Enlarged ventricular size and/or asymmetry have been found markers for psychiatric illness, including schizophrenia. However, this morphometric feature is non-specific and occurs in many other brain diseases, and its variability in healthy controls is not sufficiently understood. We studied ventricular size and shape in 3D MRI (N=20) of monozygotic (N=5) and dizygotic (N=5) twin pairs. Left and right lateral, third and fourth ventricles were segmented from high-resolution T1w SPGR MRI using supervised classification and 3D connectivity. Surfaces of binary segmentations of left and right lateral ventricles were parametrized and described by a series expansion using spherical harmonics. Objects were aligned using the intrinsic coordinate system of the ellipsoid described by the first order expansion. The metric for pairwise shape similarity was the mean squared distance (MSD) between object surfaces. Without normalization for size, MZ twin pairs only showed a trend to have more similar lateral ventricles than DZ twins. After scaling by individual volumes, however, the pairwise shape difference between right lateral ventricles of MZ twins became very small with small group variance, differing significantly from DZ twin pairs. This finding suggests that there is new information in shape not represented by size, a property that might improve understanding of neurodevelopmental and neurodegenerative changes of brain objects and of heritability of size and shape of brain structures. The findings further suggest that alignment and normalization of objects are key issues in statistical shape analysis which need further exploration.

There have been significant efforts to build a probabilistic atlas of the brain and to use it for many common applications, such as segmentation and registration. Though the work related to brain atlases can be applied to nonbrain organs, less attention has been paid to actually building an atlas for organs other than the brain. Motivated by the automatic identification of normal organs for applications in radiation therapy treatment planning, we present a method to construct a probabilistic atlas of an abdomen consisting of four organs (i.e., liver, kidneys, and spinal cord). Using 32 noncontrast abdominal computed tomography (CT) scans, 31 were mapped onto one individual scan using thin plate spline as the warping transform and mutual information (MI) as the similarity measure. Except for an initial coarse placement of four control points by the operators, the MI-based registration was automatic. Additionally, the four organs in each of the 32 CT data sets were manually segmented. The manual segmentations were warped onto the “standard ” patient space using the same transform computed from their gray scale CT data set and a probabilistic atlas was calculated. Then, the atlas was used to aid the segmentation of low-contrast organs in an additional 20 CT data sets not included in the atlas. By incorporating the atlas information into the Bayesian framework, segmentation results clearly showed improvements over a standard unsupervised segmentation method.

Medial representation of a three-dimensional (3-D) object or an ensemble of 3-D objects involves capturing the object interior as a locus of medial atoms, each atom being two vectors of equal length joined at the tail at the medial point. Medial representation has a variety of beneficial properties, among the most important of which are 1) its inherent geometry, provides an object-intrinsic coordinate system and thus provides correspondence between instances of the object in and near the object(s); 2) it captures the object interior and is, thus, very suitable for deformation; and 3) it provides the basis for an intuitive object-based multiscale sequence leading to efficiency of segmentation algorithms and trainability of statistical characterizations with limited training sets. As a result of these properties, medial representation is particularly suitable for the following image analysis tasks; how each operates will be described and will be illustrated by results:

In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields. This decomposition consists in representing the velocity field as a sum of a divergence free component and a vorticity free component. The objective is to provide a low-dimensional parametric representation of optical flows by depicting them as deformations generated by a reduced number of vortex and source particles. Both components are approximated using a discretization of the vorticity and divergence maps through regularized Dirac measures. The resulting so called irrotational and solenoidal fields consist of linear combinations of basis functions obtained through a convolution product of the Green kernel gradient and the vorticity map or the divergence map respectively. The coefficient values and the basis function parameters are obtained by minimization of a functional relying on an integrated version of mass conservation principle of fluid mechanics. Results are provided on synthet-ic examples and real world sequences. 1

We propose to use approximations of shape metrics, such as the Hausdorff distance, to define similarity measures between shapes. Our approximations being continuous and differentiable, they provide an obvious way to warp a shape onto another by solving a Partial Differential Equation (PDE), in effect a curve flow, obtained from their first order variation. This first order variation defines a normal deformation field for a given curve. We use the normal deformation fields induced by several sample shape examples to define their mean, their covariance ”operator”, and the principal modes of variation. Our theory, which can be seen as a nonlinear generalization of the linear approaches proposed by several authors, is illustrated with numerous examples. Our approach being based upon the use of distance functions is characterized by the fact that it is intrinsic, i.e. independent of the shape parametrization. 1.

Abstract. Probabilistic atlas has broad applications in medical image segmentation and registration. The most common problem building a probabilistic atlas is picking a target image upon which to map the rest of the training images. Here we present a method to choose a target image that is the closest to the mean geometry of the population under consideration as determined by bending energy. Our approach is based on forming a distance matrix based on bending energies of all pair-wise registrations and performing multidimensional scaling (MDS) on the distance matrix. 1

In this work, we extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment. Our results indicate that increasing the complexity of the deformation model improves registration accuracy significantly, especially at cortical regions.

In this work, we extend a previously demonstrated entropy based groupwise registration method to include a non-rigid deformation model based on B-splines. We describe an open source implementation of the groupwise registration algorithm using the Insight Toolkit ITK www.itk.org. We provide the source code, parameters, input and output data that we used for validation. We describe an efficient implementation of the algorithm by using a stochastic optimization scheme embedded in a multi-resolution setting. The objective function is optimized using gradient descent algorithm combined with line search for the step size. The derivative of the objective function is evaluated efficiently by computing Jacobian of B-spline deformation field locally. We demonstrate the algorithm in application to different imaging modalities including proton density, FA, T1 and T2 MR images. We validate the algorithm on synthetic datasets varying from 2 to 30 images

Abstract. In [1], a new coherent statistical framework for estimating statistical deformable templates relevant to computational anatomy (CA) has been proposed. This paper addresses the problem of population average and estimation of the underlying geometrical variability as a MAP computation problem for which deterministic and stochastic approximation schemes have been proposed. We illustrate some of the numerical issues with handwritten digit and 2D medical images and apply the estimated models to classification through maximum likelihood. 1

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