Standard image based segmentation approaches perform poorly when there is little or no contrast along boundaries of different regions. In such cases, segmentation is largely performed manually using prior knowledge of the shape and relative location of the underlying structures combined with partially discernible boundaries. We present an automated approach guided by covariant shape deformations of neighboring structures, which is an additional source of prior information. Captured by a shape atlas, these deformations are transformed into a statistical model using the logistic function. Structure boundaries, anatomical labels, and image inhomogeneities are estimated simultaneously within an Expectation-Maximization formulation of the maximum a posteriori probability estimation problem. We demonstrate the approach on 20 brain magnetic resonance images showing superior performance, particularly in cases where purely image based methods fail.

# Publications by Year: 2005

## 2005

Pohl KM, Fisher J, Kikinis R, Grimson EL, Wells WM. Shape Based Segmentation of Anatomical Structures in Magnetic Resonance Images. Comput Vis Biomed Image Appl. 2005;3765:489–98.

Donnell LO, Westin CF. White matter tract clustering and correspondence in populations. Med Image Comput Comput Assist Interv. 2005;8(Pt 1):140–7.

We present a novel method for finding white matter fiber correspondences and clusters across a population of brains. Our input is a collection of paths from tractography in every brain. Using spectral methods we embed each path as a vector in a high dimensional space. We create the embedding space so that it is common across all brains, consequently similar paths in all brains will map to points near each other in the space. By performing clustering in this space we are able to find matching fiber tract clusters in all brains. In addition, we automatically obtain correspondence of tractographic paths across brains: by selecting one or several paths of interest in one brain, the most similar paths in all brains are obtained as the nearest points in the high-dimensional space.

Wittek A, Kikinis R, Warfield SK, Miller K. Brain shift computation using a fully nonlinear biomechanical model. Med Image Comput Comput Assist Interv. 2005;8(Pt 2):583–90.

In the present study, fully nonlinear (i.e. accounting for both geometric and material nonlinearities) patient specific finite element brain model was applied to predict deformation field within the brain during the craniotomy-induced brain shift. Deformation of brain surface was used as displacement boundary conditions. Application of the computed deformation field to align (i.e. register) the preoperative images with the intraoperative ones indicated that the model very accurately predicts the displacements of gravity centers of the lateral ventricles and tumor even for very limited information about the brain surface deformation. These results are sufficient to suggest that nonlinear biomechanical models can be regarded as one possible way of complementing medical image processing techniques when conducting nonrigid registration. Important advantage of such models over the linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain tissue stress-strain relationship is linear.

Archip N, Rohling R, Cooperberg P, Tahmasebpour H, Warfield SK. Spectral clustering algorithms for ultrasound image segmentation. Med Image Comput Comput Assist Interv. 2005;8(Pt 2):862–9.

Image segmentation algorithms derived from spectral clustering analysis rely on the eigenvectors of the Laplacian of a weighted graph obtained from the image. The NCut criterion was previously used for image segmentation in supervised manner. We derive a new strategy for unsupervised image segmentation. This article describes an initial investigation to determine the suitability of such segmentation techniques for ultrasound images. The extension of the NCut technique to the unsupervised clustering is first described. The novel segmentation algorithm is then performed on simulated ultrasound images. Tests are also performed on abdominal and fetal images with the segmentation results compared to manual segmentation. Comparisons with the classical NCut algorithm are also presented. Finally, segmentation results on other types of medical images are shown.

Cosman ER, Wells WM III. Bayesian Population Modeling of Effective Connectivity. Inf Process Med Imaging. 2005;19:39–51.

A hierarchical model based on the Multivariate Autoregessive (MAR) process is proposed to jointly model neurological time-series collected from multiple subjects, and to characterize the distribution of MAR coefficients across the population from which those subjects were drawn. Thus, inference about effective connectivity between brain regions may be generalized beyond those subjects studied. The posterior on population- and subject-level connectivity parameters are estimated in a Variational Bayesian (VB) framework, and structural model parameters are chosen by the corresponding evidence criteria. The significance of resulting connectivity statistics are evaluated by permutation-based approximations to the null distribution. The method is demonstrated on simulated data and on actual multi-subject neurological time-series.

Pohl KM, Fisher J, Levitt JJ, Shenton ME, Kikinis R, Grimson EL, Wells WM. A unifying approach to registration, segmentation, and intensity correction. Med Image Comput Comput Assist Interv. 2005;8(Pt 1):310–8.

We present a statistical framework that combines the registration of an atlas with the segmentation of magnetic resonance images. We use an Expectation Maximization-based algorithm to find a solution within the model, which simultaneously estimates image inhomogeneities, anatomical labelmap, and a mapping from the atlas to the image space. An example of the approach is given for a brain structure-dependent affine mapping approach. The algorithm produces high quality segmentations for brain tissues as well as their substructures. We demonstrate the approach on a set of 22 magnetic resonance images. In addition, we show that the approach performs better than similar methods which separate the registration and segmentation problems.

Zhu L, Haker S, Tannenbaum A. Mass preserving registration for heart MR images. Med Image Comput Comput Assist Interv. 2005;8(Pt 2):147–54.

This paper presents a new algorithm for non-rigid registration between two doubly-connected regions. Our algorithm is based on harmonic analysis and the theory of optimal mass transport. It assumes an underlining continuum model, in which the total amount of mass is exactly preserved during the transformation of tissues. We use a finite element approach to numerically implement the algorithm.

Nain D, Haker S, Bobick A, Tannenbaum AR. Multiscale 3D shape analysis using spherical wavelets. Med Image Comput Comput Assist Interv. 2005;8(Pt 2):459–67.

Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data.

Friman O, Westin CF. Uncertainty in white matter fiber tractography. Med Image Comput Comput Assist Interv. 2005;8(Pt 1):107–14.

In this work we address the uncertainty associated with fiber paths obtained in white matter fiber tractography. This uncertainty, which arises for example from noise and partial volume effects, is quantified using a Bayesian modeling framework. The theory for estimating the probability of a connection between two areas in the brain is presented, and a new model of the local water diffusion profile is introduced. We also provide a theorem that facilitates the estimation of the parameters in this diffusion model, making the presented method simple to implement.

Yang Y, Zhu L, Haker S, Tannenbaum AR, Giddens DP. Harmonic skeleton guided evaluation of stenoses in human coronary arteries. Med Image Comput Comput Assist Interv. 2005;8(Pt 1):490–7.

This paper presents a novel approach that three-dimensionally visualizes and evaluates stenoses in human coronary arteries by using harmonic skeletons. A harmonic skeleton is the center line of a multi-branched tubular surface extracted based on a harmonic function, which is the solution of the Laplace equation. This skeletonization method guarantees smoothness and connectivity and provides a fast and straightforward way to calculate local cross-sectional areas of the arteries, and thus provides the possibility to localize and evaluate coronary artery stenosis, which is a commonly seen pathology in coronary artery disease.