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.

Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. It differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several two-dimensional (2-D) examples and one three-dimensional (3-D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities.

Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to concave boundaries, howevel; have limited their utility. This paper develops a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a dijhsion of the gradient vectors of a gray-level or binary edge map derived from the image. The resultant field has a large capture range and forces active contours into concave regions. Examples on simulated images and one real image are presented. 1

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.

Active contours, or snakes, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. A new type of external force for active contours, called gradient vector flow (GVF) was introduced recently to address problems associated with initialization and poor convergence to boundary concavities. GVF is computed as a di#usion of the gradient vectors of a gray-level or binary edge map derived from the image. In this paper, we generalize the GVF formulation to include two spatially varying weighting functions. This improves active contour convergence to long, thin boundary indentations, while maintaining other desirable properties of GVF, such as an extended capture range. The original GVF is a special case of this new generalized GVF (GGVF) model. An error analysis for active contour results on simulated test images is also presented. # 1998 Elsevier Science B.V. All rights reserved. Zusammenfassung Aktive Umrisse, oder Schlangen, we...

Purpose. A new technique for analyzing the morphology of the corpus callosum is presented, and it is applied to a group of elderly subjects. Methods. The proposed approach normalizes subject data into the Talairach space using an elastic deformation transformation. The properties of this transformation are used as a quantitative description of the callosal shape with respect to the Talairach atlas, which is treated as a standard. In particular, a deformation function measures the enlargement/shrinkage associated with this elastic deformation. Inter-subject comparisons are made by comparing deformation functions. Results. This technique was applied to eight male and eight female subjects. Based on the average deformation functions of each group, the posterior region of the female corpus callosum was found to be larger than its corresponding region in the males. The average callosal shape of each group was also found, demonstrating visually the callosal shape differences between the tw...

A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registering magnetic resonance images to atlas images. I. Introduction Registration of both intra-subject and inter-subject brain images has been the subject of extensive study in the medical imaging literature. The various techniques that have been proposed can be classified into three major categories: polynomial transformations, similarity-based methods, and boundary-based methods. Polynomial transformations [1, 2, 3] apply a polynomial warping and determine the coefficients of the polynomial using linear regression if a sufficient number of landmark points is provided. Numerical instabilities and the ...

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A robust fully automatic method for segmenting the brain from head MR images has been developed, which works even in the presence of RF inhomogeneities. It has been successful in segmenting the brain in every slice from head images acquired from several different MRI scanners, using different resolution images and different echo sequences. The method uses an integrated approach which employs image processing techniques based on anisotropic filters and "snakes" contouring techniques, and a-priori knowledge, which is used to remove the eyes, which are tricky to remove based on image intensity alone. It is a multi-stage process, involving first removal of the background noise leaving a head mask, then finding a rough outline of the brain, then refinement of the rough brain outline to a final mask. The paper describes the main features of the method, and gives results for some brain studies. Keywords: Magnetic Resonance Imaging, Intracranial Boundary Detection, Nonlinear Anisotropic Dif...

Active contour models are an efficient, accurate, and robust tool for the segmentation of 2D and 3D image data.