We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

The Marching Cubes (MC) algorithm is a commonly used method for generating isosurfaces. The MC algorithm also generates an excessively large number of triangles to represent an isosurface. Generating many triangles increases the rendering time which is directly proportional to the number of triangles. This paper presents a decimation method to reduce the number of triangles generated by the MC algorithm. Decimation is carried out within the framework of the MC algorithm before creating a large number of triangles. Four major steps comprise the reported implementation of the algorithm: a) surface tracking, b) merging, c) crack patching, and d) triangulation. Surface tracking is an enhanced implementation of the MC algorithm. Starting from a seed point, the surface tracker visits only those cells likely to compose part of the desired isosurface. This results in up to approximately 80% computational saving The cells making up the extracted surface are stored in an octree that is further p...

A popular technique for rendition of isosurfaces in sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell by one or more polygons whose vertices are obtained by interpolation of the sample data. That is, each polygon vertex is a point on a cell edge, between two adjacent sample points, where the function is estimated to equal the desired threshold value. The two sample points have values on opposite sides of the threshold, and the interpolated point is called an intersection point. When one cell face has an intersection point ineach of its four edges, then the correct connection among intersection points becomes ambiguous. An incorrect connection can lead to erroneous topology in the rendered surface, and possible discontinuities. We show that disambiguation methods, to be at all accurate, need to consider sample values in the neighborhood outside the cell. This paper studies the problems of disambiguation, reports on some solutions, and presents some statistics on the occurrence of such ambiguities. A natural way to incorporate neighborhood information is through the use of calculated gradients at cell corners. They provide insight into the behavior of a function in well-understood ways. We introduce two gradient-consistency heuristics that use calculated gradients at the corners of ambiguous faces, as well as the function values at those corners, to disambiguate at a reasonable computational cost. These methods give the correct topology on several examples that caused problems for other methods we examined.

We describe a fully-automatic 3Dsegmentation technique for brain MR images. By means of Markov random fields the segmentation algorithm captures three features that are of special importance for MR images: nonparametric distributions of tissue intensities, neighborhood correlations and signal inhomogeneities. Detailed simulations and real MR images demonstrate the performance of the segmentation algorithm. In particular the impact of noise, inhomogeneity, smoothing and structure thickness is analyzed quantitatively. Even singleecho MR images are well classified into grey matter, white matter, cerebrospinal fluid, scalpbone, and background. A simulated annealing and an iterated conditional modes implementation are presented. Index Terms Magnetic Resonance Imaging, Segmentation, Markov Random Fields I. INTRODUCTION Excellent soft-tissue contrast and high spatial resolution make magnetic resonance imaging the method for anatomical imaging in brain research. Segmentation of the MR imag...

Maximum projection is a volume rendering technique that, for each pixel, finds the maximum intensity along a projector. For certain important classes of data, this is an approximation to summation rendering which produces superior visualizations. In this paper we will show how maximum projection rendering with additional depth cues can be implemented using simple affine transformations in object space. This technique can be used together with 3D graphics libraries and standard graphics hardware,thus allowing interactive manipulations of the volume data. The algorithm presented in this paper allows for a wide range of tradeoffs between interactivity and image quality. 1 Introduction The existing approaches to volume visualization can be classified into two categories: direct volume rendering and model based techniques. While these two techniques have often been portrayed as competitors, we think they should actually be seen as being complementary. The method described in this paper us...

An algorithm for automatic and accurate segmentation of multi-dimensional images is presented in this paper. It improves the classical watershed transform whose results are inaccurate when applied on noisy or anisotropic data. This algorithm combines a watershed-like region growing with a very simple marker selection step. It is particularly well suited for accurate segmentation of complex objects, such as the brain in 3D Magnetic Resonance (MR) images of the head since it provides an accurate and fully 3D segmentation in a reasonable computation time. Comparative results of the segmentation obtained by this algorithm and by the classical watershed transform are shown in the case of 3D MR images. Applications of this technique to 3D visualisation and brain sulcii identification are also presented. () 1997 Elsevier Science B.V.

. The National Library of Medicine is creating a digital atlas of the human body. This project, called the Visible Human, has already produced computed tomography, magnetic resonance imaging and physical cross-sections of a human male cadaver. This paper describes a methodology and results for extracting surfaces from the Visible Male's CT data. We use surface connectivity and isosurface extraction techniques to create polygonal models of the skin, bone, muscle and bowels. Early experiments with the physical cross-sections are also reported. 1. Introduction In 1989, the National Library of Medicine (NLM) began an ambitious project to create a digital atlas of the human anatomy. The NLM Planning Panel on Electronic Image Libraries [1] recommended a project to create XRAY Computed Tomography (XRAY-CT), Magnetic Resonance Imaging (MRI) and physical sections of a human cadaver. The project is called "The Visible Man." Another cadaver, that of a 59 year-old woman, is being processe...

. Endoscopes provide real-time, high resolution video views of the interior of hollow organs and cavities that exist within the human body. Although endoscopic examinations are mostly non-invasive, the procedures still require some sedation or anesthesia to reduce patient discomfort. X-Ray Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are non-invasive diagnostic imaging techniques that display internal anatomy in cross sections called slices. For the most part, radiologists view the 2D cross sections and create mental images of the 3D structures present in the study. However, many of the tubular structuresthat exist in the body have complex morphology, passing back and forth through the cross sections. This paper illustrates techniques for the internal exploration of CT / MRI data that have been reconstructed into 3D surfaces. The views produced by the new methods simulate the types of views that can be obtained with endoscopes. Examples from the brain, cran...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii CHAPTERS 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Magnetic Resonance Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Image Formation in MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Characteristics of Medical Imagery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Segmentation of MR images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4.1 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4.2 Gray Scale Single Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4.3 Multispectral Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Validati...

this paper the design, advantages, limitations and current applications, (i.e., biopsies, craniotomies, and interstitial laser therapy) are discussed with emphasis on the integration of imaging into the procedures. Furthermore we introduce our integrated software platform for intraoperative visualization and navigation, the 3D Slicer