incorporating spatial dependence into bayesian multiple testing of statistical parametric maps in functional neuroimaging abstract the analysis of functional neuroimaging data often involves the simultaneous testing for activation at thousands of voxels leading to a massive multiple testing problem this is true whether the data analyzed are time courses observed at each voxel or a collection of summary statistics such as statistical parametric maps spms it is known that classical multiplicity corrections become strongly conservative in the presence of a massive number of tests some more popular approaches for thresholding imaging data such as the benjamini hochberg step up procedure for false discovery rate control tend to lose precision or power when the assumption of independence of the data does not hold bayesian approaches to large scale simultaneous inference also often rely on the assumption of independence we introduce a spatial dependence structure into a bayesian testing model for the analysis of spms by using spms rather than the voxel time courses much of the computational burden of bayesian analysis is mitigated increased power is demonstrated by using the dependence model to draw inference on a real dataset collected in a fmri study of cognitive control the model also is shown to lead to improved identification of neural activation patterns known to be associated with eye movement tasks

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

empirical analyses of bold fmri statistics ii spatially smoothed data collected under null hypothesis and experimental conditions in the companion to this paper e zarahn g k aguirre and m d esposito 1997 neuroimage 179 197 we describe an implementation of a general linear model for autocorrelated observations in which the voxel wise false positive rates in fmri noise datasets were stabilized and brought close to theoretical values here implementations of the model are tested for use with statistical parametric mapping analysis of spatially smoothed fmri data analyses using varying models of intrinsic temporal autocorrelation and either including or excluding a global signal covariate were conducted upon human subject data collected under null hypothesis as well as under experimental conditions we found that smoothing with an empirically derived impulse response function irf combined with a model of the intrinsic temporal autocorrelation in spatially smoothed fmri data resulted in a map wise false positive rate which did not exceed a 5 level when a nominal alpha 0 05 tabular threshold was applied use of other models of intrinsic temporal autocorrelation resulted in map wise false positive rates that significantly exceeded this level fmri data collected while subjects performed a behavioral task were used to examine a task dependent global signal changes and b the dependence of sensitivity on the temporal smoothing kernel and inclusion exclusion of a global signal covariate the global signal changes within an fmri dataset were shown to be influenced by the performance of a behavioral task however the inclusion of this measure as a covariate did not have an adverse affect upon our measure of sensitivity finally use of an empirically derived estimate of the irf of the system was shown to result in greater map wise sensitivity for signal changes than the use of a broader in time poisson parameter 8 s kernel

a new approach to computing the euler characteristic in this paper we describe a new approach to computing the euler characteristic of a three dimensional digital image our approach is based on computing the change in numbers of black components tunnels and cavities in 3 x 3 x 3 neighborhood of an object black point due to its deletion the existing algorithms to computing the euler characteristic of a 3d digital image are based on counting the numbers of all k dimensional elements 0 k 3 in a polyhedral representation of the image our approach can be modified for 6 26 18 6 6 18 and other connectivity relations of grid points a parallel implementation of the algorithm is described using the concept of sub fields

on the detection of simple points in higher dimensions using cubical homology simple point detection is an important task for several problems in discrete geometry such as topology preserving thinning in image processing to compute discrete skeletons in this paper the approach to simple point detection is based on techniques from cubical homology a framework ideally suited for problems in image processing a d dimensional unitary cube for a d dimensional digital image is associated with every discrete picture element instead of a point in spl epsi sup d the d dimensional euclidean space as has been done previously a simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image the main result is a characterization of a simple point p i e simple unitary cube in terms of the homology groups of the 3 sup d 1 neighborhood of p for arbitrary finite dimensions d

roc analysis of statistical methods used in functional mri individual subjects the complicated structure of fmri signals and associated noise sources make it difficult to assess the validity of various steps involved in the statistical analysis of brain activation most methods used for fmri analysis assume that observations are independent and that the noise can be treated as white gaussian noise these assumptions are usually not true but it is difficult to assess how severely these assumptions are violated and what are their practical consequences in this study a direct comparison is made between the power of various analytical methods used to detect activations without reference to estimates of statistical significance the statistics used in fmri are treated as metrics designed to detect activations and are not interpreted probabilistically the receiver operator characteristic roc method is used to compare the efficacy of various steps in calculating an activation map in the study of a single subject based on optimizing the ratio of the number of detected activations to the number of false positive findings the main findings are as follows preprocessing the removal of intensity drifts and high pass filtering applied on the voxel time course level is beneficial to the efficacy of analysis temporal normalization of the global image intensity smoothing in the temporal domain and low pass filtering do not improve power of analysis choices of statistics the cross correlation coefficient and t statistic as well as nonparametric mann whitney statistics prove to be the most effective and are similar in performance by our criterion task design the proper design of task protocols is shown to be crucial in an alternating block design the optimal block length is be approximately 18 s spatial clustering an initial spatial smoothing of images is more efficient than cluster filtering of the statistical parametric activation maps

on clustering fmri time series analysis of fmri time series is often performed by extracting one or more parameters for the individual voxels methods based e g on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength however these methods do not indicate whether sets of voxels are activated in a similar way or in different ways typically delays between two activated signals are not identified in this article we use clustering methods to detect similarities in activation between voxels we employ a novel metric that measures the similarity between the activation stimulus and the fmri signal we present two different clustering algorithms and use them to identify regions of similar activations in an fmri experiment involving a visual stimulus

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

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

detection of 3 d simple points for topology preserving transformations with application to thinning the problems of 3 d digital topology preservation under binary transformations and 3 d object thinning are considered in this correspondence first the authors establish the conditions under which transformation of an object voxel to a non object voxel or its inverse does not affect the image topology an efficient algorithm to detect a simple point has been proposed on the basis of those conditions in this connection some other interesting properties of 3 d digital geometry are also discussed using these properties and the simple point detection algorithm the authors have proposed an algorithm to generate a surface skeleton so that the topology of the original image is preserved the shape of the image is maintained as much as possible and the results are less affected by noise

surfaces in three dimensional digital images this is one of a series of reports on the digital geometry of three dimensional images such as those produced by computed tomography in this report we define simple surface points and simple closed surfaces and show that any connected collection of simple surface points form a simple closed surface thus proving a three dimensional analog of the two dimensional jordan curve theorem we also show that the converse is not a theorem in contrast to the two dimensional case and discuss more complex surface types finally we show that the two dimensional analog of our definition of simple closed surface characterizes simple closed curves but that several other characterizations of 2 d curves when extended to 3 d are not adequate to characterize surfaces

two point taylor approximations of the solutions of two dimensional boundary value problems abstract we consider two dimensional elliptic boundary value problems of the form l u f in r 2 bounded and open with a dirichlet boundary condition u h where l is a second order linear differential operator whose coefficients as well as the functions f and h are differentiable up to a certain degree in a recent paper c kesan taylor polynomial solutions of second order linear partial differential equations appl math comput 152 2004 29 41 a matrix algorithm is introduced to compute the standard taylor polynomial of the solution u at a certain point in we propose an alternative formulation of the problem based on a redefinition of the unknown u and the use of the standard frobenius method that simplifies the computation of the taylor coefficients of u we also consider the use of a two point taylor representation of the solution instead of the classical one point taylor representation which gives a more uniform approximation of the solution

convergence analysis of bernoulli matrix approach for one dimensional matrix hyperbolic equations of the first order abstract in this paper an approximate approach based on bernoulli operational matrices has been presented to obtain the numerical solution of first order matrix hyperbolic partial differential equations under the given initial conditions after using the operational matrices we use the completeness of bernoulli basis in which the main problem reduces to a system of algebraic equations the solutions of this algebraic system are the coefficients of the truncated double bernoulli series which are defined in the interval 0 1 also convergence analysis associated to the presented idea is provided under several mild conditions several numerical examples are considered to show the efficiency of the technique

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

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

analysis of fmri data using improved self organizing mapping and spatio temporal metric hierarchical clustering the self organizing mapping som and hierarchical clustering hc methods are integrated to detect brain functional activation functional magnetic resonance imaging fmri data are first processed by som to obtain a primary merged neural nodes image and then by hc to obtain further brain activation patterns the conventional euclidean distance metric was replaced by the correlation distance metric in som to improve clustering and merging of neural nodes to improve the use of spatial and temporal information in fmri data a new spatial distance node coordinates in the 2 d lattice and temporal correlation correlation degree of each time course in the exemplar matrix are introduced in hc to merge the primary som results two simulation studies and two in vivo fmri data that both contained block design and event related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods our results demonstrate that the improved som and hc methods are clearly superior to the statistical parametric mapping spm independent component analysis ica and conventional som methods in the block design especially in the event related experiment as revealed by their performance measured by receiver operating characteristic roc analysis our results also suggest that the proposed new integrated approach could be useful in detecting block design and event related fmri data

chebyshev polynomial solutions of second order linear partial differential equations the purpose of this study is to give a taylor polynomial approximation for the solution of second order linear partial differential equations with two variables and variable coefficients for this purpose taylor matrix method for the approximate solution of second order linear partial differential equations with specified associated conditions in terms of taylor polynomials about any point the method is based on first taking truncated taylor series of the functions in equation and then substituting their matrix forms into the given equation thereby the equation reduces to a matrix equation which corresponds to a system of linear algebraic equations with unknown taylor coefficients hence the result matrix equation can be solved and the unknown taylor coefficients can be found approximately

optimal spline smoothing of fmri time series by generalized cross validation linear parametric regression models of fmri time series have correlated residuals one approach to address this problem is to condition the autocorrelation structure by temporal smoothing smoothing splines with the degree of smoothing selected by generalized cross validation gcv spline provide a method to find an optimal smoother for an fmri time series the purpose of this study was to determine if gcv spline of fmri time series yields unbiased variance estimates of linear regression model parameters gcv spline was evaluated with a real fmri data set and bias of the variance estimator was computed for simulated time series with autocorrelation structures derived from fmri data this study only considered fmri experimental designs of boxcar type the results from the real data suggest that gcv spline determines appropriate amounts of smoothing the simulations show that the variance estimates are on average unbiased the unbiased variance estimates come at some cost to signal detection efficiency this study demonstrates that gcv spline is an appropriate method for smoothing fmri time series

topology preservation in 3d digital space abstract in a 3d two tone digital space the conditions under which sequential transformation of an object point to a non object point or its inverse does not affect the image topology are investigated the concept of border connectivity is introduced and an efficient algorithm for checking a simple point is proposed in this connection some other interesting properties of 3d digital geometry are also discussed this investigation may be used in thinning and topology preserving morphological transformations in 3d digital space

generating cubical complexes from image data and computation of the euler number abstract a number of tasks in image processing and computer vision require the computation of certain topological characteristics of objects in a given image in this paper we introduce a new method based on the notion of the algebraic topology complex to compute the euler number of a given object first we attach a cubical complex to the object of interest then we associate an algebraic structure on which a number of simplifying operations preserving the topology but not necessarily the geometric nature of the complex are possible this is a unifying dimension independent approach we show that the euler number can be obtained directly from the cubical structure or one can perform a collapsing operation that allows to reduce the given image to a lower dimension structure with equivalent topological properties this reduced structure can be used in a further process in particular for the computation of the euler number

nonparametric inference of the hemodynamic response using multi subject fmri data estimation and inferences for the hemodynamic response functions hrf using multi subject fmri data are considered within the context of the general linear model two new nonparametric estimators for the hrf are proposed the first is a kernel smoothed estimator which is used to construct hypothesis tests on the entire hrf curve in contrast to only summaries of the curve as in most existing tests to cope with the inherent large data variance we introduce a second approach which imposes tikhonov regularization on the kernel smoothed estimator an additional bias correction step which uses multi subject averaged information is introduced to further improve efficiency and reduce the bias in estimation for individual hrfs by utilizing the common properties of brain activity shared across subjects this is the main improvement over the standard methods where each subject s data is usually analyzed independently a fast algorithm is also developed to select the optimal regularization and smoothing parameters the proposed methods are compared with several existing regularization methods through simulations the methods are illustrated by an application to the fmri data collected under a psychology design employing the monetary incentive delay mid task

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

digital topology and geometry in medical imaging a survey digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids such methods have been widely used in many medical imaging applications including image segmentation visualization manipulation interpolation registration surface tracking object representation correction quantitative morphometry etc digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability fidelity and efficiency this paper presents a comprehensive yet compact survey on results principles and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications specifically this paper reviews methods related to distance analysis and path propagation connectivity surface tracking image segmentation boundary and centerline detection topology preservation and local topological properties skeletonization and object representation correction and quantitative morphometry a common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity path propagation and neighborhood analysis

some tools for functional data analysis multivariate data analysis permits the study of observations which are finite sets of numbers but modern data collection situations can involve data or the processes giving rise to them which are functions functional data analysis involves infinite dimensional processes and or data the paper shows how the theory of l splines can support generalizations of linear modelling and principal components analysis to samples drawn from random functions spline smoothing rests on a partition of a function space into two orthogonal subspaces one of which contains the obvious or structural components of variation among a set of observed functions and the other of which contains residual components this partitioning is achieved through the use of a linear differential operator and we show how the theory of polynomial splines can be applied more generally with an arbitrary operator and associated boundary constraints these data analysis tools are illustrated by a study of variation in temperature precipitation patterns among some canadian weather stations

how to estimate global activity independent of changes in local activity a method is suggested to ensure independence between the estimated global flow and changes in local flow in pet activation studies global flow is estimated as the average of all intracerebral voxels except those that exhibit a consistent change in flow as a consequence of the experimental design this is achieved by performing an initial analysis using all intracerebral voxels for estimation of global flow in which an f map depicting task related changes is produced a second analysis is performed now excluding all voxels with ap 0 05 in the f map when evaluating global flow thereby ensuring independence from areas changing in a task dependent manner the feasibility of the method is demonstrated on phantom data showing that the distribution is skewed in nonactivated areas when including the activated areas in the calculation of global flow by excluding these areas the distribution is translated toward zero and becomes consistent with the null hypothesis furthermore the usefulness of the suggested scheme is demonstrated on human data scans performed while subjects watched a movie featuring snakes were contrasted to scans performed while watching white noise producing highly significant activations of the visual system when using the traditional way of estimating global flow deactivations were observed in very large portions of the frontal parietal and temporal lobes when using the method suggested in the present paper these disappeared which would be more consistent with the expected effects of the stimulation the method was used in conjunction with both ratio and ancova adjustment with very similar results

combining spatial extent and peak intensity to test for activations in functional imaging within the framework of statistical mapping there are up to now only two tests used to assess the regional significance in functional images one is based on the magnitude of the foci and tends to detect high intensity signals while the second is based on the spatial extent of regions defined by a simple thresholding of the statistical map a test that is more sensitive to extended signals the aim of this paper is to combine the two tests into a single test that is more sensitive to a wider range of signals this combined test is based on an analytical approximation of the distribution of these two parameters size and height and is applied in the context of statistical maps the risk of error in noise only 2d or 3d volumes is assessed under a wide range of experimental conditions obtained by varying both the resolution of the map and the threshold at which clusters are defined in addition we have investigated this new test on simulated signals and applied it to an experimental pet dataset the experimental risk of error is close to the predicted one and the overall sensitivity increases when analyzing a volume containing different types of signals

when the data are functions a datum is often a continuous functionx t of a variable such as time observed over some interval one or more such functions are observed for each subject or unit of observation the extension of classical data analytic techniques designed forp variate observations to such data is discussed the essential step is the expression of the classical problem in the language of functional analysis after which the extension to functions is a straightforward matter a schematic device called the duality diagram is a very useful tool for describing an analysis and for suggesting new possibilities least squares approximation descriptive statistics principal components analysis and canonical correlation analysis are discussed within this broader framework

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

new characterizations of simple points in 2d 3d and 4d discrete spaces a point of a discrete object is called simple if it can be deleted from this object without altering topology in this article we present new characterizations of simple points which hold in dimensions 2 3 and 4 and which lead to efficient algorithms for detecting such points in order to prove these characterizations we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension this work is settled in the framework of cubical complexes which provides a sound topological basis for image analysis and allows to retrieve the main notions and results of digital topology in particular the notion of simple point

an efficient numerical approximation for the linear class of mixed integral equations in this paper an efficient numerical and analytical method for the linear class of mixed integral equations is presented the bivariate chebyshev collocation method for solving the linear volterra fredholm integral equations of the second kind is examined theoretically and numerically its focus lies mainly on the truncated bivariate chebyshev expansion and chebyshev collocation points

a new bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis in this paper a new matrix approach for solving second order linear partial differential equations pdes under given initial conditions has been proposed the basic idea includes integrating from the considered pdes and transforming them to the associated integro differential equations with partial derivatives therefore bernoulli operational matrices of differentiation and integration together with the completeness of bernoulli polynomials can be used for transforming integro differential equations to the corresponding algebraic equations a rigorous error analysis in the infinity norm is given provided that the known functions and the exact solution are sufficiently smooth and bounded a numerical example is included to demonstrate the validity and the applicability of the technique the results confirm the theoretical prediction

incorporating prior knowledge into image registration the first step in the spatial normalization of brain images is usually to determine the affine transformation that best maps the image to a template image in a standard space we have developed a rapid and automatic method for performing this registration which uses a bayesian scheme to incorporate prior knowledge of the variability in the shape and size of heads we compared affine registrations with and without incorporating the prior knowledge we found that the affine transformations derived using the bayesian scheme are much more robust and that the rate of convergence is greater

a concordance correlation coefficient to evaluate reproducibility a new reproducibility index is developed and studied this index is the correlation between the two readings that fall on the 45 degree line through the origin it is simple to use and possesses desirable properties the statistical properties of this estimate can be satisfactorily evaluated using an inverse hyperbolic tangent transformation a monte carlo experiment with 5 000 runs was performed to confirm the estimate s validity an application using actual data is given

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

two symmetrical thinning algorithms for 3d binary images based on p simple points in this paper we propose two 3d symmetrical thinning algorithms based on the parallel deletion of p simple points the first one permits surface skeletons to be obtained the second one permits curve skeletons to be extracted and as far as we know this is the only symmetrical curve thinning algorithm which preserves topology these algorithms have been conceived in order to obtain precise results on simple specific objects parallelepipeds consequently we can predict the number of deletion iterations the number of deleted points and the skeleton of these objects obtained by the two algorithms which is hardly ever possible to assess with other algorithms even on these simple objects

a new shape preserving parallel thinning algorithm for 3d digital images this paper is concerned with a new parallel thinning algorithm for three dimensional digital images that preserves the topology and maintains their shape we introduce an approach of selecting shape points and outer layer used for erosion during each iteration the approach produces good skeleton for different types of corners the concept of using two image versions in thinning is introduced and its necessity in parallel thinning is justified the robustness of the algorithm under pseudo random noise as well as rotation with respect to shape properties is studied and the results are found to be satisfactory

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

magnification of label maps with a topology preserving level set method image segmentation aims at partitioning an image into multiple segments the application of this procedure produces a label map also referred to as segmentation map that classifies the pixels of the original image in contrast to natural images label maps are nominal scale images typically represented as integer valued images nominal scaled label maps can also appear as a representation of the raw data in areas such as in geostatistics in some applications the original resolution of a label map does not suffice and a larger size map has to be generated in this paper we present a magnification algorithm for label maps and nominal images the main property of our method is that it preserves the topology during the magnification process which means that no isolated pixel vanishes to the best of our knowledge apart from nearest neighbor interpolation the problem of label map magnification has not previously been addressed in the literature the main idea of the proposed method is to accomplish a boundary refinement by smoothing the regions boundaries on a finer grid the method relies on well known methods namely the fundamental operations of morphological image processing erosion and dilation and the level set method the level set method is well suited for our purposes since it does not depend on a parametrization and it is numerically stable the topological flexibility of the level set method often found to be an advantage in applications is a drawback here since the topology of the original label map should be preserved however using the so called simple point criterion from digital topology one can adapt the conventional level set method so that the topology will not be modified throughout the magnification procedure

the impact of temporal regularization on estimates of the bold hemodynamic response function a comparative analysis in fmri data analysis it has been shown that for a wide range of situations the hemodynamic response function hrf can be reasonably characterized as the impulse response function of a linear and time invariant system an accurate and robust extraction of the hrf is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions when no assumptions are made about the hrf shape it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either fourier or delta basis functions recently regularization methods have been employed to increase the estimation efficiency of the hrf typically these methods produce more accurate hrf estimates than the least squares approach goutte c nielsen f a hansen l k 2000 modeling the haemodynamic response in fmri using smooth fir filters ieee trans med imag 19 12 1188 1201 here we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the hrf such as time to peak ttp height hr and width w of the response we implemented a bayesian approach proposed by marrelec et al marrelec g benali h ciuciu p pelegrini issac m poline j b 2003 robust estimation of the hemodynamic response function in event related bold fmri using basic physiological information hum brain mapp 19 1 17 marrelec g benali h ciuciu p poline j b bayesian estimation of the hemodynamic of the hemodynamic response function in functional mri in r f editor 2001 melville p 229 247 and its deterministic counterpart based on a combination of tikhonov regularization tikhonov a n arsenin v y 1977 solution of ill posed problems washington dc w h winston and generalized cross validation gcv wahba g 1990 spline models for observational data philadelphia siam for selecting the regularization parameter the performance of both methods is compared with least square estimates as a function of temporal resolution color and strength of the noise and the type of stimulus sequences used in almost all situations under the considered assumptions e g linearity time invariance and smooth hrf the regularization based techniques more accurately characterize the hrf compared to the least squares method our results clarify the effects of temporal resolution noise color and experimental design on the accuracy of hrf estimation

theory and algorithms for constructing discrete morse complexes from grayscale digital images we present an algorithm for determining the morse complex of a two or three dimensional grayscale digital image each cell in the morse complex corresponds to a topological change in the level sets i e a critical point of the grayscale image since more than one critical point may be associated with a single image voxel we model digital images by cubical complexes a new homotopic algorithm is used to construct a discrete morse function on the cubical complex that agrees with the digital image and has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets we make use of discrete morse theory and simple homotopy theory to prove correctness of this algorithm the resulting morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

empirical analyses of bold fmri statistics i spatially unsmoothed data collected under null hypothesis conditions temporal autocorrelation spatial coherency and their effects on voxel wise parametric statistics were examined in bold fmri null hypothesis or noise datasets seventeen normal young subjects were scanned using bold fmri while not performing any time locked experimental behavior temporal autocorrelation in these datasets was described well by a 1 frequency relationship voxel wise statistical analysis of these noise datasets which assumed independence i e ignored temporal autocorrelation rejected the null hypothesis at a higher rate than specified by the nominal alpha temporal smoothing in conjunction with the use of a modified general linear model worsley and friston 1995 neuroimage 2 173 182 brought the false positive rate closer to the nominal alpha it was also found that the noise fmri datasets contain spatially coherent time signals this observed spatial coherence could not be fully explained by a continuously differentiable spatial autocovariance function and was much greater for lower temporal frequencies its presence made voxel wise test statistics in a given noise dataset dependent and thus shifted their distributions to the right or left of 0 inclusion of a global signal covariate in the general linear model reduced this dependence and consequently stabilized i e reduced the variance of dataset false positive rates