multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

maximum likelihood estimation of functionals of discrete distributions we consider the problem of estimating functionals of discrete distributions and focus on a tight up to universal multiplicative constants for each specific functional nonasymptotic analysis of the worst case squared error risk of widely used estimators we apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional namely their bias we explicitly characterize the worst case squared error risk incurred by the maximum likelihood estimator mle in estimating the shannon entropy h p sum i 1 s p i ln p i and the power sum f alpha p sum i 1 s p i alpha alpha 0 up to universal multiplicative constants for each fixed functional for any alphabet size s leq infty and sample size n for which the risk may vanish as a corollary for shannon entropy estimation we show that it is necessary and sufficient to have n gg s observations for the mle to be consistent in addition we establish that it is necessary and sufficient to consider n gg s 1 alpha samples for the mle to consistently estimate f alpha p 0 the minimax rate optimal estimators for both problems require s ln s and s 1 alpha ln s samples which implies that the mle has a strictly sub optimal sample complexity when 1 we show that the worst case squared error rate of convergence for the mle is n 2 alpha 1 for infinite alphabet size while the minimax squared error rate is n ln n 2 alpha 1 when alpha geq 3 2 the mle achieves the minimax optimal rate n 1 regardless of the alphabet size as an application of the general theory we analyze the dirichlet prior smoothing techniques for shannon entropy estimation in this context one approach is to plug in the dirichlet prior smoothed distribution into the entropy functional while the other one is to calculate the bayes estimator for entropy under the dirichlet prior for squared error which is the conditional expectation we show that in general such estimators do not improve over the maximum likelihood estimator no matter how we tune the parameters in the dirichlet prior this approach cannot achieve the minimax rates in entropy estimation the performance of the minimax rate optimal estimator with n samples is essentially at least as good as that of dirichlet smoothed entropy estimators with n ln n samples

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

construction of a stable diagonally implicit multivalue methods this paper examines two families of diagonally implicit methods with s internal and r external stages based on the nordsieck approach and the multistep runge kutta approach two general classes of methods are constructed both with order r 1 and stage order r 1 the a stability of these methods is studied and it is shown numerically that there exist a stable diagonally implicit methods of order up to eight the stiff order of these methods is investigated numerically and it appears that the stiff order is equal to the stage order or one more than the stage order

generalized polar coordinates on lie groups and numerical integrators motivated by developments in numerical lie group integrators we introduce a family of local coordinates on lie groups denoted generalized polar coordinates fast algorithms are derived for the computation of the coordinate maps their tangent maps and the inverse tangent maps in particular we discuss algorithms for all the classical matrix lie groups and optimal complexity integrators for n spheres

class based feature matching across unrestricted transformations we develop a novel method for class based feature matching across large changes in viewing conditions the method is based on the property that when objects share a similar part the similarity is preserved across viewing conditions given a feature and a training set of object images we first identify the subset of objects that share this feature the transformation of the feature s appearance across viewing conditions is determined mainly by properties of the feature rather than of the object in which it is embedded therefore the transformed feature will be shared by approximately the same set of objects based on this consistency requirement corresponding features can be reliably identified from a set of candidate matches unlike previous approaches the proposed scheme compares feature appearances only in similar viewing conditions rather than across different viewing conditions as a result the scheme is not restricted to locally planar objects or affine transformations the approach also does not require examples of correct matches we show that by using the proposed method a dense set of accurate correspondences can be obtained experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes finally we show that the scheme can be successfully used for invariant object recognition

nonsmooth ica contrast minimization using a riemannian nelder mead method this brief concerns the design and application of a riemannian nelder mead algorithm to minimize a hartley entropy based contrast function to reliably estimate the sources from their mixtures despite its nondifferentiability the contrast function is endowed with attractive properties such as discriminacy and hence warrants an effort to be effectively handled by a derivative free optimizer aside from tailoring the nelder mead technique to the constraint set namely oblique manifold the source separation results attained in an empirical study with quasi correlated synthetic signals and digital images are presented which favor the proposed method on a comparative basis

using spanning graphs for efficient image registration we provide a detailed analysis of the use of minimal spanning graphs as an alignment method for registering multimodal images this yields an efficient graph theoretic algorithm that for the first time jointly estimates both an alignment measure and a viable descent direction with respect to a parameterized class of spatial transformations we also show how prior information about the interimage modality relationship from prealigned image pairs can be incorporated into the graph based algorithm a comparison of the graph theoretic alignment measure is provided with more traditional measures based on plug in entropy estimators this highlights previously unrecognized similarities between these two registration methods our analysis gives additional insight into the tradeoffs the graph based algorithm is making and how these will manifest themselves in the registration algorithm s performance

maximum likelihood image matching image matching applications such as tracking and stereo commonly use the sum of squared difference ssd measure to determine the best match however this measure is sensitive to outliers and is not robust to template variations alternative measures have also been proposed that are more robust to these issues we improve upon these using a probabilistic formulation for image matching in terms of maximum likelihood estimation that can be used for both edge template matching and gray level image matching this formulation generalizes previous edge matching methods based on distance transforms we apply the techniques to stereo matching and feature tracking uncertainty estimation techniques allow feature selection to be performed by choosing features that minimize the localization uncertainty

a penalized likelihood approach to image warping discussion a warping is a function that deforms images by mapping between image domains the choice of function is formulated statistically as maximum penalized likelihood where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping the paper addresses two issues simultaneously of how to choose the warping function and how to assess the alignment a new fourier von mises image model is identified with phase differences between fourier transformed images having von mises distributions also new null set distortion criteria are proposed with each criterion uniquely minimized by a particular set of polynomial functions a conjugate gradient algorithm is used to estimate the warping function which is numerically approximated by a piecewise bilinear function the method is motivated by and used to solve three applied problems to register a remotely sensed image with a map to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images

order results for implicit runge kutta methods applied to stiff systems an extensive order analysis is given for the local and global errors of certain classes of runge kutta methods applied to general nonlinear stiff initial value problems it turns out that there are three order levels for linear problems y ay the classical orders apply for general nonlinear problems however two types of order reductions occur there a distinction has to be made between stiff problems where only f y is large and stiff problems where also some of the other derivatives f t f tt f yy cdots are large for these two classes of problems order results can be guaranteed which differ only by one power of the stepsize parameter h the order levels for both classes of problems are considerably lower than the respective conventional orders these order results are optimal in the sense that higher orders would contradict numerical observations made with particular initial value problems

robust matching cost function for stereo correspondence using matching by tone mapping and adaptive orthogonal integral image real world stereo images are inevitably affected by radiometric differences including variations in exposure vignetting lighting and noise stereo images with severe radiometric distortion can have large radiometric differences and include locally nonlinear changes in this paper we first introduce an adaptive orthogonal integral image which is an improved version of an orthogonal integral image after that based on matching by tone mapping and the adaptive orthogonal integral image we propose a robust and accurate matching cost function that can tolerate locally nonlinear intensity distortion by using the adaptive orthogonal integral image the proposed matching cost function can adaptively construct different support regions of arbitrary shapes and sizes for different pixels in the reference image so it can operate robustly within object boundaries furthermore we develop techniques to automatically estimate the values of the parameters of our proposed function we conduct experiments using the proposed matching cost function and compare it with functions employing the census transform supporting local binary pattern and adaptive normalized cross correlation as well as a mutual information based matching cost function using different stereo data sets by using the adaptive orthogonal integral image the proposed matching cost function reduces the error from 21 51 to 15 73 in the middlebury data set and from 15 9 to 10 85 in the kitti data set as compared with using the orthogonal integral image the experimental results indicate that the proposed matching cost function is superior to the state of the art matching cost functions under radiometric variation

efficient registration of nonrigid 3 d bodies we present a novel method to perform an accurate registration of 3 d nonrigid bodies by using phase shift properties of the dual tree complex wavelet transform dt bbcwt since the phases of dt bbcwt coefficients change approximately linearly with the amount of feature displacement in the spatial domain motion can be estimated using the phase information from these coefficients the motion estimation is performed iteratively first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field we use a parametric affine model to describe the motion where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations from the estimated affine parameters the motion field between the sensed and the reference data sets can be generated and the sensed data set then can be shifted and interpolated spatially to align with the reference datafeature displacement set

three dimensional elastic matching of volumes registering volumes that have been deformed with respect to each other involves recovery of the deformation a 3 d elastic matching algorithm has been developed to use surface information for registering volumes surface extraction is performed in two steps extraction of contours in 2 d image planes using active contours and forming triangular patch surface models from the stack of 2 d contours one volume is modeled as being deformed with respect to another goal volume correspondences between surfaces in the two image volumes are used to warp the deformed volume towards its goal this process of contour extraction surface formation and matching and warping is repeated a number of times with decreasing image volume stiffness as the iterations continue the stretched volume is refined towards its goal volume registration examples of deformed volumes are presented

a linear discriminant analysis method based on mutual information maximization we present a new linear discriminant analysis method based on information theory where the mutual information between linearly transformed input data and the class labels is maximized first we introduce a kernel based estimate of mutual information with a variable kernel size furthermore we devise a learning algorithm that maximizes the mutual information w r t the linear transformation two experiments are conducted the first one uses a toy problem to visualize and compare the transformation vectors in the original input space the second one evaluates the performance of the method for classification by employing cross validation tests on four datasets from the uci repository various classifiers are investigated our results show that this method can significantly boost class separability over conventional methods especially for nonlinear classification

modelling continuous exposures with a spike at zero a new procedure based on fractional polynomials a common task in epidemiology is to estimate the dose response function for a continuous exposure often a proportion of subjects is unexposed typical examples are cigarette consumption alcohol intake or occupational exposures the question arises as to how to model such variables statistically the fractional polynomial method of modelling continuous exposure variables is extended to allow for a proportion unexposed a binary variable for the unexposed fraction is added to the model in a two stage procedure we assess whether the binary variable and or the continuous function for the exposed individuals is required for a good fit to the data extension to the multivariable situation is described three data sets with different characteristics are used as illustrations the analyses of the three studies using the proposed procedure give differing results in one example only the binary variable seems to be required in the other two examples the binary variable and fractional polynomial functions of the exposure variable are needed one function is monotonic and the other has a minimum in the third example adjusting for confounders has almost no effect on the function selected in conclusion the new procedure offers a worthwhile extension of dose response modelling with an unexposed fraction it is simple to carry out with standard software

an r squared measure of goodness of fit for some common nonlinear regression models abstract for regression models other than the linear model r squared type goodness of fit summary statistics have been constructed for particular models using a variety of methods we propose an r squared measure of goodness of fit for the class of exponential family regression models which includes logit probit poisson geometric gamma and exponential this r squared is defined as the proportionate reduction in uncertainty measured by kullback leibler divergence due to the inclusion of regressors under further conditions concerning the conditional mean function it can also be interpreted as the fraction of uncertainty explained by the fitted model

some explicit formulas for the matrix exponential formulas are derived for the exponential of an arbitrary 2 2 matrix in terms of either its eigenvalues or entries these results are then applied to the second order mechanical vibration equation with weak or strong damping some formulas for the exponential of n n matrices are given for matrices that satisfy an arbitrary quadratic polynomial besides the above mentioned 2 2 matrices these results encompass involutory rank 1 and idempotent matrices consideration is then given to n n matrices that satisfy a special cubic polynomial these results are applied to the case of a 3 3 skew symmetric matrix whose exponential represents the constant rotation of a rigid body about a fixed axis

an introduction to lie group integrators basics new developments and applications we give a short and elementary introduction to lie group methods a selection of applications of lie group integrators are discussed finally a family of symplectic integrators on cotangent bundles of lie groups is presented and the notion of discrete gradient methods is generalised to lie groups

a frequency domain technique for range data registration this work introduces an original method for registering pairs of 3d views consisting of range data sets which operates in the frequency domain the fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters our algorithm exploits this well known property by suggesting a three step procedure the rotation parameters are estimated by the first two steps through convenient representations and projections of the fourier transforms magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation the performance of the algorithm which is well suited for unsupervised registration is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3d rigid motion are achievable our algorithm can be used as a prealignment tool for more accurate space domain registration techniques like the icp algorithm

a diagnostic for cox regression and general conditional likelihoods abstract diagnostics for changes in the maximum likelihood estimate of due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models for the cox proportional hazards model and in conditional models for arbitrarily matched or stratified data diagnostics derived from augmented regression models are again useful and easy to compute these diagnostics are applicable to different formulations for the multiplicative covariable effects over time or over strata an exact or approximate treatment of tied failure times or multiple case matching and time dependent covariates

assessing the adequacy of the logistic regression model for matched case control studies we apply results for the detection of outliers in logistic regression to the analysis of matched pairs data and illustrate the techniques with data from a matched pairs study of the relationship between iron binding proteins and mortality in the solomon islands although the study includes 90 matched pairs the conclusions change substantially with deletion of one or two pairs thus even with reasonably large data sets single observations may have a great impact on the results of an analysis the identification of influential observations should constitute part of the analysis of matched case control data

dispersion tests and adjustments for survival and case control studies cox and snell have pointed out that when the empirical variance of a measured response y is quite different from its nominal variance under an assumed probability model standard errors that are not adjusted for the discrepancy may yield misleading inferences this article describes a test for assessing departures from nominal dispersion in survival analysis and case control studies also a robust procedure for adjusting standard errors for these models is given

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

high dimensional statistical measure for region of interest tracking this paper deals with region of interest roi tracking in video sequences the goal is to determine in successive frames the region which best matches in terms of a similarity measure a roi defined in a reference frame some tracking methods define similarity measures which efficiently combine several visual features into a probability density function pdf representation thus building a discriminative model of the roi this approach implies dealing with pdfs with domains of definition of high dimension to overcome this obstacle a standard solution is to assume independence between the different features in order to bring out low dimension marginal laws and or to make some parametric assumptions on the pdfs at the cost of generality we discard these assumptions by proposing to compute the kullback leibler divergence between high dimensional pdfs using the k th nearest neighbor framework in consequence the divergence is expressed directly from the samples i e without explicit estimation of the underlying pdfs as an application we defined 5 7 and 13 dimensional feature vectors containing color information including pixel based gradient based and patch based and spatial layout the proposed procedure performs tracking allowing for translation and scaling of the roi experiments show its efficiency on a movie excerpt and standard test sequences selected for the specific conditions they exhibit partial occlusions variations of luminance noise and complex motion

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

mutual information aspects of scale space images in image registration mutual information is a well performing measure based on principles of uncertainty similarly in image analysis the gaussian scale space based on minimal assumptions of the image is used to derive intrinsic properties of an image this paper starts an investigation of a combination of both methods this combination results in a double parameterized mutual information measure using local information of the image for single modality matching best response is found for coinciding parameters then critical values are found for which the parameterized mutual information has extrema first results on multi modality matching show that different parameter values instead of coinciding values yield the best response for the parameterized mutual information

multiplicative models and cohort analysis abstract three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age calendar year specific death rates the first method which assumes that the baseline rates are known from national vital statistics is a multiple regression analysis of the standardized mortality ratio the second method is a variant of cox s proportional hazards analysis in which the baseline rates are treated as unknown nuisance parameters the third method consists of case control sampling from the risk sets formed in the course of applying cox s model it requires substantially less computation than do the other two in illustrative analysis of respiratory cancer deaths among a cohort of smelter workers all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure the discussion centers on the tradeoff between efficiency and bias in the selection of a particular method of analysis and on practica

sampling for conditional inference on case control data summary the problem of exact conditional inference for discrete multivariate case control data has two forms the first is grouped case control data where monte carlo computations can be done using the importance sampling method of booth and butler 1999 biometrika86 321 332 or a proposed alternative sequential importance sampling method the second form is matched case control data for this analysis we propose a new exact sampling method based on the conditional poisson distribution for conditional testing with one binary and one integral ordered covariate this method makes computations on data sets with large numbers of matched sets fast and accurate we provide detailed derivation of the constraints and conditional distributions for conditional inference on grouped and matched data the methods are illustrated on several new and old data sets

maximum likelihood and quasi likelihood for nonlinear exponential family regression models abstract linear and nonlinear exponential family and quasi likelihood regression models form a class of models with a structure that invites using one algorithmic framework to compute parameter estimates and regression diagnostics this framework extends our work on nonlinear least squares it includes iteratively reweighted least squares but also encompasses secant updates for part of the hessian matrix of the likelihood or quasi likelihood function along with tests for when to use this information the framework also provides basic machinery for computing leave one out style regression diagnostics we describe the framework discuss some implementation details and present some numerical experience

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

a hyperelastic regularization energy for image registration image registration is one of the most challenging problems in image processing where ill posedness arises due to noisy data as well as nonuniqueness and hence the choice of regularization is crucial this paper presents hyperelasticity as a regularizer and introduces a new and stable numerical implementation on one hand hyperelastic registration is an appropriate model for large and highly nonlinear deformations for which a linear elastic model needs to fail on the other hand the hyperelastic regularizer yields very regular and diffeomorphic transformations while hyperelasticity might be considered as just an additional outstanding regularization option for some applications it becomes inevitable for applications involving higher order distance measures like mass preserving registration the paper gives a short introduction to image registration and hyperelasticity the hyperelastic image registration problem is phrased in a variational setting and an existence proof is provided the focus of th

nonparametric hypothesis tests for statistical dependency determining the structure of dependencies among a set of variables is a common task in many signal and image processing applications including multitarget tracking and computer vision in this paper we present an information theoretic machine learning approach to problems of this type we cast this problem as a hypothesis test between factorizations of variables into mutually independent subsets we show that the likelihood ratio can be written as sums of two sets of kullback leibler kl divergence terms the first set captures the structure of the statistical dependencies within each hypothesis whereas the second set measures the details of model differences between hypotheses we then consider the case when the signal prior models are unknown so that the distributions of interest must be estimated directly from data showing that the second set of terms is asymptotically negligible and quantifying the loss in hypothesis separability when the models are completely unknown we demonstrate the utility of nonparametric estimation methods for such problems providing a general framework for determining and distinguishing between dependency structures in highly uncertain environments additionally we develop a machine learning approach for estimating lower bounds on kl divergence and mutual information from samples of high dimensional random variables for which direct density estimation is infeasible we present empirical results in the context of three prototypical applications association of signals generated by sources possessing harmonic behavior scene correspondence using video imagery and detection of coherent behavior among sets of moving objects

a class of variable step explicit nordsieck multivalue methods existing integrators for nonstiff initial value problems often use adams explicit runge kutta or extrapolation methods few integrators based on explicit multivalue methods have been developed even though their generality can potentially lead to improved performance exploratory results are presented for a class of variable step three step three stage explicit nordsieck multivalue methods of order six the methods use the order six formula to advance approximations to the solution and scaled first derivatives from the previous three steps an embedded order five formula is used to form the local error estimate the methods have stage order five which enables us to construct a local continuous extension of order five without performing extra derivative evaluations the numerical results show despite the exploratory nature of the work that the new methods are competitive with 5 6 explicit runge kutta pairs

a model based on local graphs for colour images and its application for gaussian noise smoothing in this paper a new model for processing colour images is presented a graph is built for each image pixel taking into account some constraints on links each pixel is characterized depending on the features of its related graph which allows to process it appropriately as an example we provide a characterization of each pixel based on the link cardinality of its connected component this feature enables us to properly distinguish flat image regions respect to edge and detail regions according to this we have designed a hybrid filter for colour image smoothing it combines a filter able to properly process flat image regions with another one that is more appropriate for details and texture experimental results show that our model performs appropriately we also see that our proposed filter is competitive with respect to state of the art methods it is close closer to the corresponding optimal switching filter respect to other analogous hybrid method

data analytic methods for matched case control studies the recent introduction of complex multivariate statistical models in matched case control studies is a mixed blessing their use can lead to a better understanding of the way in which many variables contribute to the risk of disease on the other hand these powerful methods can obscure salient features in the data that might have been detected by other less sophisticated methods this shortcoming is due to a lack of support methodology for the routine use of these models satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model goodness of fit must be examined if inferences are to be trusted this paper is concerned with the analysis of matched case control studies with logistic models analogies of these models to linear regression models are emphasized in particular basic concepts such as analysis of variance multiple correlation coefficient one degree of freedom tests and residual analysis are discussed the fairly new field of regression diagnostics is also introduced all procedures are illustrated on a study of bladder cancer in males

statistical inference for familial disease clusters in many epidemiologic studies the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units the concept of clustering is contrasted with incidence we assume that all individuals are exchangeable except for their disease status this assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease conditional on the number of diseased cases and the distribution of the sizes of the various family units new parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering we consider models and an example that takes covariates into account ascertainment bias is described and the appropriate sampling distribution is demonstrated four numerical examples with real data illustrate these methods

the dichotomy of stiffness pragmatism versus theory the problem of stiffness occuring in ordinary differential equations is now well understood and various concepts such as nonlinear stability b convergence and stiff order have been introduced as being relevant to an understanding of the behaviour of numerical methods when applied to stiff problems however it is often the case that some of these properties are not always attainable when methods are implemented efficiently and in this paper we will investigate this paradox in some detail in addition we will give a resume of some of the recent theoretical developments in the applicability of numerical methods to stiff problems and make some comparisons between existing codes based on runge kutta and linear multistep methods we will conclude this discussion with the introduction of a very general family of methods called multivalue methods and show how the important concepts of cheap implementation stage order and stability apply to these methods

nonlinear registration using variational principle for mutual information we extend the multimodal image registration method described in alexander and summers fast registration algorithm using a variational principle for mutual information proc spie int soc opt eng 5032 2003 1053 1063 to nonlinear registration a variational principle maximizing mutual information leads to an euler lagrange el equation for the displacement field represented here in a basis of cubic b spline functions a cost function is constructed from the sum of squares of the residuals of the el equation at a subset of pixels where the magnitude of the spatial gradient of intensity exceeds a user chosen threshold the unknown coefficients in the displacement field representation are evaluated using a levenberg marquardt minimization procedure the proposed method was successfully applied to several image pairs of the same and different modalities and an artificially constructed series of images containing nonlinear distortions and noise

motion estimation based on mutual information and adaptive multi scale thresholding this paper proposes a new method of calculating a matching metric for motion estimation the proposed method splits the information in the source images into multiple scale and orientation subbands reduces the subband values to a binary representation via an adaptive thresholding algorithm and uses mutual information to model the similarity of corresponding square windows in each image a moving window strategy is applied to recover a dense estimated motion field whose properties are explored the proposed matching metric is a sum of mutual information scores across space scale and orientation this facilitates the exploitation of information diversity in the source images experimental comparisons are performed amongst several related approaches revealing that the proposed matching metric is better able to exploit information diversity generating more accurate motion fields

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

evaluation of optimization methods for nonrigid medical image registration using mutual information and b splines a popular technique for nonrigid registration of medical images is based on the maximization of their mutual information in combination with a deformation field parameterized by cubic b splines the coordinate mapping that relates the two images is found using an iterative optimization procedure this work compares the performance of eight optimization methods gradient descent with two different step size selection algorithms quasi newton nonlinear conjugate gradient kiefer wolfowitz simultaneous perturbation robbins monro and evolution strategy special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives the optimization methods are tested on manually deformed ct images of the heart on follow up ct chest scans and on mr scans of the prostate acquired using a bffe tl and t2 protocol registration accuracy is assessed by computing the overlap of segmented edges precision and convergence properties are studied by comparing deformation fields the results show that the robbins monro method is the best choice in most applications with this approach the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image randomly selected in every iteration to compute the derivative of the mutual information from the other methods the quasi newton and the nonlinear conjugate gradient method achieve a slightly higher precision at the price of larger computation times

rigid shape matching by segmentation averaging we use segmentations to match images by shape the new matching technique does not require point to point edge correspondence and is robust to small shape variations and spatial shifts to address the unreliability of segmentations computed bottom up we give a closed form approximation to an average over all segmentations our method has many extension yielding new algorithms for tracking object detection segmentation and edge preserving smoothing for segmentation instead of a maximum a posteriori approach we compute the central segmentation minimizing the average distance to all segmentations of an image for smoothing instead of smoothing images based on local structures we smooth based on the global optimal image structures our methods for segmentation smoothing and object detection perform competitively and we also show promising results in shape based tracking

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

resistant fits for some commonly used logistic models with medical application logistic regression type models are used in many applications some examples include the classical dose response experiment prospective and retrospective studies of disease incidence with and without matching and the analysis of ordinal data in most instances the model is fitted by the method of maximum likelihood which like least squares is sensitive to atypical observations an alternative to maximum likelihood is proposed and illustrated by examples

measures of dependence for censored survival data in the linear regression model with normal errors the squared product moment correlation provides the standard measure of dependence between the explanatory variable and the response variable using the concept of information gain a measure of dependence can also be defined for more general regression models used in survival analysis such as the weibull regression model or cox s proportional hazards model further this measure of dependence can be conveniently estimated even when the response variable is subject to censoring and a simple approximation is available

assessing the fit of the logistic regression model to individual matched sets of case control data we develop exact conditional methods for checking the fit of a logistic regression model to individual matched sets in case control studies justifications are given for preferring this approach to conventional maximum likelihood based methods data from two studies are used to illustrate the techniques

geometric direct search algorithms for image registration a widely used approach to image registration involves finding the general linear transformation that maximizes the mutual information between two images with the transformation being rigid body i e belonging to se 3 or volume preserving i e belonging to sl 3 in this paper we present coordinate invariant geometric versions of the nelder mead optimization algorithm on the groups sl 3 se 3 and their various subgroups that are applicable to a wide class of image registration problems because the algorithms respect the geometric structure of the underlying groups they are numerically more stable and exhibit better convergence properties than existing local coordinate based algorithms experimental results demonstrate the improved convergence properties of our geometric algorithms