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

symmetry detection by generalized complex gc moments a close form solution this paper presents a unified method for detecting both reflection symmetry and rotation symmetry of 2d images based on an identical set of features i e the first three nonzero generalized complex gc moments this method is theoretically guaranteed to detect all the axes of symmetries of every 2d image if more nonzero gc moments are used in the feature set furthermore we establish the relationship between reflectional symmetry and rotational symmetry in an image which can be used to check the correctness of symmetry detection this method has been demonstrated experimentally using more than 200 images

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

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

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

detection of partial symmetry using correlation with rotated reflected images abstract symmetry is one of the important structural properties of a figure both in visual psychology and in computer vision symmetrical properties of planar two dimensional figures are considered and a new method for the extraction of rotational symmetry and reflectional symmetry is presented a figure is said to have symmetry if it is invariant with some congruent transformation which consists of translation rotation and reflection the approach is to obtain the congruent transformations which make the transformed image a good match with the original image the directional correlation of edge features is used to evaluate how well the original and transformed images match this method does not require any segmentation nor knowledge of the centroid position and the symmetrical properties of partially symmetric figures can also be detected the approach is described and this method is applied to synthetic and real images

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

the second order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized f statistic in this paper we derive the second order derivatives of an orthogonal matrix of eigenvectors and of a matrix of eigenvalues of a real symmetric matrix obtained expressions depend on the first order derivatives of these matrices which were presented in linear algebra appl 264 1997 489 these results we use to find the main term of the bias of a generalized f statistic biometrical j 38 1996 5 in the case of normal population a simulation experiment is carried out in which we compare the sample mean and unbiased estimator of f statistic with its asymptotic mean which was obtained in linear algebra appl 321 2000 27

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

normally ordering some multimode exponential operators by virtue of the iwop technique the author shows that the technique of integration within an ordered product iwop provides one with a very simple approach to deriving the normal product form of some multimode exponential operators which greatly simplifies the calculations of normalising some state vectors in hilbert space

approximation of the non null distribution of generalized t2 statistics abstract the non null distributions of hotelling s t 2 statistic and a generalized f statistic biometrics 52 1996 964 are approximated by asymptotic normal distributions the distributions are derived under assumption of ellipticity of the population from where results for the normal population also follow the main term of the bias of hotelling s t 2 statistic is found in the case of normal population a simulation experiment is carried out and its results presented in appendix a derivatives of a rectangular matrix of eigenvectors of a symmetric matrix and corresponding eigevalue matrix are found

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

permutation operators in hilbert space gained via iwop technique a kind of permutation operators in hilbert space are derived in terms of the technique of integration within ordered product iwop these operators are shown to be quantum maps imaged by certain permutation transformations in classical space some operator identities about the relationship between permutation operators and transposition operators are also derived

exact solution and berry phase for the dissipative two mode optical system we have explored the dynamical algebraic structure of the dissipative two mode system on the basis of the algebraic structure we have obtained the exact eigensolutions of the liouvillian superoperator of its master equation by using an algebraic dynamical method then we investigate the berry phase of the system within the density matrix formalism

computation of the mid sagittal plane in 3 d brain images we present a new method to automatically compute reorient and recenter the mid sagittal plane in anatomical and functional three dimensional 3 d brain images this iterative approach is composed of two steps at first given an initial guess of the mid sagittal plane generally the central plane of the image grid the computation of local similarity measures between the two sides of the head allows to identify homologous anatomical structures or functional areas by way of a block matching procedure the output is a set of point to point correspondences the centers of homologous blocks subsequently we define the mid sagittal plane as the one best superposing the points on one side and their counterparts on the other side by reflective symmetry practically the computation of the parameters characterizing the plane is performed by a least trimmed squares estimation then the estimated plane is aligned with the center of the image grid and the whole process is iterated until convergence the robust estimation technique we use allows normal or abnormal asymmetrical structures or areas to be treated as outliers and the plane to be mainly computed from the underlying gross symmetry of the brain the algorithm is fast and accurate even for strongly tilted heads and even in presence of high acquisition noise and bias field as shown on a large set of synthetic data the algorithm has also been visually evaluated on a large set of real magnetic resonance mr images we present a few results on isotropic as well as anisotropic anatomical mr and computed tomography and functional single photon emission computed tomography and positron emission tomography real images for normal and pathological subjects

critical behaviour in aperiodic systems the author considers layered systems with aperiodically modulated couplings and study the effect of inhomogeneity on the critical behaviour using scaling arguments a relevance irrelevance type criterion is formulated and for relevant inhomogeneities the scaling form of singular quantities is determined the author has performed exact calculations for the surface magnetization of aperiodic quantum ising chains and for a 1 1 dimensional directed polymer in a longitudinal aperiodic environment the results for both systems are in accord with scaling considerations for a marginal aperiodicity the critical exponents are found to be non universal

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

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

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

robust midsagittal plane extraction from normal and pathological 3 d neuroradiology images this paper focuses on extracting the ideal midsagittal plane imsp from three dimensional 3 d normal and pathological neuroimages the main challenges in this work are the structural asymmetry that may exist in pathological brains and the anisotropic unevenly sampled image data that is common in clinical practice we present an edge based cross correlation approach that decomposes the plane fitting problem into discovery of two dimensional symmetry axes on each slice followed by a robust estimation of plane parameters the algorithm s tolerance to brain asymmetries input image offsets and image noise is quantitatively evaluated we find that the algorithm can extract the imsp from input 3 d images with 1 large asymmetrical lesions 2 arbitrary initial rotation offsets 3 low signal to noise ratio or high bias field the imsp algorithm is compared with an approach based on maximization of mutual information registration and is found to exhibit superior performance under adverse conditions finally no statistically significant difference is found between the midsagittal plane computed by the imsp algorithm and that estimated by two trained neuroradiologists

canonical coherent state representation of some squeeze operators using the iwop technique integration within an ordered product the authors find canonical coherent state representations of two kinds of squeeze operators these representations manifestly show that they are quantum maps imaged by certain symplectic transformations in coordinate momentum phase space in terms of this formalism the coherent state propagator of parametric amplifiers is easily obtained

permutation operators in hilbert space gained via the iwop technique fermion case for the case of fermions permutation operators in hilbert space are derived in terms of the fermion coherent state and the technique of integration within ordered products with the integration variables being grassmann numbers these operators are shown to be quantum maps imaged by a certain permutation transformation of the numbers some new fermi operator identities are also obtained with the use of the same technique

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

new applications of the coherent state in calculating the class operator of the rotation group the authors show by exploiting the properties of the coherent state and the integration within the ordered product technique that it is possible to derive an explicit expression for the class operator of the su 2 group which has not been obtained before

squeezing in the triatomic linear molecule model revealed by virtue of the iwop technique for a typical triatomic linear molecule with different atomic masses one finds a unitary operator which is closely related to squeezing transformations caused by frequency jumps the coordinate representation of the unitary operator is identified which provides an alternative approach for calculating the wavefunction of internal motion of the molecule the author also shows that the unitary operator is equivalent to a two mode squeezing rotating combination operator multiplied from the right by two single mode squeezing operators the discussion is mainly based on the technique of integration within an ordered product iwop of operators

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

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

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

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

3 d object recognition with symmetric models symmetry extraction and encoding object recognition systems which employ solid models and range data have been a topic of interest for several years model databases have the potential to become large in some environments this paper proposes a pair of techniques for incorporating knowledge of the symmetries of object models into the recognition process the effects of symmetric models on the speed of an object recognition system is examined in the context of an implemented system employing invariant feature indexing as a correspondence building mechanism groups of model surfaces are enumerated and examined to yield a list of segment label permutations which summarize the model s symmetry this symmetry extraction process is followed by a symmetry encoding procedure which replaces groups of features which are indistinguishable because of symmetry with a single prototype feature group experiments with a large model database demonstrate the utility of these symmetry extraction and encoding techniques

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

curved glide reflection symmetry detection we generalize the concept of bilateral reflection symmetry to curved glide reflection symmetry in 2d euclidean space such that classic reflection symmetry becomes one of its six special cases we propose a local feature based approach for curved glide reflection symmetry detection from real unsegmented 2d images furthermore we apply curved glide reflection axis detection for curved reflection surface detection in 3d images our method discovers groups and connects statistically dominant local glide reflection axes in an axis parameter space aps without preassumptions on the types of reflection symmetries quantitative evaluations and comparisons against state of the art algorithms on a diverse 64 test image set and 1 125 swedish leaf data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent respectively and superior performance over existing reflection symmetry detection algorithms potential applications in computer vision particularly biomedical imaging include saliency detection from unsegmented images and quantification of deviations from normality we make our 64 test image set publicly available

exact t and f tests for analyzing studies with multiple endpoints summary the paper describes some methods of forming sum aggregates in multivariate analysis these methods are useful for the statistical analysis of investigations with multiple endpoints in particular the sum statistics can be applied if differences between two or more populations have to be tested and a factorial structure of the means and covariances can be supposed for this approach the calculation of principal components has great importance the central mathematical problem is to construct statistics which permit exact t and f tests i e tests keeping the error of first kind at the prescribed level the paper is based on the theory of spherical matrix distributions treated extensively in the book by fang and zhang 1990 generalized multivariate analysis this paper refers to the problem of the analysis of high dimensional observations which often occurs in clinical studies we start from the proposal of o brien 1984 to use sum aggregates of the form p e xi 1 1 i i

the derivative of an orthogonal matrix of eigenvectors of a symmetric matrix abstract the authors supply the derivative of an orthogonal matrix of eigenvectors of a real symmetric matrix to illustrate the applicability of their result they consider a real symmetric random matrix for which a more or less standard convergence in distribution is assumed to hold the well known delta method is then used to get the asymptotic distribution of the orthogonal eigenmatrix of the random matrix