clustering with a new distance measure based on a dual rooted tree abstract this paper introduces a novel distance measure for clustering high dimensional data based on the hitting time of two minimal spanning trees mst grown sequentially from a pair of points by prim s algorithm when the proposed measure is used in conjunction with spectral clustering we obtain a powerful clustering algorithm that is able to separate neighboring non convex shaped clusters and to account for local as well as global geometric features of the data set remarkably the new distance measure is a true metric even if the prim algorithm uses a non metric dissimilarity measure to compute the edges of the mst this metric property brings added flexibility to the proposed method in particular the method is applied to clustering non euclidean quantities such as probability distributions or spectra using the kullback leibler divergence as a base measure we reduce computational complexity by applying consensus clustering to a small ensemble of dual rooted msts we show that the resultant consensus spectral clustering with dual rooted mst is competitive with other clustering methods both in terms of clustering performance and computational complexity we illustrate the proposed clustering algorithm on public domain benchmark data for which the ground truth is known on one hand and on real world astrophysical data on the other hand

cortical surface based analysis ii inflation flattening and a surface based coordinate system the surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds as such it is a difficult domain for computational as well as visualization purposes we have therefore designed a set of procedures for modifying the representation of the cortical surface to i inflate it so that activity buried inside sulci may be visualized ii cut and flatten an entire hemisphere and iii transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surface based coordinate system r 1999 academic press

improved estimates of partial volume coefficients from noisy brain mri using spatial context this paper addresses the problem of accurate voxel level estimation of tissue proportions in the human brain magnetic resonance imaging mri due to the finite resolution of acquisition systems mri voxels can contain contributions from more than a single tissue type the voxel level estimation of this fractional content is known as partial volume coefficient estimation in the present work two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods concretely a novel markov random field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation in addition a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes based on the obtained results the main conclusions are that 1 both markov random field modelling and non local means filtering improved the partial volume coefficient estimation results and 2 non local means filtering was the better of the two strategies for partial volume coefficient estimation

consensus strategy for clustering using rc images contrary to most of the existing 3d shape clustering methods in which all the objects in a dataset must be classified in clusters in this paper we tackle an incomplete but reliable unsupervised clustering solution the central idea lies in obtaining coherent 3d shape groups using a consensus between different similarity measures which are defined in a common 3d shape representation framework our goal therefore is to extract some consistent groups of objects considering the incomplete classification if this occurs as a natural result the weighted cone curvature wcc is defined as an overall feature which synthesizes a set of curvature levels on the nodes of a standard triangular mesh representation the wcc concept is used to define a master descriptor called an rc image on which up to eight similarity measures are defined a hierarchical clustering process is then carried out for all the measures and evaluated by means of a clustering confidence measure finally a consensus between the best measures is achieved to provide a coherent group of objects the proposed clustering approach has been tested on a set of mesh models belonging to a wide variety of free shape objects yielding promising results the results of our experiments demonstrate that both the 3d shape descriptor used and the clustering strategy proposed might be useful for future developments in the unsupervised grouping field this work eliminates the imposition of a unique metric and a complete clustering rc image is an original 3d shape descriptor which represents the whole object clustering consensus between several similarity metrics under a common framework consistent clusters understanding at the expense of an incomplete classification successful test on a set of mesh models of a wide variety of free shape objects

on the density density critical indices in interacting fermi systems the behaviour of correlation functions of d 1 interacting fermionic systems is determined by a small number of critical indices we prove that one of them is exactly zero as a consequence the behavior of the fourier transform of the density density correlation at zero momentum is qualitatively unaffected by the interaction contrary to what happens at if is the fermi momentum the result is obtained by implementing ward identities in a renormalization group approach

graph partitioned spatial priors for functional magnetic resonance images abstract spatial models of functional magnetic resonance imaging fmri data allow one to estimate the spatial smoothness of general linear model glm parameters and eschew pre process smoothing of data entailed by conventional mass univariate analyses recently diffusion based spatial priors harrison l m penny w daunizeau j and friston k j 2008 diffusion based spatial priors for functional magnetic resonance images neuroimage were proposed which provide a way to formulate an adaptive spatial basis where the diffusion kernel of a weighted graph laplacian wgl is used as the prior covariance matrix over glm parameters an advantage of these is that they can be used to relax the assumption of isotropy and stationarity implicit in smoothing data with a fixed gaussian kernel the limitation of diffusion based models is purely computational due to the large number of voxels in a brain volume one solution is to partition a brain volume into slices using a spatial model for each slice this reduces computational burden by approximating the full wgl with a block diagonal form where each block can be analysed separately while fmri data are collected in slices the functional structures exhibiting spatial coherence and continuity are generally three dimensional calling for a more informed partition we address this using the graph laplacian to divide a brain volume into sub graphs whose shape can be arbitrary their shape depends crucially on edge weights of the graph which can be based on the euclidean distance between voxels isotropic or on glm parameters anisotropic encoding functional responses the result is an approximation the full wgl that retains its 3d form and also has potential for parallelism we applied the method to high resolution 1 mm3 fmri data and compared models where a volume was divided into either slices or graph partitions models were optimized using expectation maximization and the approximate log evidence computed to compare these different ways to partition a spatial prior the high resolution fmri data presented here had greatest evidence for the graph partitioned anisotropic model which was best able to preserve fine functional detail

incorporating local image structure in normalized cut based graph partitioning for grouping of pixels abstract graph partitioning for grouping of image pixels has been explored a lot with normalized cut based graph partitioning being one of the popular ones in order to have a credible allegiance to the perceptual grouping taking place in early human vision we propose and study in this paper the incorporation of local image structure context in normalized cut based graph partitioning for grouping of image pixels similarity and proximity which have been studied earlier for grouping of image pixels are only two among many perceptual cues that act during grouping in early human vision in addition to the said two cues we study three other such cues namely common fate common region and continuity and find indications of local image structure utilization during grouping of image pixels appropriate incorporation of local image structure context is achieved by representing it using neighborhood in the form of histogram and fuzzy set we demonstrate both qualitatively and quantitatively through experimental results that the incorporation of local image structure improves performance of grouping of image pixels

entropic one class classifiers the one class classification problem is a well known research endeavor in pattern recognition the problem is also known under different names such as outlier and novelty anomaly detection the core of the problem consists in modeling and recognizing patterns belonging only to a so called target class all other patterns are termed nontarget and therefore they should be recognized as such in this paper we propose a novel one class classification system that is based on an interplay of different techniques primarily we follow a dissimilarity representation based approach we embed the input data into the dissimilarity space ds by means of an appropriate parametric dissimilarity measure this step allows us to process virtually any type of data the dissimilarity vectors are then represented by weighted euclidean graphs which we use to determine the entropy of the data distribution in the ds and at the same time to derive effective decision regions that are modeled as clusters of vertices since the dissimilarity measure for the input data is parametric we optimize its parameters by means of a global optimization scheme which considers both mesoscopic and structural characteristics of the data represented through the graphs the proposed one class classifier is designed to provide both hard boolean and soft decisions about the recognition of test patterns allowing an accurate description of the classification process we evaluate the performance of the system on different benchmarking data sets containing either feature based or structured patterns experimental results demonstrate the effectiveness of the proposed technique

functional integral construction of the massive thirring model verification of axioms and massless limit we present a complete construction of a quantum field theory for the massive thirring model by following a functional integral approach this is done by introducing an ultraviolet and an infrared cutoff and by proving that if the bare parameters are suitably chosen the schwinger functions have a well defined limit satisfying the osterwalder schrader axioms when the cutoffs are removed our results which are restricted to weak coupling are uniform in the value of the mass the control of the effective coupling which is the main ingredient of the proof is achieved by using the ward identities of the massless model in the approximated form they take in the presence of the cutoffs as a byproduct we show that when the cutoffs are removed theward identities have anomalies which are not linear in the bare coupling moreover we find for the interacting propagator of the massless theory a closed equation which is different from that usually stated in the physical literature

cumulative voting consensus method for partitions with variable number of clusters over the past few years there has been a renewed interest in the consensus clustering problem several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble in this paper we propose new consensus clustering algorithms with linear computational complexity in n we consider clusterings generated with a random number of clusters which we describe by categorical random variables we introduce the idea of cumulative voting as a solution for the problem of cluster label alignment where unlike the common one to one voting scheme a probabilistic mapping is computed we seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy we describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble given the arbitrary number of clusters of the input partitions we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves the maximum relevant information an efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized jensen shannon divergence within the cluster the empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

extended scaling relations for planar lattice models it is widely believed that the critical properties of several planar lattice systems like the eight vertex or the ashkin teller models are well described by an effective continuum fermionic theory obtained as a formal scaling limit on the basis of this assumption several extended scaling relations among their indices were conjectured we prove the validity of some of them among which the ones predicted by kadanoff phys rev lett 39 903 905 1977 and by luther and peschel phys rev b 12 3908 3917 1975

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

isoperimetric graph partitioning for image segmentation spectral graph partitioning provides a powerful approach to image segmentation we introduce an alternate idea that finds partitions with a small isoperimetric constant requiring solution to a linear system rather than an eigenvector problem this approach produces the high quality segmentations of spectral methods but with improved speed and stability

automated graph based analysis and correction of cortical volume topology the human cerebral cortex is topologically equivalent to a sheet and can be considered topologically spherical if it is closed at the brainstem low level segmentation of magnetic resonance mr imagery typically produces cerebral volumes whose tessellations are not topologically spherical the authors present a novel algorithm that analyzes and constrains the topology of a volumetric object graphs are formed that represent the connectivity of voxel segments in the foreground and background of the image these graphs are analyzed and minimal corrections to the volume are made prior to tessellation the authors apply the algorithm to a simple test object and to cerebral white matter masks generated by a low level tissue identification sequence the authors tessellate the resulting objects using the marching cubes algorithm and verify their topology by computing their euler characteristics a key benefit of the algorithm is that it localizes the change to a volume to the specific areas of its topological defects

lazy random walks for superpixel segmentation we present a novel image superpixel segmentation approach using the proposed lazy random walk lrw algorithm in this paper our method begins with initializing the seed positions and runs the lrw algorithm on the input image to obtain the probabilities of each pixel then the boundaries of initial superpixels are obtained according to the probabilities and the commute time the initial superpixels are iteratively optimized by the new energy function which is defined on the commute time and the texture measurement our lrw algorithm with self loops has the merits of segmenting the weak boundaries and complicated texture regions very well by the new global probability maps and the commute time strategy the performance of superpixel is improved by relocating the center positions of superpixels and dividing the large superpixels into small ones with the proposed optimization algorithm the experimental results have demonstrated that our method achieves better performance than previous superpixel approaches

convergence and divergence of thickness correlations with diffusion connections across the human cerebral cortex cortical thickness correlation across individuals has been observed so far it remains unclear to what extent such a correlation in thickness is a reflection of underlying fiber connection here we explicitly compared the patterns of cortical thickness correlation and diffusion based fiber connection across the entire cerebral cortex in 95 normal adults interregional thickness correlations were extracted by using computational neuroanatomy algorithms based on structural mri and diffusion connections were detected by using diffusion probabilistic tractography approximately 35 40 of thickness correlations showed convergent diffusion connections across the cerebral cortex intriguingly the observed convergences between thickness correlation and diffusion connection are mostly focused on the positive thickness correlations while almost all of the negative correlations 90 did not have a matched diffusion connection suggesting different mechanisms behind the positive and negative thickness correlations the latter not being mediated by a direct fiber pathway furthermore graph theoretic analysis reveals that the thickness correlation network has a more randomized overall topology whereas the nodal characteristics of cortical regions in these two networks are statistically correlated these findings indicate that thickness correlations partly reflect underlying fiber connections but they contains exclusive information and therefore should not be simply taken as a proxy measure for fiber connections

iterative image segmentation with feature driven heuristic four color labeling a heuristic four color labeling method is proposed to give robust initial foul phase partition for multiphase multiple piecewise constant mmpc model a regional adjacency cracking method is proposed to remove unnecessary adjacency constraints which impede the four color labeling compared with the random four color labeling the color map of heuristic coloring shows better consistency for the homogenous regions the heuristic four color labeling based approach reaches the good or even better segmentation with fewer iterations multilabel segmentation is an important research branch in image segmentation field in our previous work multiphase multiple piecewise constant and geodesic active contour mmpc gac model was proposed which can effectively describe multiple objects and background with intensity inhomogeneity it can be approximately solved with multiple layer graph mlg methods to make the optimization more efficient and limit the approximate error four color labeling theorem was further introduced which can limit the mlg within three layers representing four phases however the adopted random four color labeling method usually provides chaotic color maps with obvious inhomogeneity for those semantic consistent regions for this case a new and alternative method named heuristic four color labeling is proposed in this paper which aims to generate more reasonable color maps with a global view of the whole image and compared with the random four color labeling strategy the whole iterative algorithm based on our method usually produces better segmentations with faster convergence particularly for images with clutters and complicated structures this strategy is a good substitute for random coloring method when the latter produces unsatisfactory messy segmentation experiments conducted on public dataset demonstrate the effectiveness of the proposed method

hamilton jacobi skeleton on cortical surfaces in this paper we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces in our approach a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts which can guarantee global optimality after that we extend the method of hamilton jacobi skeleton to subsets of triangulated surfaces together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns compared with previous work that uses skeletons of 3 d volumes to represent sulcal patterns the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry in our experiments we demonstrate our method on two different cortical surface models its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions

automated 3 d extraction and evaluation of the inner and outer cortical surfaces using a laplacian map and partial volume effect classification accurate reconstruction of the inner and outer cortical surfaces of the human cerebrum is a critical objective for a wide variety of neuroimaging analysis purposes including visualization morphometry and brain mapping the anatomic segmentation using proximity asp algorithm previously developed by our group provides a topology preserving cortical surface deformation method that has been extensively used for the aforementioned purposes however constraints in the algorithm to ensure topology preservation occasionally produce incorrect thickness measurements due to a restriction in the range of allowable distances between the gray and white matter surfaces this problem is particularly prominent in pediatric brain images with tightly folded gyri this paper presents a novel method for improving the conventional asp algorithm by making use of partial volume information through probabilistic classification in order to allow for topology preservation across a less restricted range of cortical thickness values the new algorithm also corrects the classification of the insular cortex by masking out subcortical tissues for 70 pediatric brains validation experiments for the modified algorithm constrained laplacian asp clasp were performed by three methods i volume matching between surface masked gray matter gm and conventional tissue classified gm ii surface matching between simulated and clasp extracted surfaces and iii repeatability of the surface reconstruction among 16 mri scans of the same subject in the volume based evaluation the volume enclosed by the clasp wm and gm surfaces matched the classified gm volume 13 more accurately than using conventional asp in the surface based evaluation using synthesized thick cortex the average difference between simulated and extracted surfaces was 4 6 t 1 4 mm for conventional asp and 0 5 t 0 4 mm for clasp in a repeatability study clasp produced a 30 lower rms error for the gm surface and a 8 lower rms error for the

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

the elastic ratio introducing curvature into ratio based image segmentation we present the first ratio based image segmentation method that allows imposing curvature regularity of the region boundary our approach is a generalization of the ratio framework pioneered by jermyn and ishikawa so as to allow penalty functions that take into account the local curvature of the curve the key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment among ratios whose discrete counterparts can be globally minimized with our approach we focus in particular on the elastic ratio 0l c i c s c s ds vl c 0l c c s qds that depends given an image i on the oriented boundary c of the segmented region candidate minimizing this ratio amounts to finding a curve neither small nor too curvy through which the brightness flux is maximal we prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions we also prove that the discrete minimizers provided by our graph based algorithm converge as the resolution increases to continuous minimizers in contrast to most existing segmentation methods with computable and meaningful i e nondegenerate global optima the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations furthermore our results allow drawing conclusions about global optima of a parameterization independent version of the snakes functional the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution

automated 3 d extraction of inner and outer surfaces of cerebral cortex from mri automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging mri is greatly aided by deformable models which are used to extract identify and quantify specific neuroanatomic structures a general method of deforming polyhedra is presented here with two novel features first explicit prevention of self intersecting surface geometries is provided unlike conventional deformable models which use regularization constraints to discourage but not necessarily prevent such behavior second deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model based constraints such as expected thickness of an anatomic surface these two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human mr images accurately locating the depths of the sulci even where noise and partial volume artifacts in the image obscure the visibility of sulci the extracted surfaces are enforced to be simple two dimensional manifolds having the topology of a sphere even though the data may have topological holes this automatic 3 d cortex segmentation technique has been applied to 150 normal subjects simultaneously extracting both the gray white and gray cerebrospinal fluid interface from each individual the collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter three alternative criteria for defining cortical thickness at each cortical location were developed and compared these results are shown to corroborate published postmortem and in vivo measurements of cortical thickness

fast and robust parameter estimation for statistical partial volume models in brain mri due to the finite spatial resolution of imaging devices a single voxel in a medical image may be composed of mixture of tissue types an effect known as partial volume effect pve partial volume estimation that is the estimation of the amount of each tissue type within each voxel has received considerable interest in recent years much of this work has been focused on the mixel model a statistical model of pve we propose a novel trimmed minimum covariance determinant tmcd method for the estimation of the parameters of the mixel pve model in this method each voxel is first labeled according to the most dominant tissue type voxels that are prone to pve are removed from this labeled set following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class comparisons between different methods for parameter estimation based on classified images as well as expectation maximization like em like procedure for simultaneous parameter and partial volume estimation are reported the robust estimators based on a pruned classification as presented here are shown to perform well even if the initial classification is of poor quality the results obtained are comparable to those obtained using the em like procedure but require considerably less computation time segmentation results of real data based on partial volume estimation are also reported in addition to considering the parameter estimation problem we discuss differences between different approximations to the complete mixel model in summary the proposed tmcd method allows for the accurate robust and efficient estimation of partial volume model parameters which is crucial to a variety of brain mri data analysis procedures such as the accurate estimation of tissue volumes and the accurate delineation of the cortical surface

polynomial time algorithms for ratio regions and a variant of normalized cut in partitioning clustering and grouping problems a typical goal is to group together similar objects or pixels in the case of image processing at the same time another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large these goals are often combined as a ratio optimization problem one example of such a problem is a variant of the normalized cut problem another is the ratio regions problem we devise here the first polynomial time algorithms solving optimally the ratio region problem and the variant of normalized cut as well as a few other ratio problems the algorithms are efficient and combinatorial in contrast with nonlinear continuous approaches used in the image segmentation literature which often employ spectral techniques such techniques deliver solutions in real numbers which are not feasible to the discrete partitioning problem furthermore these continuous approaches are computationally expensive compared to the algorithms proposed here the algorithms presented here use as a subroutine a minimum s t cut procedure on a related graph which is of polynomial size the output consists of the optimal solution to the respective ratio problem as well as a sequence of nested solutions with respect to any relative weighting of the objectives of the numerator and denominator

a graph theoretical clustering method based on two rounds of minimum spanning trees many clustering approaches have been proposed in the literature but most of them are vulnerable to the different cluster sizes shapes and densities in this paper we present a graph theoretical clustering method which is robust to the difference based on the graph composed of two rounds of minimum spanning trees mst the proposed method 2 mstclus classifies cluster problems into two groups i e separated cluster problems and touching cluster problems and identifies the two groups of cluster problems automatically it contains two clustering algorithms which deal with separated clusters and touching clusters in two phases respectively in the first phase two round minimum spanning trees are employed to construct a graph and detect separated clusters which cover distance separated and density separated clusters in the second phase touching clusters which are subgroups produced in the first phase can be partitioned by comparing cuts respectively on the two round minimum spanning trees the proposed method is robust to the varied cluster sizes shapes and densities and can discover the number of clusters experimental results on synthetic and real datasets demonstrate the performance of the proposed method

surface based partial volume correction for high resolution pet abstract tissue radioactivity concentrations measured with positron emission tomography pet are subject to partial volume effects pve due to the limited spatial resolution of the scanner last generation high resolution pet cameras with a full width at half maximum fwhm of 2 4 mm are less prone to pves than previous generations corrections for pves are still necessary especially when studying small brain stem nuclei or small variations in cortical neuroreceptor concentrations which may be related to cytoarchitectonic differences although several partial volume correction pvc algorithms exist these are frequently based on a priori assumptions about tracer distribution or only yield corrected values of regional activity concentrations without providing pve corrected images we developed a new iterative deconvolution algorithm idsurf for pvc of pet images that aims to overcome these limitations by using two innovative techniques 1 the incorporation of anatomic information from a cortical gray matter surface representation extracted from magnetic resonance imaging mri and 2 the use of anatomically constrained filtering to attenuate noise pve corrected images were generated with idsurf implemented into a non interactive processing pipeline idsurf was validated using simulated and clinical pet data sets and compared to a frequently used standard pvc method geometric transfer matrix gtm the results on simulated data sets show that idsurf consistently recovers accurate radiotracer concentrations within 1 5 of true values both radiotracer concentrations and non displaceable binding potential bpnd values derived from clinical pet data sets with idsurf were highly correlated with those obtained with the standard pvc method r2 0 99 error 0 3 2 these results suggest that idsurf is a valid and potentially clinically useful pvc method for automatic processing of large numbers of pet data sets

clustering and embedding using commute times this paper exploits the properties of the commute time between nodes of a graph for the purposes of clustering and embedding and explores its applications to image segmentation and multibody motion tracking our starting point is the lazy random walk on the graph which is determined by the heat kernel of the graph and can be computed from the spectrum of the graph laplacian we characterize the random walk using the commute time that is the expected time taken for a random walk to travel between two nodes and return and show how this quantity may be computed from the laplacian spectrum using the discrete green s function our motivation is that the commute time can be anticipated to be a more robust measure of the proximity of data than the raw proximity matrix in this paper we explore two applications of the commute time the first is to develop a method for image segmentation using the eigenvector corresponding to the smallest eigenvalue of the commute time matrix we show that our commute time segmentation method has the property of enhancing the intragroup coherence while weakening intergroup coherence and is superior to the normalized cut the second application is to develop a robust multibody motion tracking method using an embedding based on the commute time our embedding procedure preserves commute time and is closely akin to kernel pca the laplacian eigenmap and the diffusion map we illustrate the results on both synthetic image sequences and real world video sequences and compare our results with several alternative methods

combining multiple clusterings using evidence accumulation we explore the idea of evidence accumulation eac for combining the results of multiple clusterings first a clustering ensemble a set of object partitions is produced given a data set n objects or patterns in d dimensions different ways of producing data partitions are 1 applying different clustering algorithms and 2 applying the same clustering algorithm with different values of parameters or initializations further combinations of different data representations feature spaces and clustering algorithms can also provide a multitude of significantly different data partitionings we propose a simple framework for extracting a consistent clustering given the various partitions in a clustering ensemble according to the eac concept each partition is viewed as an independent evidence of data organization individual data partitions being combined based on a voting mechanism to generate a new n times n similarity matrix between the n patterns the final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix we have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation based on the concept of mutual information between data partitions stability of the results is evaluated using bootstrapping techniques a detailed discussion of an evidence accumulation based clustering algorithm using a split and merge strategy based on the k means clustering algorithm is presented experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies and with individual clustering results produced by well known clustering algorithms

anomalous universality in the anisotropic ashkin teller model the ashkin teller at model is a generalization of ising 2 d to a four states spin model it can be written in the form of two ising layers in general with different couplings interacting via a four spin interaction it was conjectured long ago by kadanoff and wegner wu and lin baxter and others that at has in general two critical points and that universality holds in the sense that the critical exponents are the same as in the ising model except when the couplings of the two ising layers are equal isotropic case we obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points we find the somewhat unexpected feature that despite universality holds for the specific heat nevertheless nonuniversal critical indexes appear for instance the distance between the critical points rescale with an anomalous exponent as we let the couplings of the two ising layers coincide isotropic limit and so does the constant in front of the logarithm in the specific heat our result also explains how the crossover from universal to nonuniversal behaviour is realized

a tree structured framework for purifying complex clusters with structural roles of individual data how can we find a natural clustering of a complex dataset which may contain an unknown number of overlapping clusters of arbitrary shape and be contaminated by noise a tree structured framework is proposed in this paper to purify such clusters by exploring the structural role of each data in practice each individual object within the internal organization of the data has its own specific role centroid hub or outlier due to distinctive associations with their respective neighbors adjacent centroids always interact on each other and serve as mediate nodes of one tree being members of some cluster hubs closed to some centroid become leaf nodes responsible for the termination of the growth of trees outliers that weakly touch with any centroid are often discarded from any trees as global noise all the data can thus be labeled by a specified criterion of centroids connected structural consistency ccsc free of domain specific information our framework with ccsc could widely adapt to many clustering related applications theoretical and experimental contributions both confirm that our framework is easy to interpret and implement efficient and effective in complex clustering

universality of one dimensional fermi systems i response functions and critical exponents the critical behavior of one dimensional interacting fermi systems is expected to display universality features called luttinger liquid behavior critical exponents and certain thermodynamic quantities are expected to be related among each other by model independent formulas we establish such relations the proof of which has represented a challenging mathematical problem for a general model of spinning fermions on a one dimensional lattice interactions are short ranged and satisfy a positivity condition which makes the model critical at zero temperature proofs are reported in two papers in the present one we demonstrate that the zero temperature response functions in the thermodynamic limit are borel summable and have anomalous power law decay with multiplicative logarithmic corrections critical exponents are expressed in terms of convergent expansions and depend on all the model details all results are valid for the special case of the hubbard model

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

an information theoretic approach to spectral variability similarity and discrimination for hyperspectral image analysis a hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths as a result a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability similarity and discrimination we present a new hyperspectral measure the spectral information measure sim to describe spectral variability and two criteria spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination respectively the spectral information measure is an information theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution spectral information divergence sid compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures the spectral discriminatory probability calculates spectral probabilities of a spectral database library relative to a pixel to be identified so as to achieve material identification in order to compare the discriminatory power of one spectral measure relative to another a criterion is also introduced for performance evaluation which is based on the power of discriminating one pixel from another relative to a reference pixel the experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper sam

effective action for the yukawa 2 quantum field theory using a rigorous version of the renormalization group we construct the effective action for they2 model the construction starts with integrating out the bosonic field which eliminates the large fields problem studying the soobtained purely fermionic theory proceeds by a series of convergent perturbation expansions we show that the continuum limit of the effective action exists and its perturbation expansion is borel summable

a novel quantitative cross validation of different cortical surface reconstruction algorithms using mri phantom cortical surface reconstruction is important for functional brain mapping and morphometric analysis of the brain cortex several methods have been developed for the faithful reconstruction of surface models which represent the true cortical surface in both geometry and topology however there has been no explicit comparison study among those methods because each method has its own procedures file formats coordinate systems and use of the reconstructed surface there has also been no explicit evaluation method except visual inspection to validate the whole cortical surface models quantitatively in this study we presented a novel phantom based validation method of the cortical surface reconstruction algorithm and quantitatively cross validated the three most prominent cortical surface reconstruction algorithms which are used in freesurfer brainvisa and clasp respectively the validation included geometrical accuracy and mesh characteristics such as euler number fractal dimension fd total surface area and local density of points clasp showed the best geometric topologic accuracy and mesh characteristics such as fd and total surface area compared to freesurfer and brainvisa in the validation of local density of points freesurfer and brainvisa showed more even distribution of points on the cortical surface compared to clasp

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

regularized tree partitioning and its application to unsupervised image segmentation in this paper we propose regularized tree partitioning approaches we study normalized cut ncut and average cut acut criteria over a tree forming two approaches 1 normalized tree partitioning ntp and 2 average tree partitioning atp we give the properties that result in an efficient algorithm for ntp and atp in addition we present the relations between the solutions of ntp and atp over the maximum weight spanning tree of a graph and ncut and acut over this graph to demonstrate the effectiveness of the proposed approaches we show its application to image segmentation over the berkeley image segmentation data set and present qualitative and quantitative comparisons with state of the art methods

surface area and cortical thickness descriptors reveal different attributes of the structural human brain networks recently a related morphometry based connection concept has been introduced using local mean cortical thickness and volume to study the underlying complex architecture of the brain networks in this article the surface area is employed as a morphometric descriptor to study the concurrent changes between brain structures and to build binarized connectivity graphs the statistical similarity in surface area between pair of regions was measured by computing the partial correlation coefficient across 186 normal subjects of the cuban human brain mapping project we demonstrated that connectivity matrices obtained follow a small world behavior for two different parcellations of the brain gray matter the properties of the connectivity matrices were compared to the matrices obtained using the mean cortical thickness for the same cortical parcellations the topology of the cortical thickness and surface area networks were statistically different demonstrating that both capture distinct properties of the interaction or different aspects of the same interaction mechanical anatomical chemical etc between brain structures this finding could be explained by the fact that each descriptor is driven by distinct cellular mechanisms as result of a distinct genetic origin to our knowledge this is the first time that surface area is used to study the morphological connectivity of brain networks

self validated labeling of markov random fields for image segmentation this paper addresses the problem of self validated labeling of markov random fields mrfs namely to optimize an mrf with unknown number of labels we present graduated graph cuts ggc a new technique that extends the binary s t graph cut for self validated labeling specifically we use the split and merge strategy to decompose the complex problem to a series of tractable subproblems in terms of gibbs energy minimization a suboptimal labeling is gradually obtained based upon a set of cluster level operations by using different optimization structures we propose three practical algorithms tree structured graph cuts tsgc net structured graph cuts nsgc and hierarchical graph cuts hgc in contrast to previous methods the proposed algorithms can automatically determine the number of labels properly balance the labeling accuracy spatial coherence and the labeling cost i e the number of labels and are computationally efficient independent to initialization and able to converge to good local minima of the objective energy function we apply the proposed algorithms to natural image segmentation experimental results show that our algorithms produce generally feasible segmentations for benchmark data sets and outperform alternative methods in terms of robustness to noise speed and preservation of soft boundaries

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

agglomerative clustering via maximum incremental path integral abstract agglomerative clustering which iteratively merges small clusters is commonly used for clustering because it is conceptually simple and produces a hierarchy of clusters in this paper we propose a novel graph structural agglomerative clustering algorithm where the graph encodes local structures of data the idea is to define a structural descriptor of clusters on the graph and to assume that two clusters have large affinity if their structural descriptors undergo substantial change when merging them into one cluster a key insight of this paper to treat a cluster as a dynamical system and its samples as states based on that path integral which has been introduced in statistical mechanics and quantum mechanics is utilized to measure the stability of a dynamical system it is proposed as the structural descriptor and the affinity between two clusters is defined as incremental path integral which can be computed in a closed form exact solution with linear time complexity with respect to the maximum size of clusters a probabilistic justification of the algorithm based on absorbing random walk is provided experimental comparison on toy data and imagery data shows that it achieves considerable improvement over the state of the art clustering algorithms

graph characteristics from the heat kernel trace graph structures have been proved important in high level vision since they can be used to represent structural and relational arrangements of objects in a scene one of the problems that arises in the analysis of structural abstractions of objects is graph clustering in this paper we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering the heat kernel is the solution of the heat equation and is a compact representation of the path length distribution on a graph the trace of the heat kernel is given by the sum of the laplacian eigenvalues exponentiated with time we explore three different approaches to characterizing the heat kernel trace as a function of time our first characterization is based on the zeta function which from the mellin transform is the moment generating function of the heat kernel trace our second characterization is unary and is found by computing the derivative of the zeta function at the origin the third characterization is derived from the heat content i e the sum of the elements of the heat kernel we show how the heat content can be expanded as a power series in time and the coefficients of the series can be computed using the laplacian spectrum we explore the use of these characterizations as a means of representing graph structure for the purposes of clustering and compare them with the use of the laplacian spectrum experiments with the synthetic and real world databases reveal that each of the three proposed invariants is effective and outperforms the traditional laplacian spectrum moreover the heat content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real world object recognition problems

image segmentation with ratio cut this paper proposes a new cost function cut ratio for segmenting images using graph based methods the cut ratio is defined as the ratio of the corresponding sums of two different weights of edges along the cut boundary and models the mean affinity between the segments separated by the boundary per unit boundary length this new cost function allows the image perimeter to be segmented guarantees that the segments produced by bipartitioning are connected and does not introduce a size shape smoothness or boundary length bias the latter allows it to produce segmentations where boundaries are aligned with image edges furthermore the cut ratio cost function allows efficient iterated region based segmentation as well as pixel based segmentation these properties may be useful for some image segmentation applications while the problem of finding a minimum ratio cut in an arbitrary graph is np hard one can find a minimum ratio cut in the connected planar graphs that arise during image segmentation in polynomial time while the cut ratio alone is not sufficient as a baseline method for image segmentation it forms a good basis for an extended method of image segmentation when combined with a small number of standard techniques we present an implemented algorithm for finding a minimum ratio cut prove its correctness discuss its application to image segmentation and present the results of segmenting a number of medical and natural images using our techniques

trace a topological graph representation for automatic sulcal curve extraction a proper geometric representation of the cortical regions is a fundamental task for cortical shape analysis and landmark extraction however a significant challenge has arisen due to the highly variable convoluted cortical folding patterns in this paper we propose a novel topological graph representation for automatic sulcal curve extraction trace in practice the reconstructed surface suffers from noise influences introduced during image acquisition surface reconstruction in the presence of noise on the surface trace determines stable sulcal fundic regions by employing the line simplification method that prevents the sulcal folding pattern from being significantly smoothed out the sulcal curves are then traced over the connected graph in the determined regions by the dijkstra s shortest path algorithm for validation we used the state of the art surface reconstruction pipelines on a reproducibility data set the experimental results showed higher reproducibility and robustness to noise in trace than the existing method li et al 2010 with over 20 relative improvement in error for both surface reconstruction pipelines in addition the extracted sulcal curves by trace were well aligned with manually delineated primary sulcal curves we also provided a choice of parameters to control quality of the extracted sulcal curves and showed the influences of the parameter selection on the resulting curves

three dimensional topology preserving reduction on the 4 subfields this paper discusses thinning on 3d binary images with the 4 subfield approach although a thinning algorithm concerns binary images the algorithm itself can be represented as a set of three color reduction templates a thinning algorithm is topology preserving if the set of all three color templates is topology preserving sufficient and necessary conditions of time complexity o n were proposed for verifying the topological soundness of a 3d 4 subfield thinning algorithm of n three color templates theories and techniques for computerizing such conditions were discussed two 4 subfield thinning algorithms on 3d images one for generating medial curves and the other one for generating medial surfaces are proposed and proved to preserve topology by our sufficient and necessary conditions

skull stripping using graph cuts removal of non brain tissues particularly dura is an important step in enabling accurate measurement of brain structures many popular methods rely on iterative surface deformation to fit the brain boundary and tend to leave residual dura similar to other approaches the method proposed here uses intensity thresholding followed by removal of narrow connections to obtain a brain mask however instead of using morphological operations to remove narrow connections a graph theoretic image segmentation technique was used to position cuts that isolate and remove dura this approach performed well on both the standardized ibsr test data sets and empirically derived data compared to the hybrid watershed algorithm hwa segonne et al 2004 the novel approach achieved an additional 10 30 of dura removal without incurring further brain tissue erosion the proposed method is best used in conjunction with hwa as the errors produced by the two approaches often occur at different locations and cancel out when their masks are combined our experiments indicate that this combination can substantially decrease and often fully avoid cortical surface overestimation in subsequent segmentation

massless sine gordon and massive thirring models proof of coleman s equivalence we prove coleman s conjecture on the equivalence between the massless sine gordon model with finite volume interaction and the thirring model with a finite volume mass term

structured weak semantic space construction for visual categorization visual features have been widely used for image representation and categorization however visual features are often inconsistent with human perception besides constructing explicit semantic space is still an open problem to alleviate these two problems in this paper we propose to construct structured weak semantic space for image representation exemplar classifier is first trained to separate each training image from other images for weak semantic space construction however each exemplar classifier separates one training image from other images and it only has limited semantic separability besides the outputs of exemplar classifiers are inconsistent with each other we jointly construct the weak semantic space using structured constraint this is achieved by imposing low rank constraint on the outputs of exemplar classifiers with sparsity constraint an alternative optimization procedure is used to learn the exemplar classifiers since the proposed method does not dependent on the initial image representation strategy we can make use of various visual features for efficient exemplar classifier training e g fisher vector based methods and convolutional neural networks based methods we apply the proposed structured weak semantic space based image representation method for categorization the experimental results on several public image data sets prove the effectiveness of the proposed method

spectral based automatic labeling and refining of human cortical sulcal curves using expert provided examples we present a spectral based method for automatically labeling and refining major sulcal curves of a human cerebral cortex given a set of input unlabeled sulcal curves automatically extracted from a cortical surface and a collection of expert provided examples labeled sulcal curves our objective is to identify the input major sulcal curves and assign their neuroanatomical labels and then refines these curves based on the expert provided example data without employing any atlas based registration scheme as preprocessing in order to construct the example data neuroanatomists manually labeled a set of 24 major sulcal curves 12 each for the left and right hemispheres for each individual subject according to a precise protocol we collected 30 sets of such curves from 30 subjects given the raw input sulcal curve set of a subject we choose the most similar example curve to each input curve in the set to label and refine the latter according to the former we adapt a spectral matching algorithm to choose the example curve by exploiting the sulcal curve features and their relationship the high dimensionality of sulcal curve data in spectral matching is addressed by using their multi resolution representations which greatly reduces time and space complexities our method provides consistent labeling and refining results even under high variability of cortical sulci across the subjects through experiments we show that the results are comparable in accuracy to those done manually most output curves exhibited accuracy values higher than 80 and the mean accuracy values of the curves in the left and the right hemispheres were 84 69 and 84 58 respectively

on the efficient evaluation of probabilistic similarity functions for image retrieval probabilistic approaches are a promising solution to the image retrieval problem that when compared to standard retrieval methods can lead to a significant gain in retrieval accuracy however this occurs at the cost of a significant increase in computational complexity in fact closed form solutions for probabilistic retrieval are currently available only for simple probabilistic models such as the gaussian or the histogram we analyze the case of mixture densities and exploit the asymptotic equivalence between likelihood and kullback leibler kl divergence to derive solutions for these models in particular 1 we show that the divergence can be computed exactly for vector quantizers vqs and 2 has an approximate solution for gauss mixtures gms that in high dimensional feature spaces introduces no significant degradation of the resulting similarity judgments in both cases the new solutions have closed form and computational complexity equivalent to that of standard retrieval approaches

the scaling limit of the energy correlations in non integrable ising models we obtain an explicit expression for the multipoint energy correlations of a non solvable two dimensional ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory which generalizes the one originally used by schultz mattis and lieb for the nearest neighbor ising model the interacting model is then analyzed by a multiscale method first proposed by pinson and spencer if the lattice spacing is finite then the correlations cannot be computed in closed form rather they are expressed in terms of infinite convergent power series in in the scaling limit these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable ising model up to a finite renormalization of the parameters explicit bounds on the speed of convergence to the scaling limit are derived

spectral partitioning works planar graphs and finite element meshes abstract spectral partitioning methods use the fiedler vector the eigenvector of the second smallest eigenvalue of the laplacian matrix to find a small separator of a graph these methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well in this paper we show that spectral partitioning methods work well on bounded degree planar graphs and finite element meshes the classes of graphs to which they are usually applied while naive spectral bisection does not necessarily work we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is o n for bounded degree planar graphs and two dimensional meshes and o n1 d for well shaped d dimensional meshes the heart of our analysis is an upper bound on the second smallest eigenvalues of the laplacian matrices of these graphs we prove a bound of o 1 n for bounded degree planar graphs and o 1 n2 d for well shaped d dimensional meshes

a probabilistic spectral framework for grouping and segmentation this paper presents an iterative spectral framework for pairwise clustering and perceptual grouping our model is expressed in terms of two sets of parameters firstly there are cluster memberships which represent the affinity of objects to clusters secondly there is a matrix of link weights for pairs of tokens we adopt a model in which these two sets of variables are governed by a bernoulli model we show how the likelihood function resulting from this model may be maximised with respect to both the elements of link weight matrix and the cluster membership variables we establish the link between the maximisation of the log likelihood function and the eigenvectors of the link weight matrix this leads us to an algorithm in which we iteratively update the link weight matrix by repeatedly refining its modal structure each iteration of the algorithm is a three step process first we compute a link weight matrix for each cluster by taking the outer product of the vectors of current cluster membership indicators for that cluster second we extract the leading eigenvector from each modal link weight matrix third we compute a revised link weight matrix by taking the sum of the outer products of the leading eigenvectors of the modal link weight matrices

sense factors for reliable cortical thickness measurement the purposes of this study were to examine the effect of sensitivity encoding sense factors on cortical thickness measurements and to determine which sense factor to use to reliably measure cortical thickness in 3 0 t and 1 5 t t1 weighted mri images the 3d t1 tfe images were acquired from 11 healthy volunteers with 6 different sense acceleration factors from 1 0 without sense acceleration to 4 0 on a 1 5 t scanner and 9 different sense factors from 1 0 to 6 0 plus a second day 1 0 acquisition on a 3 0 t scanner cortical thickness was calculated for the entire cortical surface that was further subdivided into 33 regions repeated measures multivariate analysis of variance revealed that the main effect of sense factors f 12 485 df 7 p 0 006 was a significant underestimation of cortical thickness at sense 5 0 p 0 022 and 6 0 p 0 011 at 3 0 t and at sense 4 0 p 0 000 at 1 5 t repeated measures anova showed that thickness measurements at the insula superior temporal sulcus the medial part of the superior frontal lobe and cingulate cortex are highly affected by sense factors sense factors affect thickness estimation more significantly at 1 5 t and thus 1 5 t imaging provides less reliable estimates using sense techniques faster imaging can be done without too much loss of reliability using a high sense factor such as 3 0 at 3 0 t with acquisition time being inversely proportional to the sense factor

cross sectional versus longitudinal designs for function estimation with an application to cerebral cortex development motivated by studies of the development of the human cerebral cortex we consider the estimation of a mean growth trajectory and the relative merits of cross sectional and longitudinal data for that task we define a class of relative efficiencies that compare function estimates in terms of aggregate variance of a parametric function estimate these generalize the classical design effect for estimating a scalar with cross sectional versus longitudinal data and are shown to be bounded above by it in certain cases turning to nonparametric function estimation we find that longitudinal fits may tend to have higher aggregate variance than cross sectional ones but that this may occur because the former have higher effective degrees of freedom reflecting greater sensitivity to subtle features of the estimand these ideas are illustrated with cortical thickness data from a longitudinal neuroimaging study

on clustering tree structured data with categorical nature clustering consists in partitioning a set of objects into disjoint and homogeneous clusters for many years clustering methods have been applied in a wide variety of disciplines and they also have been utilized in many scientific areas traditionally clustering methods deal with numerical data i e objects represented by a conjunction of numerical attribute values however nowadays commercial or scientific databases usually contain categorical data i e objects represented by categorical attributes in this paper we present a dissimilarity measure which is capable to deal with tree structured categorical data thus it can be used for extending the various versions of the very popular k means clustering algorithm to deal with such data we discuss how such an extension can be achieved moreover we empirically prove that the proposed dissimilarity measure is accurate compared to other well known dis similarity measures for categorical data

automatic segmentation and reconstruction of the cortex from neonatal mri abstract segmentation and reconstruction of cortical surfaces from magnetic resonance mr images are more challenging for developing neonates than adults this is mainly due to the dynamic changes in the contrast between gray matter gm and white matter wm in both t1 and t2 weighted images t1w and t2w during brain maturation in particular in neonatal t2w images wm typically has higher signal intensity than gm this causes mislabeled voxels during cortical segmentation especially in the cortical regions of the brain and in particular at the interface between gm and cerebrospinal fluid csf we propose an automatic segmentation algorithm detecting these mislabeled voxels and correcting errors caused by partial volume effects our results show that the proposed algorithm corrects errors in the segmentation of both gm and wm compared to the classic expectation maximization em scheme quantitative validation against manual segmentation demonstrates good performance the mean dice value 0 758 0 037 for gm and 0 794 0 078 for wm the inner central and outer cortical surfaces are then reconstructed using implicit surface evolution a landmark study is performed to verify the accuracy of the reconstructed cortex the mean surface reconstruction error 0 73 mm for inner surface and 0 63 mm for the outer both segmentation and reconstruction have been tested on 25 neonates with the gestational ages ranging from 27 to 45 weeks this preliminary analysis confirms previous findings that cortical surface area and curvature increase with age and that surface area scales to cerebral volume according to a power law while cortical thickness is not related to age or brain growth

clustering and outlier detection using isoperimetric number of trees we propose a graph based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria we show that our basic clustering algorithm runs in o nlogn and with post processing in almost o nlogn average case and o n 2 worst case time where n is the size of the data set it is also shown that our generalized graph model which also allows the use of potentials at vertices can be used to extract an extra piece of information related to anomalous data patterns and outliers in this regard we propose an algorithm that extracts outliers in parallel to data clustering we also provide a comparative performance analysis of our algorithms with other related ones and we show that they behave quite effectively on hard synthetic data sets as well as real world benchmarks

component analysis approach to estimation of tissue intensity distributions of 3d images many segmentation algorithms in medical imaging rely on accurate modeling and estimation of tissue intensity probability density functions gaussian mixture modeling currently the most common approach has several drawbacks such as reliance on a gaussian model and iterative local optimization used to estimate the model parameters it also does not take advantage of substantially larger amount of data provided by 3d acquisitions which are becoming standard in clinical environment we propose a novel and completely non parametric algorithm to estimate the tissue intensity probabilities in 3d images instead of relying on traditional framework of iterating between classification and estimation we pose the problem as an instance of a blind source separation problem where the unknown distributions are treated as sources and histograms of image subvolumes as mixtures the new approach performed well on synthetic data and real magnetic resonance imaging mri scans of the brain robustly capturing intensity distributions of even small image structures and partial volume voxels

clustering ensembles models of consensus and weak partitions clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions however finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph based combinatorial or statistical perspectives this study extends previous research on clustering ensembles in several respects first we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem second we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings a combined partition is found as a solution to the corresponding maximum likelihood problem using the em algorithm third we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition finally we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits a simple explanatory model is offered for the behavior of combinations of such weak clustering components combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions we also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus experimental results demonstrate the effectiveness of the proposed methods on several real world data sets

construction of a fetal spatio temporal cortical surface atlas from in utero mri application of spectral surface matching abstract in this study we construct a spatio temporal surface atlas of the developing cerebral cortex which is an important tool for analysing and understanding normal and abnormal cortical development in utero magnetic resonance imaging mri of 80 healthy fetuses was performed with a gestational age range of 21 7 to 38 9 weeks topologically correct cortical surface models were extracted from reconstructed 3d mri volumes accurate correspondences were obtained by applying a joint spectral analysis to cortices for sets of subjects close to a specific age sulcal alignment was found to be accurate in comparison to spherical demons a state of the art registration technique for aligning 2d cortical representations average frechet distance 0 4 mm at 30 weeks we construct consistent unbiased average cortical surface templates for each week of gestation from age matched groups of surfaces by applying kernel regression in the spectral domain these were found to accurately capture the average cortical shape of individuals within the cohort suggesting a good alignment of cortical geometry each spectral embedding and its corresponding cortical surface template provide a dual reference space where cortical geometry is aligned and a vertex wise morphometric analysis can be undertaken

replica inference approach to unsupervised multiscale image segmentation we apply a replica inference based potts model method to unsupervised image segmentation on multiple scales this approach was inspired by the statistical mechanics problem of community detection and its phase diagram specifically the problem is cast as identifying tightly bound clusters communities or solutes against a background or solvent within our multiresolution approach we compute information theory based correlations among multiple solutions replicas of the same graph over a range of resolutions significant multiresolution structures are identified by replica correlations manifest by information theory overlaps we further employ such information theory measures such as normalized mutual information and variation of information thermodynamic quantities such as the system entropy and energy and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases within the solvable phase transitions between contending solutions such as those corresponding to segmentations on different scales may also appear with the aid of these correlations as well as thermodynamic measures the phase diagram of the corresponding potts model is analyzed at both zero and finite temperatures optimal parameters corresponding to a sensible unsupervised segmentations appear within the easy phase of the potts model our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images

heritability estimates of cortical anatomy the influence and reliability of different estimation strategies twin study designs have been previously used to investigate the heritability of neuroanatomical measures such as regional cortical volumes volume can be fractionated into surface area and cortical thickness where both measures are considered to have independent genetic and environmental bases region of interest roi and vertex wise approaches have been used to calculate heritability of cortical thickness and surface area in twin studies in our study we estimate heritability using the human connectome project magnetic resonance imaging dataset composed of healthy young twin and non twin siblings mean age of 29 sample size of 757 both roi and vertex wise methods were used to compare regional heritability of cortical thickness and surface area heritability estimates were controlled for age sex and total ipsilateral surface area or mean cortical thickness in both approaches heritability estimates of cortical thickness and surface area were lower when accounting for average ipsilateral cortical thickness and total surface area respectively when comparing both approaches at a regional level the vertex wise approach showed higher surface area and lower cortical thickness heritability estimates compared to the roi approach the calcarine fissure had the highest surface area heritability estimate roi 44 vertex wise 50 and posterior cingulate gyrus had the highest cortical thickness heritability roi 50 vertex wise 40 we also observed that limitations in image processing and variability in spatial averaging errors based on regional size may make obtaining true estimates of cortical thickness and surface area challenging in smaller regions it is important to identify which approach is best suited to estimate heritability based on the research hypothesis and the size of the regions being investigated

magnetic resonance image tissue classification using a partial volume model abstract we describe a sequence of low level operations to isolate and classify brain tissue within t1 weighted magnetic resonance images mri our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering edge detection and mathematical morphology we compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic b spline gain field to local estimates of the image nonuniformity spaced throughout the mri volume the local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point the measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit voxels in the intensity normalized image are then classified into six tissue types using a maximum a posteriori classifier this classifier combines the partial volume tissue measurement model with a gibbs prior that models the spatial properties of the brain we validate each stage of our algorithm on real and phantom data using data from the 20 normal mri brain data sets of the internet brain segmentation repository our method achieved average indices of 0 746 0 114 for gray matter gm and 0 798 0 089 for white matter wm compared to expert labeled data our method achieved average indices 0 893 0 041 for gm and 0 928 0 039 for wm compared to the ground truth labeling on 12 volumes from the montreal neurological institute s brainweb phantom

artificial shifting of fmri activation localized by volume and surface based analyses spatial smoothing is an important post processing procedure that is used to increase the signal to noise ratio snr of blood oxygenation level dependent signals bold in common functional magnetic resonance imaging fmri applications however recent studies have shown that smoothing artificially shifts probabilistic local maxima of fmri activations in this study we show shifting of the localization of functional centers in hand motor areas of the cerebral cortex by three dimensional isotropic gaussian kernel smoothing or two dimensional heat kernel smoothing in volume and surface based fmri analyses activation maps derived from smoothed echo planar imaging epi data by volume and surface based analyses were assigned to the nodes of individual cortical surface models and local maxima in the primary motor area m1 and the primary somatosensory cortex s1 were compared with those derived from non smoothed risk map analysis which is commonly used in presurgical applications for each analysis the euclidean and geodesic distances between the correlation coefficients of local maxima derived from smoothed and non smoothed epi data were measured the results show that the correlation coefficients derived from the volume and surface based analyses were about 29 4 and 42 9 higher for smoothed than for non smoothed risk map analyses and show minimum shifting of localizations by 12 1 mm and 6 9 mm on average in euclidean distance respectively and about 9 5 mm and 5 7 mm on average in geodesic distance respectively

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model