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This paper presents a survey of the work done in modeling deformable objects within the computer graphics research community. The research has a long history and a wide variety of approaches have been used. This paper organizes the diversity of research by the technique used rather than by the application, although applications are discussed throughout. This paper presents some purely geometric approaches for modeling deformable objects, but focuses on physically based approaches. In the latter category are mass-spring models, nite element models, approximate continuum models, and low degree of freedom models. Special emphasis is placed on nite element models, which o er the greatest accuracy, but have seen limited use in computer graphics. The paper also suggests important areas for future research. 1

Abstract — This paper presents a new technique for the automatic model-based segmentation of three-dimensional (3-D) objects from volumetric image data. The development closely follows the seminal work of Taylor and Cootes on active shape models, but is based on a hierarchical parametric object description rather than a point distribution model. The segmentation system includes both the building of statistical models and the automatic segmentation of new image data sets via a restricted elastic deformation of shape models. Geometric models are derived from a sample set of image data which have been segmented by experts. The surfaces of these binary objects are converted into parametric surface representations, which are normalized to get an invariant object-centered coordinate system. Surface representations are expanded into series of spherical harmonics which provide parametric descriptions of object shapes. It is

Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of self-intersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model-based constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple two-dimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3-D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness. © 2000 Academic Press 1.

We present a novel method to extract iso-surfaces from distance volumes. It generates high quality semi-regular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multi-scale force-based solver refines the initial mesh into a semi-regular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete iso-distance ribbons are rapidly built and connected while respecting the topology of the iso-surface implied by the data. Subsequent multi-scale refinement is driven by a simple force-based solver designed to combine good iso-surface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the iso-surface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.

Statistical models of shape and appearance are powerful tools for interpreting medical images. We assume a training set of images in which corresponding `landmark' points have been marked on every image. From this data we can compute a statistical model of the shape variation, a model of the texture variation and a model of the correlations between shape and texture. With enough training examples such models should be able to synthesize any image of normal anatomy. By finding the parameters which optimize the match between a synthesized model image and a target image we can locate all the structures represented by the model. Two approaches to the matching will be described. The Active Shape Model essentially matches a model to boundaries in an image. The Active Appearance Model finds model parameters which synthesize a complete image which is as similar as possible to the target image. By using a `difference decomposition' approach the current difference between target image and synthesi...

Abstract. In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A level set formulation of the active contour is presented. The existence of the solution to the energy minimization is also established. We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.

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Vessel segmentation algorithms are the critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms. We put the various vessel extraction approaches and techniques in perspective by means of a classification of the existing research. While we have mainly targeted the extraction of blood vessels, neurosvascular structure in particular, we have also reviewed some of the segmentation methods for the tubular objects that show similar characteristics to vessels. We have divided vessel segmentation algorithms and techniques into six main categories: (1) pattern recognition techniques, (2) model-based approaches, (3) tracking-based approaches, (4) artificial intelligence-based approaches, (5) neural network-based approaches, and (6) miscellaneous tube-like object detection approaches. Some of these categories are further divided into sub- categories. We have also created tables to compare the papers in each category against such criteria as dimensionality, input type, pre-processing, user interaction, and result type.

M-reps (formerly called DSLs) are a multiscale medial means for modeling and rendering 3D solid geometry. They are particularly well suited to the modeling of anatomic objects, producing models that can be used to capture prior geometric information effectively in deformable models segmentation approaches. The representation is based on figural models, defined at coarse scale by a hierarchy of figures -- protrusions, indentations, neighboring figures, and included figures -- which represent solid regions and their boundaries simultaneously. The linked collection of figural components imply a fuzzy, i.e., probabilistically described boundary position with a width-proportional tolerance. At small scale these figural boundaries are made precise by displacing a dense sampling of the m-rep implied boundary. While these models can exist in 2D, we focus on models of 3D objects. A model for a single figure is made from a net, i.e., a mesh or chain, of medial atoms (hence the name m-reps), each...