecture we prove in this paper that broue s abelian defect group conjecture is true for a non principal 3 block a with an elementary abelian defect group p of order 9 of the harada norton simple group hn it then turns out that broue s abelian defect group conjecture holds for all primes p and for all p blocks of the harada norton simple group hn

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

applying tensor based morphometry to parametric surfaces can improve mri based disease diagnosis many methods have been proposed for computer assisted diagnostic classification full tensor information and machine learning with 3d maps derived from brain images may help detect subtle differences or classify subjects into different groups here we develop a new approach to apply tensor based morphometry to parametric surface models for diagnostic classification we use this approach to identify cortical surface features for use in diagnostic classifiers first with holomorphic 1 forms we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so called slit domain next the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map to analyze anatomical differences we then analyze the full riemannian surface metric tensors which retain multivariate information on local surface geometry as the number of voxels in a 3d image is large sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy focusing on vertices with greatest effect sizes we train a diagnostic classifier using the surface features selected by an l1 norm based sparse learning method stability selection is applied to validate the selected feature sets we tested the algorithm on mri derived cortical surfaces from 42 subjects with genetically confirmed williams syndrome and 40 age matched controls multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other tbm based statistics including analysis of the jacobian determinant and the largest eigenvalue of the surface metric our method also gave reasonable classification results relative to the jacobian determinant the pair of eigenvalues of the jacobian matrix and volume features this analysis pipeline may boost the power of morphometry studies and may assist with image based classification

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

broue s conjecture holds for principal 3 blocks with elementary abelian defect group of order 9 abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a finite group g has an abelian sylow p subgroup p then the derived categories of the principal p blocks of g and of the normalizer ng p of p in g are equivalent we prove in this paper that broue inage kus conjecture holds for the principal 3 block of an arbitrary finite group g with an elementary abelian sylow 3 subgroup p of order 9 by using initiated works for the case where g is simple which are due to puig okuyama waki miyachi and the authors the result depends on the classification of finite simple groups

whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves cortical surfaces and images this paper introduces a novel large deformation diffeomorphic metric mapping algorithm for whole brain registration where sulcal and gyral curves cortical surfaces and intensity images are simultaneously carried from one subject to another through a flow of diffeomorphisms to the best of our knowledge this is the first time that the diffeomorphic metric from one brain to another is derived in a shape space of intensity images and point sets such as curves and surfaces in a unified manner we describe the euler lagrange equation associated with this algorithm with respect to momentum a linear transformation of the velocity vector field of the diffeomorphic flow the numerical implementation for solving this variational problem which involves large scale kernel convolution in an irregular grid is made feasible by introducing a class of computationally friendly kernels we apply this algorithm to align magnetic resonance brain data our whole brain mapping results show that our algorithm outperforms the image based lddmm algorithm in terms of the mapping accuracy of gyral sulcal curves sulcal regions and cortical and subcortical segmentation moreover our algorithm provides better whole brain alignment than combined volumetric and surface registration postelnicu et al 2009 and hierarchical attribute matching mechanism for elastic registration hammer shen and davatzikos 2002 in terms of cortical and subcortical volume segmentation

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

broueʼs abelian defect group conjecture holds for the double cover of the higman sims sporadic simple group abstract in the representation theory of finite groups there is a well known and important conjecture due to broue saying that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent we prove in this paper that broue s abelian defect group conjecture and even rickard s splendid equivalence conjecture are true for the faithful 3 block a with an elementary abelian defect group p of order 9 of the double cover 2 hs of the higman sims sporadic simple group it then turns out that both conjectures hold for all primes p and for all p blocks of 2 hs

tps hammer improving hammer registration algorithm by soft correspondence matching and thin plate splines based deformation interpolation we present an improved mr brain image registration algorithm called tps hammer which is based on the concepts of attribute vectors and hierarchical landmark selection scheme proposed in the highly successful hammer registration algorithm we demonstrate that tps hammer algorithm yields better registration accuracy robustness and speed over hammer owing to 1 the employment of soft correspondence matching and 2 the utilization of thin plate splines tps for sparse to dense deformation field generation these two aspects can be integrated into a unified framework to refine the registration iteratively by alternating between soft correspondence matching and dense deformation field estimation compared with hammer tps hammer affords several advantages 1 unlike the gaussian propagation mechanism employed in hammer which can be slow and often leaves unreached blotches in the deformation field the deformation interpolation in the non landmark points can be obtained immediately with tps in our algorithm 2 the smoothness of deformation field is preserved due to the nice properties of tps 3 possible misalignments can be alleviated by allowing the matching of the landmarks with a number of possible candidate points and enforcing more exact matches in the final stages of the registration extensive experiments have been conducted using the original hammer as a comparison baseline to validate the merits of tps hammer the results show that tps hammer yields significant improvement in both accuracy and speed indicating high applicability for the clinical scenario

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

multidirectional and topography based dynamic scale varifold representations with application to matching developing cortical surfaces the human cerebral cortex is marked by great complexity as well as substantial dynamic changes during early postnatal development to obtain a fairly comprehensive picture of its age induced and or disorder related cortical changes one needs to match cortical surfaces to one another while maximizing their anatomical alignment methods that geodesically shoot surfaces into one another as currents a distribution of oriented normals and varifolds a distribution of non oriented normals provide an elegant riemannian framework for generic surface matching and reliable statistical analysis however both conventional current and varifold matching methods have two key limitations first they only use the normals of the surface to measure its geometry and guide the warping process which overlooks the importance of the orientations of the inherently convoluted cortical sulcal and gyral folds second the conversion of a surface into a current or a varifold operates at a fixed scale under which geometric surface details will be neglected which ignores the dynamic scales of cortical foldings to overcome these limitations and improve varifold based cortical surface registration we propose two different strategies the first strategy decomposes each cortical surface into its normal and tangent varifold representations by integrating principal curvature direction field into the varifold matching framework thus providing rich information of the orientation of cortical folding and better characterization of the complex cortical geometry the second strategy explores the informative cortical geometric features to perform a dynamic scale measurement of the cortical surface that depends on the local surface topography e g principal curvature thereby we introduce the concept of a topography based dynamic scale varifold we tested the proposed varifold variants for registering 12 pairs of dynamically developing cortical surfaces from 0 to 6 months of age both variants improved the matching accuracy in terms of closeness to the target surface and the goodness of alignment with regional anatomical boundaries when compared with three state of the art methods 1 diffeomorphic spectral matching 2 conventional current based surface matching and 3 conventional varifold based surface matching

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

synthesizing average 3d anatomical shapes abstract average shape estimates are often used to characterize normal morphological variation and discriminate dysmorphology in populations the purpose of this paper is to estimate average or the most representative shapes in populations by using high resolution medical images as input the average shape is computed from high dimensional spatial transformations used to co register each subject in the population rather than the image intensities inverse consistent image registration is used to help minimize correspondence errors and produce better population average estimates testing the method was done using a population of adult mr brain scans from 22 individuals with no know structural abnormalities population averages were computed using the spatial transformation method and local changes in morphology were mapped results suggest that this method is a feasible means for robust estimation of population average shape it is also shown that using inverse consistent transformations produces average shape estimates with less error compared to those produced with transformations with nontrivial inverse consistent errors

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

broueʼs abelian defect group conjecture holds for the sporadic simple conway group co3 in the representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block an of the normaliser ng p of p in g are derived equivalent rickard equivalent this conjecture is called strong version of broue s abelian defect group conjecture in this paper we prove that the strong version of broue s abelian defect group conjecture is true for the non principal 2 block a with an elementary abelian defect group p of order 8 of the sporadic simple conway group co3 this result completes the verification of the strong version of broue s abelian defect group conjecture for all primes p and for all p blocks of co3

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

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

an adaptive error penalization method for training an efficient and generalized svm a novel training method has been proposed for increasing efficiency and generalization of support vector machine svm the efficiency of svm in classification is directly determined by the number of the support vectors used which is often huge in the complicated classification problem in order to represent a highly convoluted separation hypersurface for better nonlinear classification however the separation hypersurface of svm might be unnecessarily over convoluted around extreme outliers as these outliers can easily dominate the objective function of svm this situation eventually affects the efficiency and generalization of svm in classifying unseen testing samples to avoid this problem we propose a novel objective function for svm i e an adaptive penalty term is designed to suppress the effects of extreme outliers thus simplifying the separation hypersurface and increasing the classification efficiency since maximization of the margin distance of hypersurface is no longer dominated by those extreme outliers our generated svm tends to have a wider margin i e better generalization ability importantly as our designed objective function can be reformulated as a dual problem similar to that of standard svm any existing svm training algorithm can be borrowed for the training of our proposed svm the performances of our method have been extensively tested on the uci machine learning repository as well as a real clinical problem i e tissue classification in prostate ultrasound images experimental results show that our method is able to simultaneously increase the classification efficiency and the generalization ability of the svm

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

a comparative study of transformation functions for nonrigid image registration transformation functions play a major role in nonrigid image registration in this paper the characteristics of thin plate spline tps multiquadric mq piecewise linear pl and weighted mean wm transformations are explored and their performances in nonrigid image registration are compared tps and mq are found to be most suitable when the set of control point correspondences is not large fewer than a thousand and variation in spacing between the control points is not large when spacing between the control points varies greatly pl is found to produce a more accurate registration than tps and mq when a very large set of control points is given and the control points contain positional inaccuracies wm is preferred over tps mq and pl because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations use of transformation functions in the detection of incorrect correspondences is also discussed

the hall paige conjecture and synchronization for affine and diagonal groups abstract the hall paige conjecture asserts that a finite group has a complete mapping if and only if its sylow subgroups are not cyclic the conjecture is now proved and one aim of this paper is to document the final step in the proof for the sporadic simple group j 4 we apply this result to prove that primitive permutation groups of simple diagonal type with three or more simple factors in the socle are non synchronizing we also give the simpler proof that for groups of affine type or simple diagonal type with two socle factors synchronization and separation are equivalent synchronization and separation are conditions on permutation groups which are stronger than primitivity but weaker than 2 homogeneity the second of these being stronger than the first empirically it has been found that groups which are synchronizing but not separating are rather rare it follows from our results that such groups must be primitive of almost simple type

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

morphological classification of brains via high dimensional shape transformations and machine learning methods a high dimensional shape transformation posed in a mass preserving framework is used as a morphological signature of a brain image population differences with complex spatial patterns are then determined by applying a nonlinear support vector machine svm pattern classification method to the morphological signatures significant reduction of the dimensionality of the morphological signatures is achieved via wavelet decomposition and feature reduction methods applying the method to mr images with simulated atrophy shows that the method can correctly detect subtle and spatially complex atrophy even when the simulated atrophy represents only a 5 variation from the original image applying this method to actual mr images shows that brains can be correctly determined to be male or female with a successful classification rate of 97 using the leave one out method this proposed method also shows a high classification rate for old adults age classification even under difficult test scenarios the main characteristic of the proposed methodology is that by applying multivariate pattern classification methods it can detect subtle and spatially complex patterns of morphological group differences which are often not detectable by voxel based morphometric methods because these methods analyze morphological measurements voxel by voxel and do not consider the entirety of the data simultaneously

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

accuracy assessment of global and local atrophy measurement techniques with realistic simulated longitudinal alzheimer s disease images the evaluation of atrophy quantification methods based on magnetic resonance imaging have been usually hindered by the lack of realistic gold standard data against which to judge these methods or to help refine them recently camara et al 2006 we presented a technique in which atrophy is realistically simulated in different tissue compartments or neuroanatomical structures with a phenomenological model in this study we have generated a cohort of realistic simulated alzheimers disease ad images with known amounts of atrophy mimicking a set of 19 real controls and 27 probable ad subjects with an improved version of our atrophy simulation methodology this database was then used to assess the accuracy of several well known computational anatomy methods which provide global bsi and siena or local jacobian integration estimates of longitudinal atrophy in brain structures using mr images siena and bsi results correlated very well with gold standard data pearson coefficient of 0 962 and 0 969 respectively achieving small mean absolute differences with respect to the gold standard percentage change from baseline volume bsi of 0 23 0 26 siena of 0 22 0 28 jacobian integration was guided by both fluid and ffd based registration techniques and resulting deformation fields and associated jacobians were compared region by region with gold standard ones the ffd based technique outperformed the fluid one in all evaluated structures mean absolute differences from the gold standard in percentage change from baseline volume whole brain ffd 0 31 fluid 0 58 lateral ventri cles ffd 0 79 fluid 1 45 left hippocampus ffd 0 82 fluid 1 42 right hippocampus ffd 0 95 fluid 1 62 the largest errors for both local techniques occurred in the sulcal csf ffd 2 27 fluid 3 55 regions for large structures such as the whole brain these mean absolute differences relative to the applied atrophy repre sented similar percentages for the bsi siena and ffd techniques controls patients bsi 51 99 16 36 siena 62 34 21 59 ffd 41 02 24 95 for small struc tures such as the hippocampi these percentages were larger specially for controls where errors were approximately equal to the small applied changes controls patients ffd 92 82 43 61 however these apparently large relative errors have not prevented the global or hippocampal measures from finding significant group separation in our study the evaluation framework presented here will help in quantifying whether the accuracy of future methodological developments is sufficient for analyzing change in smaller or less atrophied local brain regions results obtained in our experiments with realistic simulated data confirm previously published estimates of accuracy for both evaluated global techniques regarding jacobian integration methods the ffd based one demonstrated promising results and potential for being used in clinical studies alongside or in place of the more common global methods the generated gold standard data has also allowed us to identify some stages and sets of parameters in the evaluated techniques the brain extraction step in the global techniques and the number of multi resolution levels and the stopping criteria in the registration based methods that are critical for their accuracy

consistency driven alternating optimization for multigraph matching a unified approach the problem of graph matching gm in general is nondeterministic polynomial complete and many approximate pairwise matching techniques have been proposed for a general setting in real applications it typically requires to find the consistent matching across a batch of graphs sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence and the sequences generated in different pairwise matching orders can lead to contradictory solutions motivated by devising a robust and consistent multiple gm model we propose a unified alternating optimization framework for multi gm in addition we define and use two metrics related to graphwise and pairwise consistencies the former is used to find an appropriate reference graph which induces a set of basis variables and launches the iteration procedure the latter defines the order in which the considered graphs in the iterations are manipulated we show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix respectively our multi gm model has two major characters 1 the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistency driven mechanism and 2 the framework is flexible to incorporate various existing pairwise gm solvers in an out of box fashion and also can proceed with the output of other multi gm methods the experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state of the art

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

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

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

the radical 2 subgroups of the sporadic simple groups j4 co2 and th for a finite group g and a prime divisor p of its order a nontrivial p subgroup r of g is called radical if o n r r with the poset p g b g of radical p subgroups of g with respect to inclusion we naturally p associate the simplicial complex of its chains denoted b g which is p known to be g homotopy equivalent to the complex associated with the poset of nontrivial p subgroups as well as that of nontrivial elementary abelian p subgroups of g see e g 5 6 6 the latter are important tools to investigate the structure of g concerning the prime p see e g 5 chap 6 thus the smaller complex b g has enough information to p understand behaviors of g on p the following fact a corollary of the borel tits theorem 5 6 8 4 shows the further importance of b g for a finite group of lie type p defined over a field in characteristic p the complex b g is the p barycentric subdivision of the building for g thus for an arbitrary finite group g we may think of the complex b g as a generalization of the p concept of buildings in fact as is observed in 14 for each sporadic simple group g of characteristic p type b g is homotopy equivalent to p some smaller simplicial complex previously constructed by an ad hoc method and referred to as a p local geometry of g this suggests the importance of examining minimal complexes which are homotopy equiva lent to b g for every specifically sporadic simple group g see also p the introduction of 17

locally linear diffeomorphic metric embedding lldme for surface based anatomical shape modeling this paper presents the algorithm locally linear diffeomorphic metric embedding lldme for constructing efficient and compact representations of surface based brain shapes whose variations are characterized using large deformation diffeomorphic metric mapping lddmm our hypothesis is that the shape variations in the infinite dimensional diffeomorphic metric space can be captured by a low dimensional space to do so traditional locally linear embedding lle that reconstructs a data point from its neighbors in euclidean space is extended to lldme that requires interpolating a shape from its neighbors in the infinite dimensional diffeomorphic metric space this is made possible through the conservation law of momentum derived from lddmm it indicates that initial momentum a linear transformation of the initial velocity of diffeomorphic flows at a fixed template shape determines the geodesic connecting the template to a subject s shape in the diffeomorphic metric space and becomes the shape signature of an individual subject this leads to the compact linear representation of the nonlinear diffeomorphisms in terms of the initial momentum since the initial momentum is in a linear space a shape can be approximated by a linear combination of its neighbors in the diffeomorphic metric space in addition we provide efficient computations for the metric distance between two shapes through the first order approximation of the geodesic using the initial momentum as well as for the reconstruction of a shape given its low dimensional euclidean coordinates using the geodesic shooting with the initial momentum as the initial condition experiments are performed on the hippocampal shapes of 302 normal subjects across the whole life span 18 94years compared with principal component analysis and isomap lldme provides the most compact and efficient representation of the age related hippocampal shapes even though the hippocampal volumes among young adults are as variable as those in older adults lldme disentangles the hippocampal local shape variation from the hippocampal size and thus reveals the nonlinear relationship of the hippocampal morphometry with age

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

the broue conjecture for the faithful 3 blocks of 4 m22 abstract we verify broue s conjecture for the faithful 3 blocks of defect 2 of the non split central extension of the sporadic simple mathieu group m 22 by a cyclic group of order 4 the proof is based on a strategy due to okuyama and rickard where a stable equivalence is lifted to a derived equivalence the stable equivalence in turn is provided by exploiting a result due to puig to handle this particular example next to theoretical investigations we apply a whole bunch of computational tools

commuting involution graphs for sporadic simple groups let kless than or equals slantgless than or equals slantaut k where k is one of the 26 sporadic finite simple groups and let tset membership variantg be an involution and x tg the commuting involution graph view the mathml source has x as its vertex set with two distinct elements of x joined by an edge whenever they commute in g for most of the sporadic simple groups we compute the diameter of view the mathml source and give detailed information about the elements at a given distance from a fixed involution t

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

timer tensor image morphing for elastic registration we propose a novel diffusion tensor imaging dti registration algorithm called tensor image morphing for elastic registration timer which leverages the hierarchical guidance of regional distributions and local boundaries both extracted directly from the tensors currently available dti registration methods generally extract tensor scalar features from each tensor to construct scalar maps subsequently regional integration and other operations such as edge detection are performed to extract more features to guide the registration however there are two major limitations with these approaches first the computed regional features might not reflect the actual regional tensor distributions second by the same token gradient maps calculated from the tensor derived scalar feature maps might not represent the actual tissue tensor boundaries to overcome these limitations we propose a new approach which extracts regional and edge information directly from a tensor neighborhood regional tensor distribution information such as mean and variance is computed in a multiscale fashion directly from the tensors by taking into account the voxel neighborhood of different sizes and hence capturing tensor information at different scales which in turn can be employed to hierarchically guide the registration such multiscale scheme can help alleviate the problem of local minimum and is also more robust to noise since one can better determine the statistical properties of each voxel by taking into account the properties of its surrounding also incorporated in our method is edge information extracted directly from the tensors which is crucial to facilitate registration of tissue boundaries experiments involving real subjects simulated subjects fiber tracking and atrophy detection indicate that timer performs better than the other methods yang et al 2008 zhang et al 2006

decomposition numbers of non principal blocks of j4 for characteristic 3 abstract in this paper the decomposition numbers of the non principal blocks of the largest janko group j 4 z janko a new finite simple group of order 86 775 571 046 077 562 880 which possesses m 24 and the full covering group of m 22 as subgroups j algebra 42 1976 564 596 for characteristic 3 are determined up to some unknown parameters we are also concerned with the decomposition numbers of maximal 2 local subgroups of j 4 in odd characteristics

robust non rigid point set registration using spatially constrained gaussian fields estimating transformations from degraded point sets is necessary for many computer vision and pattern recognition applications in this paper we propose a robust non rigid point set registration method based on spatially constrained context aware gaussian fields we first construct a context aware representation e g shape context for assignment initialization then we use a graph laplacian regularized gaussian fields to estimate the underlying transformation from the likely correspondences on the one hand the intrinsic manifold is considered and used to preserve the geometrical structure and a priori knowledge of the point set is extracted on the other hand by using the deterministic annealing the presented method is extended to a projected high dimensional feature space i e reproducing kernel hilbert space through a kernel trick to solve the transformation in which the local structure is propagated by the coarse to fine scaling strategy in this way the proposed method gradually recovers much more correct correspondences and then estimates the transformation parameters accurately and robustly when facing degradations experimental results on 2d and 3d synthetic and real data point sets demonstrate that the proposed method reaches better performance than the state of the art algorithms

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

transitive subgroups of primitive permutation groups abstract we investigate the finite primitive permutation groups g which have a transitive subgroup containing no nontrivial subnormal subgroup of g the conclusion is that such primitive groups are rather rare and that their existence is intimately connected with factorisations of almost simple groups a corollary is obtained on primitive groups which contain a regular subgroup heavily involved in our proofs are some new results on subgroups of simple groups which have orders divisible by various primes for example another corollary implies that for every simple group t apart from l 3 3 u 3 3 and l 2 p with p a mersenne prime there is a collection consisting of two or three odd prime divisors of t such that if m is a subgroup of t of order divisible by every prime in then m is divisible by all the prime divisors of t and we obtain a classification of such subgroups m

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

surface fluid registration of conformal representation application to detect disease burden and genetic influence on hippocampus in this paper we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1 forms inverse consistent surface fluid registration and multivariate tensor based morphometry mtbm first we conformally map a surface onto a planar rectangle space with holomorphic 1 forms second we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface third we align the feature image with a chosen template image via the fluid image registration algorithm which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization the inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images this alignment induces a corresponding deformation on the surface we tested the system on alzheimer s disease neuroimaging initiative adni baseline dataset to study ad symptoms on hippocampus in our system by modeling a hippocampus as a 3d parametric surface we nonlinearly registered each surface with a selected template surface then we used mtbm to analyze the morphometry difference between diagnostic groups experimental results show that the new system has better performance than two publicly available subcortical surface registration tools first and spharm we also analyzed the genetic influence of the apolipoprotein e 4 allele apoe4 which is considered as the most prevalent risk factor for ad our work successfully detected statistically significant difference between apoe4 carriers and non carriers in both patients of mild cognitive impairment mci and healthy control subjects the results show evidence that the apoe genotype may be associated with accelerated brain atrophy so that our work provides a new mri analysis tool that may help presymptomatic ad research

a new maximal subgroup of the monster we use our computer construction of the monster sporadic simple group m to find a new maximal subgroup pgl2 29 in particular we prove containment of l2 29 in m thereby answering a long standing open question

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

multimodality image registration by maximization of quantitative qualitative measure of mutual information this paper presents a novel image similarity measure referred to as quantitative qualitative measure of mutual information q mi for multimodality image registration conventional information measures e g shannon s entropy and mutual information mi reflect quantitative aspects of information because they only consider probabilities of events in fact each event has its own utility to the fulfillment of the underlying goal which can be independent of its probability of occurrence thus it is important to consider both quantitative i e probability and qualitative i e utility measures of information in order to fully capture the characteristics of events accordingly in multimodality image registration q mi should be used to integrate the information obtained from both the image intensity distributions and the utilities of voxels in the images different voxels can have different utilities for example in brain images two voxels can have the same intensity value but their utilities can be different e g a white matter wm voxel near the cortex can have higher utility than a wm voxel inside a large uniform wm region in q mi the utility of each voxel in an image can be determined according to the regional saliency value calculated from the scale space map of this image since the voxels with higher utility values or saliency values contribute more in measuring q mi of the two images the q mi based registration method is much more robust compared to conventional mi based registration methods also the q mi based registration method can provide a smoother registration function with a relatively larger capture range in this paper the proposed q mi has been validated and applied to the rigid registrations of clinical brain images such as mr ct and pet images

broue s abelian defect group conjecture for the held group and the sporadic suzuki group abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding p block b of ng p are derived equivalent we demonstrate in this paper that broue s conjecture holds for non principal 3 blocks a with elementary abelian defect group p of order 9 of the simple held group and the sporadic simple suzuki group

non rigid image registration of brain magnetic resonance images using graph cuts we present a graph cuts based method for non rigid medical image registration on brain magnetic resonance images in this paper the non rigid medical image registration problem is reformulated as a discrete labeling problem based on a voxel to voxel intensity similarity measure each voxel in the source image is assigned a displacement label which represents a displacement vector indicating which position in the floating image it is spatially corresponding to in the proposed method a smoothness constraint based on the first derivative is used to penalize sharp changes in the adjacent displacement labels across voxels the image registration problem is therefore modeled by two energy terms based on intensity similarity and smoothness of the displacement field these energy terms are submodular and can be optimized by using the graph cuts method via email protected expansions which is a powerful combinatorial optimization tool and capable of yielding either a global minimum or a local minimum in a strong sense using the realistic brain phantoms obtained from the simulated brain database we compare the registration results of the proposed method with two state of the art medical image registration approaches free form deformation based method and demons method in addition the registration results are also compared with that of the linear programming based image registration method it is found that the proposed method is more robust against different challenging non rigid registration cases with consistently higher registration accuracy than those three methods and gives realistic recovered deformation fields

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 fast diffeomorphic image registration algorithm abstract this paper describes dartel which is an algorithm for diffeomorphic image registration it is implemented for both 2d and 3d image registration and has been formulated to include an option for estimating inverse consistent deformations nonlinear registration is considered as a local optimisation problem which is solved using a levenberg marquardt strategy the necessary matrix solutions are obtained in reasonable time using a multigrid method a constant eulerian velocity framework is used which allows a rapid scaling and squaring method to be used in the computations dartel has been applied to intersubject registration of 471 whole brain images and the resulting deformations were evaluated in terms of how well they encode the shape information necessary to separate male and female subjects and to predict the ages of the subjects

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

spatial and anatomical regularization of svm a general framework for neuroimaging data this paper presents a framework to introduce spatial and anatomical priors in svm for brain image analysis based on regularization operators a notion of proximity based on prior anatomical knowledge between the image points is defined by a graph e g brain connectivity graph or a metric e g fisher metric on statistical manifolds a regularization operator is then defined from the graph laplacian in the discrete case or from the laplace beltrami operator in the continuous case the regularization operator is then introduced into the svm which exponentially penalizes high frequency components with respect to the graph or to the metric and thus constrains the classification function to be smooth with respect to the prior it yields a new svm optimization problem whose kernel is a heat kernel on graphs or on manifolds we then present different types of priors and provide efficient computations of the gram matrix the proposed framework is finally applied to the classification of brain magnetic resonance mr images based on gray matter gm concentration maps and cortical thickness measures from 137 patients with alzheimer s disease ad and 162 elderly controls the results demonstrate that the proposed classifier generates less noisy and consequently more interpretable feature maps with high classification performances

multiple kernel point set registration the finite gaussian mixture model with kernel correlation is a flexible tool that has recently received attention for point set registration while there are many algorithms for point set registration presented in the literature an important issue arising from these studies concerns the mapping of data with nonlinear relationships and the ability to select a suitable kernel kernel selection is crucial for effective point set registration we focus here on multiple kernel point set registration we make several contributions in this paper first each observation is modeled using the student s rm t distribution which is heavily tailed and more robust than the gaussian distribution second by automatically adjusting the kernel weights the proposed method allows us to prune the ineffective kernels this makes the choice of kernels less crucial after parameter learning the kernel saliencies of the irrelevant kernels go to zero thus the choice of kernels is less crucial and it is easy to include other kinds of kernels finally we show empirically that our model outperforms state of the art methods recently proposed in the literature

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

registration of challenging image pairs initialization estimation and decision our goal is an automated 2d image pair registration algorithm capable of aligning images taken of a wide variety of natural and man made scenes as well as many medical images the algorithm should handle low overlap substantial orientation and scale differences large illumination variations and physical changes in the scene an important component of this is the ability to automatically reject pairs that have no overlap or have too many differences to be aligned well we propose a complete algorithm including techniques for initialization for estimating transformation parameters and for automatically deciding if an estimate is correct keypoints extracted and matched between images are used to generate initial similarity transform estimates each accurate over a small region these initial estimates are rank ordered and tested individually in succession each estimate is refined using the dual bootstrap icp algorithm driven by matching of multiscale features a three part decision criteria combining measurements of alignment accuracy stability in the estimate and consistency in the constraints determines whether the refined transformation estimate is accepted as correct experimental results on a data set of 22 challenging image pairs show that the algorithm effectively aligns 19 of the 22 pairs and rejects 99 8 percent of the misalignments that occur when all possible pairs are tried the algorithm substantially out performs algorithms based on keypoint matching alone

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 theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed