Xiaodong Tao

Hierarchical active shape models, using the wavelet transform

Active shape models (ASMs) are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability. This paper presents a method that overcomes this limitation, by using a hierarchical formulation of active shape models, using the wavelet transform. The statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis, and used as priors in the contours deformation. Some of these priors reflect relatively global shape characteristics of the object boundaries, whereas, some of them capture local and high-frequency shape characteristics and, thus, serve as local smoothness constraints. This formulation achieves two objectives. First, it is robust when only a limited number of training samples is available. Second, by using local statistics as smoothness constraints, it eliminates the need for adopting ad hoc physical models, such as elasticity or other smoothness models, which do not necessarily reflect true biological variability. Examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved, even with as few as five training samples.

Using a statistical shape model to extract sulcal curves on the outer cortex of the human brain

A method for automated segmentation of major cortical sulci on the outer brain boundary is presented, with emphasis on automatically determining point correspondence and on labeling cortical regions. The method is formulated in a general optimization framework defined on the unit sphere, which serves as parametric domain for convoluted surfaces of spherical topology. A statistical shape model, which includes a network of deformable curves on the unit sphere, seeks geometric features such as high curvature regions and labels such features via a deformation process that is confined within a spherical map of the outer brain boundary. The limitations of the customary spherical coordinate system, which include discontinuities at the poles and nonuniform sampling, are overcome by defining the statistical prior of shape variation in terms of projections of landmark points onto corresponding tangent planes of the sphere. The method is tested against and shown to be as accurate as manually defined segmentations.

Cortical surface segmentation and mapping

Segmentation and mapping of the human cerebral cortex from magnetic resonance (MR) images plays an important role in neuroscience and medicine. This paper describes a comprehensive approach for cortical reconstruction, flattening, and sulcal segmentation. Robustness to imaging artifacts and anatomical consistency are key achievements in an overall approach that is nearly fully automatic and computationally fast. Results demonstrating the application of this approach to a study of cortical thickness changes in aging are presented.

Statistical Study on Cortical Sulci of Human Brains

A method for building a statistical shape model of sulci of the human brain cortex is described. The model includes sulcal fundi that are defined on a spherical map of the cortex. The sulcal fundi are first extracted in a semi-automatic way using an extension of the fast marching method. They are then transformed to curves on the unit sphere via a conformal mapping method that maps each cortical point to a point on the unit sphere. The curves that represent sulcal fundi are parameterized with piecewise constant-speed parameterizations. Intermediate points on these curves correspond to sulcal landmarks, which are used to build a point distribution model on the unit sphere. Statistical information of local properties of the sulci, such as curvature and depth, are embedded in the model. Experimental results are presented to show how the models are built.

A method for registering diffusion weighted magnetic resonance images

Diffusion weighted magnetic resonance (DWMR or DW) imaging is a fast evolving technique to investigate the connectivity of brain white matter by measuring the self-diffusion of the water molecules in the tissue. Registration is a key step in group analysis of the DW images that may lead to understanding of functional and structural variability of the normal brain, understanding disease process, and improving neurosurgical planning. In this paper, we present a new method for registering DW images. The method works directly on the diffusion weighted images without using tensor reconstruction, fiber tracking, and fiber clustering. Therefore, the performance of the method does not rely on the accuracy and robustness of these steps. Moreover, since all the information in the original diffusion weighted images is used for registration, the results of the method is robust to imaging noise. We demonstrate the method on intra-subject registration with an affine transform using DW images acquired on the same scanner with the same imaging protocol. Extension to deformable registration for images acquired on different scanners and/or with different imaging protocols is also discussed.

Applications of wavelets in morphometric analysis of medical images

Morphometric analysis of medical images is playing an increasingly important role in understanding brain structure and function, as well as in understanding the way in which these change during development, aging and pathology. This paper presents three wavelet-based methods with related applications in morphometric analysis of magnetic resonance (MR) brain images. The first method handles cases where very limited datasets are available for the training of statistical shape models in the deformable segmentation. The method is capable of capturing a larger range of shape variability than the standard active shape models (ASMs) can, by using the elegant spatial-frequency decomposition of the shape contours provided by wavelet transforms. The second method addresses the difficulty of finding correspondences in anatomical images, which is a key step in shape analysis and deformable registration. The detection of anatomical correspondences is completed by using wavelet-based attribute vectors as morphological signatures of voxels. The third method uses wavelets to characterize the morphological measurements obtained from all voxels in a brain image, and the entire set of wavelet coefficients is further used to build a brain classifier. Since the classification scheme operates in a very-high-dimensional space, it can determine subtle population differences with complex spatial patterns. Experimental results are provided to demonstrate the performance of the proposed methods.

An automated method for finding curves of sulcal fundi on human cortical surfaces

We present a method for automatically finding curves representing the sulcal fundi on the human brain cortex. A flattened map of the cortical surface is used as the reference space in which the curves are modeled. The map is also used to transfer planar curves back to the cortical surface to extract sulcal fundal curves. Instead of modeling the curves by densely sampled landmark points, as it is done in the traditional active shape models, we model sulcal curves by a small number of anchor points that correspond to salient features, such as end points or points of intersections. The full sulcal curves connecting the anchor points are reconstructed by an extension of the fast marching method. Each anchor point carries a wavelet based attribute vector whose goal is to provide a distinctive morphological signature for the anchor point. This allows us to efficiently solve the problem in a low-dimensional space. Moreover, because each anchor point has this signature, and because anchor points are chosen to be salient features, the cost function defined in this low-dimensional space is presumed to have few local minima. Experimental results show that the sulcal curves extracted using the automatic method agrees well with the manually drawn sulcal curves.

Using the fast marching method to extract curves with given global properties

Curves are often used as anatomical features to match surfaces that represent biological objects, such as the human brain. Automated and semi-automated methods for extracting these curves usually rely on local properties of the surfaces such as the mean surface curvature without considering the global appearance of the curves themselves. These methods may require additional human intervention, and sometimes produce erroneous results. In this paper, we present an algorithm that is based on the fast marching method (FMM) to extract weighted geodesic curves. Instead of directly using the local image properties as a weight function, we use the surface properties, together with the global properties of the curves, to compute a weight function. This weight function is then used by the FMM to extract curves between given points. The general framework can be used to extract curves with different global properties. The resulting curves are guaranteed to be weighted geodesic curves without cusps usually introduced by intermediate points through which the curves are forced to pass. We show some results on both a simulated image and a highly convoluted human brain cortical surface.

Assisted labeling techniques for the human brain cortex

With the improvements in techniques for generating surface models from magnetic resonance (MR) images, it has recently become feasible to study the morphological characteristics of the human brain cortex in vivo. Studies of the entire surface are important for measuring global features, but analysis of specific cortical regions of interest provides a more detailed understanding of structure. We have previously developed a method for automatically segmenting regions of interest from the cortical surface using a watershed transform. Each segmented region corresponds to a cortical sulcus and is thus termed a sulcal region. In this work, we describe three important augmentations of this methodology. First, we describe a user interface that allows for the efficient labeling of the segmented sulcal regions called the Interactive Program for Sulcal Labeling (IPSL). Two additional augmentations of the methodology allow for even finer division of regions on the cortex. Both employ the fast marching technique to track curves of interest on the cortical surface. These curves are then used to separate segmented regions. Validation experiments indicate that the proposed methodology gives highly repeatable results.