This article surveys deformable models, a promising and vigorously researched computer-assisted medical image analysis technique. Among model-based techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the model-based image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.

The development of algorithms for the spatial transformation and registration of tomographic brain images is a key issue in several clinical and basic science medical applications, including computer aided neurosurgery, functional image analysis, and morphometrics. This paper describes a technique for the spatial transformation of brain images, which is based on elastically deformable models. A deformable surface algorithm is used to find a parametric representation of the outer cortical surface and then and then to define a map between corresponding cortical regions in two brain images. Based on the resulting map, a three-dimensional elastic warping transformation is then determined, which brings two images into register. This transformation models images as inhomogeneous elastic objects which are deformed into registration with each other by external force fields. The elastic properties of the images can vary from one region to the other, allowing more variable brain regions, such as...

Objective. The spatial normalization and registration of tomographic images from different subjects is a major problem in several medical imaging areas, including functional image analysis, morphometrics, and computer aided neurosurgery. The focus of this paper is the development of a computerized methodology for the spatial normalization of 3D images. Materials and Methods. We propose a technique which is based on geometric deformable models. In particular, we first describe a deformable surface algorithm which finds a mathematical representation of the outer cortical surface. Based on this representation, a procedure for obtaining a map between corresponding regions of the outer cortex in two different images is established. This map is subsequently used to derive a three-dimensional elastic warping transformation, which brings two images in register. Results. The performance of our algorithm is demonstrated on several datasets. In particular, we first test our deformable surface a...

The cortical sulci are brain structures resembling thin convoluted ribbons embedded in 3D. The importance of the sulci lies primarily in their relation to the cytoarchitectonic and functional organization of the underlying cortex, and in their utilization as features in non-rigid registration methods. This paper presents a methodology for extracting parametric representations of the cerebral sulci from magnetic resonance images. The proposed methodology is based on deformable models utilizing characteristics of the cortical shape. Specifically, a parametric representation of a sulcus is determined by the motion of an active contour along the medial surface of the corresponding cortical fold. The active contour is initialized along the outer boundary of the brain, and deforms toward the deep root of a sulcus under the influence of an external force field restricting it to lie along the medial surface of the particular cortical fold. A parametric representation of the medial surface of...

A key issue in several brain imaging applications, including computer aided neurosurgery, functional image analysis, and morphometrics, is the spatial normalization and registration of tomographic images from different subjects. This paper proposes a technique for spatial normalization of brain images based on elastically deformable models. In our approach we use a deformable surface algorithm to find a parametric representation of the outer cortical surface and then use this representation to obtain a map between corresponding regions of the outer cortex in two different images. Based on the resulting map we then derive a three-dimensional elastic warping transformation which brings two images in register. This transformation models images as inhomogeneous elastic objects which are deformed into registration with each other by external force fields. The elastic properties of the images can vary from one region to the other, allowing more variable brain regions, such as the ventricles,...

Parametric representations of anatomical structures provide useful mathematical descriptions for many medical imaging applications, including morphological analysis of the brain. In this paper, we develop a methodology for obtaining a parametric representation of the deep cortical folds of the brain utilizing characteristics of the cortical shape. We first find a mathematical representation of the outer cortical surface using a deformable surface algorithm. Using the principal curvatures of the resulting surface, we then identify the edges on the sulci on it, and we initialize active contours along them. An external force field guides an active contour to the deep edge of a sulcus, along the medial surface of a cortical fold. A parametric description of a sulcal surface is obtained as the active contour traverses the sulcus, sweeping a surface resembling a convoluted ribbon embedded in 3D. In this paper we present results using magnetic resonance images. 1. Introduction The representa...

. A computer algorithm for determining optimal surgical paths in the brain is presented. The algorithm computes a cost function associated with each point on the outer brain boundary, which is treated as a candidate entry point. The cost function is determined partly based on a segmentation of the patients images into gray and white matter, and partly based on a spatially transformed atlas of the human brain registered to the patient's MR images. The importance of various structures, such as thalamic nuclei, optic nerve and radiations, and individual Brodman's areas, can be defined on the atlas and transferred onto the patient's images through the spatial transformation. The cost of a particular path associated with each critical structure, as well as the total cost of each path are computed and displayed, allowing the surgeon to define a low cost path, to visualize an arbitrary cross-section through the patient's MR images that contains this path, and to examine all the cross-sectiona...

Volume segmentation is an important part of computer based medical applications for diagnosis and analysis of anatomical data. With rapid advances in medical imaging modalities and volume visualization techniques, computer based diagnosis is fast becoming a reality. These computer based tools allow scientists and physicians to understand and diagnose anatomical structures by virtually interacting with them. Volume segmentation plays a critical role by facilitating automatic or semiautomatic extraction of the anatomical organ or region-of-interest. In this review, we provide an introduction to various segmentation algorithms found in the literature. We classify the algorithms into three categories: structural techniques, statistical techniques and hybrid techniques. Under structural techniques we will review algorithms which take into consideration structural information for segmentation. Stochastic techniques are those which perform segmentation based on statistical analysis methods and under hybrid techniques we will review algorithms which make use