Search

Shape abnormalities in the basal ganglia are shown to contribute to the motor, social and communication dysfunctions of a sample of boys with autism spectrum disorder (ASD). Comparison between the shape of the right basal ganglia of typically developing boys and ASD boys is presented.

In large-deformation diffeomorphic metric mapping (LDDMM), the diffeomorphic matching of images are modeled as evolution in time, or a flow, of an associated smooth velocity vector field v controlling the evolution. The initial momentum parameterizes the whole geodesic and encodes the shape and form of the target image. Thus, methods such as principal component analysis (PCA) of the initial momentum leads to analysis of anatomical shape and form in target images without being restricted to small-deformation assumption in the analysis of linear displacements. We apply this approach to a study of dementia of the Alzheimer type (DAT). The left hippocampus in the DAT group shows significant shape abnormality while the right hippocampus shows similar pattern of abnormality. Further, PCA of the initial momentum leads to correct classification of 12 out of 18 DAT subjects and 22 out of 26 control subjects. Index Terms--Alzheimer's disease, geodesic, LDDMM, momentum, PCA.

Functional and structural maps, such as a curvature, cortical thickness, and functional magnetic resonance imaging (MRI) maps, indexed over the local coordinates of the cortical manifold play an important role in neuropsychiatric studies. Due to the highly convoluted nature of the cerebral cortex and image quality, these functions are generally uninterpretable without proper methods of association and smoothness onto the local coordinate system. In this paper, we generalized the spline smoothing problem (Wahba, 1990) from a sphere to any arbitrary two-dimensional (2-D) manifold with boundaries. We first seek a numerical solution to orthonormal basis functions of the Laplace-Beltrami (LB) operator with Neumann boundary conditions for a 2-D manifold M then solve the spline smoothing problem in a reproducing kernel Hilbert space (r.k.h.s.) of real-valued functions on manifold M with kernel constructed from the basis functions. The explicit discrete LB representation is derived using the finite element method calculated directly on the manifold coordinates so that finding discrete LB orthonormal basis functions is equivalent to solving an algebraic eigenvalue problem. And then smoothed functions in r.k.h.s can be represented as a linear combination of the basis functions. We demonstrate numerical solutions of spherical harmonics on a unit sphere and brain orthonormal basis functions on a planum temporale manifold. Then synthetic data is used to quantify the goodness of the smoothness compared with the ground truth and discuss how many basis functions should be incorporated in the smoothing. We present applications of our approach to smoothing sulcal mean curvature, cortical thickness, and functional statistical maps on submanifolds of the neocortex. Index Terms--Cortical thickness, curvature, Laplace-Beltrami (LB) operator, Neumann boundary conditions, reproducing kernel Hilbert space, spline smoothing.

This paper proposes a method to match diffusion tensor magnetic resonance images (DT-MRIs) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphisms on such vector fields, and provide an extension of the Large Deformation Diffeomorphic Metric Mapping framework to this type of dataset, resulting in optimizing for geodesics on the space of diffeomorphisms connecting two images. Existence of the minimizers under smoothness assumptions on the compared vector fields is proved, and coarse to fine hierarchical strategies are detailed, to reduce both ambiguities and computation load. This is illustrated by numerical experiments on DT-MRI heart images. Index Terms--Diffeomorphism, diffusion tensor MRI, image registration, variational methods, vector field.

The functional magnetic resonance imagery responses of declarative memory tasks in the medial temporal lobe (MTL) are examined by using large deformation diffeomorphic metric mapping (LDDMM) to remove anatomical variations across subjects. LDDMM is used to map the structures of the MTL in multiple subjects into extrinsic atlas coordinates; these same diffeomorphic mappings are used to transfer the corresponding functional data activation to the same extrinsic coordinates. The statistical power in the averaged LDDMM mapped signals is significantly increased over conventional Talairach-Tournoux averaging. Activation patterns are highly localized within the MTL. Whereas the present demonstration has been aimed at enhancing alignment within the MTL, this technique is general and can be applied throughout the brain. computational anatomy | functional MRI

The human cerebral cortex is a laminar structure about 3 mm thick, and is easily visualized with current magnetic resonance (MR) technology. The thickness of the cortex varies locally by region, and is likely to be influenced by such factors as development, disease and aging. Thus, accurate measurements of local cortical thickness are likely to be of interest to other researchers. We develop a parametric stochastic model relating the laminar structure of local regions of the cerebral cortex to MR image data. Parameters of the model include local thickness, and statistics describing white, gray and cerebrospinal fluid (CSF) image intensity values as a function of the normal distance from the center of a voxel to a local coordinate system anchored at the gray/white matter interface. Our fundamental data object, the intensity-distance histogram (IDH), is a two-dimensional (2-D) generalization of the conventional 1-D image intensity histogram, which indexes voxels not only by their intensity value, but also by their normal distance to the gray/white interface. We model the IDH empirically as a marked Poisson process with marking process a Gaussian random field model of image intensity indexed against normal distance. In this paper, we relate the parameters of the IDH model to the local geometry of the cortex. A maximum-likelihood framework estimates the parameters of the model from the data. Here, we show estimates of these parameters for 10 volumes in the posterior cingulate, and 6 volumes in the anterior and posterior banks of the central sulcus. The accuracy of the estimates is quantified via Cramer-Rao bounds. We believe that this relatively crude model can be extended in a straightforward fashion to other biologically and theoretically interesting problems such as segmentation, surface area estimation, and estimating the thickness distribution in a variety of biologically relevant contexts. Index Terms--Cortical thickness, intensity-distance histogram (IDH), normal distance, partial volume effect.

One of the central problems in Automated Target Recognition is to accommodate the infinite variety of clutter in real military environments. The principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter. Such metrics are formulated using second-order random field models. Our results indicate that this approach significantly improves detection/ classification rates of targets in clutter. Index Terms--Riemannian metrics, deformable templates, Automated Target Recognition (ATR).

This paper derives bounds on the performance of statistical object recognition systems, wherein an image of a target is observed by a remote sensor. Detection and recognition problems are modeled as composite hypothesis testing problems involving nuisance parameters. We develop information-theoretic performance bounds on target recognition based on statistical models for sensors and data, and examine conditions under which these bounds are tight. In particular, we examine the validity of asymptotic approximations to probability of error in such imaging problems. Problems involving Gaussian, Poisson, and multiplicative noise, and random pixel deletions are considered, as well as least-favorable Gaussian clutter. A sixth application involving compressed sensor image data is considered in some detail. This study provides a systematic and computationally attractive framework for analytically characterizing target recognition performance under complicated, non-Gaussian models and optimizing system parameters. Index Terms--Object recognition, automatic target recognition, imaging sensors, multisensor data fusion, data compression, performance metrics.

Deformable template representations of observed imagery, model the variability of target pose via the actions of the matrix Lie groups on rigid templates. In this paper, we study the construction of minimum mean squared error estimators on the special orthogonal group, SO(n), for pose estimation. Due to the nonflat geometry of SO(n), the standard Bayesian formulation, of optimal estimators and their characteristics, requires modifications. By utilizing Hilbert-Schmidt metric defined on GL(n), a larger group containing SO(n), a mean squared criterion is defined on SO(n). The Hilbert-Schmidt estimate (HSE) is defined to be a minimum mean squared error estimator, restricted to SO(n). The expected error associated with the HSE is shown to be a lower bound, called the Hilbert-Schmidt bound (HSB), on the error incurred by any other estimator. Analysis and algorithms are presented for evaluating the HSE and the HSB in case of both ground-based and airborne targets. Index Terms - Pose estimation, ATR, Hilbert-Schmidt bounds, Bayesian approach, performance analysis, orthogonal groups.

This paper presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier-Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration. Index Terms - Brain mapping, global shape models, medical imaging, pattern theory.

Random sampling algorithm based on jump-diffusion dynamics enables simultaneous detection, tracking and automatic target recognition in air-to-ground and ground-to-air scenarios. A Bayesian approach is adopted for inference of scenes. New objects are detected, and discrete jump moves through parameter space are studied for identification of objects. The algorithm explores scenes of different complexities. Continuous diffusions generate scale and rotation group transformations between jumps. The method combines dynamics-based tracking within one estimation framework.

A novel approach for accommodating local shape variation associated with mapping a two-dimensional or three-dimensional template image into alignment with an image similar in topology has been developed. Vector-field transformation is used to accommodate local shape variability and to constrain the transformation. Unlike quadratic penalty methods, the stress associated with restraining motion relaxes over time to allow large-magnitude deformations.

A maximum a posteriori (MAP) algorithm is presented for the estimation of spin-density and spin-spin decay distributions from frequency and phase-encoded magnetic resonance imaging data. Linear spatial localization gradients are assumed: the y-encode gradient applied during the phase preparation time of duration [Tau] before measurement collection, and the x-encode gradient applied during the full data collection time t [greater than or equal to] 0. The MRI signal model developed in [22] is used in which a signal resulting from M phase encodes (rows) and N frequency encode dimensions (columns) is modeled as a super-position of MN sinc-modulated exponentially decaying sinusoids with unknown spin-density and spin-spin decay parameters. The nonlinear least-squares MAP estimate of the spin density and spin-spin decay distributions solves for the 2MN spin-density and decay parameters minimizing the squared-error between the measured data and the sinc-modulated exponentially decay signal model using an iterative expectation-maximization algorithm. A covariance diagonalizing transformation is derived which decouples the joint estimation of MN sinusoids into M separate N sinusoid optimizations, yielding an order of magnitude speed up in convergence. The MAP solutions are demonstrated to deliver a decrease in standard deviation of image parameter estimates on brain phantom data of greater than a factor of two over Fourier-based estimators of the spin density and spin-spin decay distributions. A parallel processor implementation is demonstrated which maps the N sinusoid coupled minimization to separate individual simple minimizations, one for each processor.

An iterative algorithm associated with maximum likelihood (ML) Toeplitz covariance estimation was used to calculate ML estimates of complex sinusoids when subjected to stationary unknown Gaussian noise. This algorithm iterated between mean estimations for a given current covariance and vice versa subsequent to estimating the initial Toeplitz covariance and mean. These covariant estimates were compared with Cramer-Rao bounds and conventional estimators.

Mathematical techniques that facilitate the conversion of digital anatomical textbooks from the ideal to the individual ensure the observation of changes in normal human anatomies. The textbooks' symbolic values and multisensor properties facilitate automatic registration, segmentation and fusion. A fixed coordinate system, with the existing information regarding the physical attributes of neuroanatomies, forms the foundation for the ideal textbook.

The theory of large deviations for Gibbs random fields is used to show that the asymptotic number of bits per symbol for Ziv-Lempel codes in two dimensions is given by the maximal entropy of all Gibbs fields with the same interaction. The error probability is shown to converge exponentially fast to zero. In addition, the stronger version of the Shannon-McMillan theorem proved by Ornstein and Weiss is formulated and proved in terms of the exponential decay of the probability of the nontypical sequences. Index Terms--Errorless coding, image compression.

The entropies and combinatories of trees that branch according to fixed but finite numbers of rules are studied. Context-free grammars are used to categorize the ways in which nodes branch to yield daughter nodes, thus providing an organized setting to examine the entropies for random branching processes whose realizations are trees and whose probabilities are determined by probabilities associated to the substitution rules of the grammar. Normalized entropy rates H are derived for the critical branching rate (p = 1) and supercritical branching rate (p > 1) processes. An equipartition theorem is proven for the supercritical processes proving that L-generation trees normalized by their number of nodes have log probability converging to the entropy rate H with L, almost everywhere in the nonextinction set. A strong departure from classical theorems for Markov sources occurs for super-critical branching processes p > 1 as the typical sets have super-geometric growth rates. Defining the [Delta]-typical set of trees to be the L-generation trees with log of their negative log probability within [Delta] of log p, then the typical set has probability equaling the nonextinction probability and log growth rate of [p.sub.L]. The combinatories of the set of all trees that can be generated from the context-free substitution rules is also studied. It is proven that for all context-free grammars that are strongly connected and have at least one substitution rule with two daughters or more, the combinatoric growth rate of the set of trees is also supergeometric and equals the largest growth rate of any random branching process with the same substitution rules. Instances of regular, pseudo-linear and context-free grammars are studied for demonstrating the theory, and as a particular example it is shown that the arithmetic expression language has log-number of unique L-generation programs growing at a rate [1.75488.sup.L]. Index Terms--Context-free languages, branching processes, trees, entropy, equipartition-theorem.

1. INTRODUCTION Current magnetic resonance image (MRI) studies investigate abnormalities of cortical and subcortical structures in neurodevelopmental and neurodegenerative disorders. These studies require a delineation of a region of interest [...], This paper describes the application of the alternating Kernel mixture (AKM) segmentation algorithm to high resolution MRI subvolumes acquired from a 1.5T scanner (hippocampus, n = 10 and prefrontal cortex, n = 9) and a 3T scanner (hippocampus, n = 10 and occipital lobe, n = 10). Segmentation of the subvolumes into cerebrospinal fluid, gray matter, and white matter tissue is validated by comparison with manual segmentation. When compared with other segmentation methods that use traditional Bayesian segmentation, AKM yields smaller errors (P < .005, exact Wilcoxon signed rank test) demonstrating the robustness and wide applicability of AKM across different structures. By generating multiple mixtures for each tissue compartment, AKM mimics the increased variation of manual segmentation in partial volumes due to the highly folded tissues. AKM's superior performance makes it useful for tissue segmentation of subcortical and cortical structures in large-scale neuroimaging studies.

1. INTRODUCTION Major depressive disorder (MDD) is a mental disorder affecting about 16% of the US adult population, and is a major cause for concern not only in the United [...], By analyzing interpoint comparisons, we obtain significant results describing the relationship in 'hippocampus shape space' of clinically depressed, high-risk, and control populations. In particular, our analysis demonstrates that the high-risk population is closer in shape space to the control population than to the clinically depressed population.

A family of conditionally Gaussian signal models for synthetic aperture radar (SAR) imagery is presented, extending a related class of models developed for high resolution radar range profiles. This signal model is robust with respect to the variations of the complex-valued radar signals due to the coherent combination of returns from scatterers as those scatterers move through relative distances on the order of a wavelength of the transmitted signal (target speckle). The target type and the relative orientations of the sensor, target, and ground plane parameterize the conditionally Gaussian model. Based upon this model, algorithms to jointly estimate both the target type and pose are developed. Performance results for both target pose estimation and target recognition are presented for publicly released data from the MSTAR program.

We consider the problem of recognizing CAD models at arbitrary orientations observed via the projective transformation on an imaging sensor with noise. Bounds on codebook size are established through the rate-distortion curve for a distortion measure derived from the Hilbert-Schmidt norm for elements of the orthogonal group. Index Terms--Computer vision, deformable templates, image understanding.

This paper presents measures characterizing the information content of remote observations of ground scenes imaged via optical and infrared sensors. Object recognition is posed in the context of deformable templates; the special Euclidean group is used to accommodate geometric variation of object pose. Principal component analysis of object signatures is used to represent and efficiently accommodate variation in object signature due to changes in the thermal state of the object surface. Mutual information measures, which are independent of the recognition system, are calculated quantifying both the information gain due to remote observations of the scene and the information loss due to signature variability. Signature model mismatch is quantitatively examined using the Kullback-Leibler divergence. Expressions are derived quadratically approximating the posterior conditional entropy on the orthogonal group for high signal-to-noise ratio. It is demonstrated that quadratic modules accurately characterize the posterior entropy for broad ranges of signal-to-noise ratio. Information gain in multiple-sensor scenarios is quantified, and it is demonstrated that the cost of signature uncertainty for the Comanche series of FLIR images collected by the U.S. Army Night Vision Electronic Sensors Directorate is approximately 0.8 bits with an associated near doubling of mean-squared error uncertainty in pose. Index Terms--Infrared imaging, mutual information, object recognition, performance analysis of recognition systems.

This correspondence investigates the asymptotic performance of Bayesian target recognition algorithms using deformable-template representations. Rigid computer-aided design (CAD) models represent the underlying targets; low-dimensional matrix Lie-groups (rotation and translation) extend them to particular instances. Remote sensors observing the targets are modeled as projective transformations, converting three-dimensional scenes into random images. Bayesian target recognition corresponds to hypothesis selection in the presence of nuisance parameters; its performance is quantified as the Bayes' error. Analytical expressions for this error probability in small noise situations are derived, yielding asymptotic error rates for exponential error probability decay. Index Terms--Bayesian ATR, deformable templates, Laplace's asymptotics, nuisance integration.

Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic difference equations determined by finitely supported, stationary, linear difference operators, adjusted to be nonstationary at the boundaries. It is shown that as the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximum-likelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models are used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds. Index Terms--Gaussian Markov random fields, texture segmentation, stochastic difference equations.

Research is presented concerning the conditions required for the existence of solutions in the space of diffeomorphisms. The importance of landmark matching of large deformations in medical imaging is discussed.