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20
Marching cubes: A high resolution 3D surface construction algorithm
 COMPUTER GRAPHICS
, 1987
"... We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divideandconquer approach to generate interslice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical d ..."
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Cited by 2119 (4 self)
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We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divideandconquer approach to generate interslice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scanline 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 interslice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and singlephoton 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.
OctreeBased Decimation of Marching Cubes Surfaces
, 1996
"... 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 triangle ..."
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Cited by 108 (0 self)
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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...
Topological Considerations in Isosurface Generation
 ACM Transactions on Graphics
, 1994
"... 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 e ..."
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Cited by 96 (0 self)
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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 wellunderstood ways. We introduce two gradientconsistency 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.
Markov Random Field Segmentation of Brain MR Images
, 1997
"... We describe a fullyautomatic 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 inhomo ..."
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Cited by 56 (0 self)
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We describe a fullyautomatic 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 softtissue contrast and high spatial resolution make magnetic resonance imaging the method for anatomical imaging in brain research. Segmentation of the MR imag...
Brownian Strings: Segmenting Images with Stochastically Deformable Models
, 1995
"... Abstract—This paper describes an image segmentation technique in which an arbitrarily shaped contour was deformed stochastically until it fitted around an object of interest. The evolution of the contour was controlled by a simulated annealing process which caused the contour to settle into the glob ..."
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Cited by 32 (0 self)
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Abstract—This paper describes an image segmentation technique in which an arbitrarily shaped contour was deformed stochastically until it fitted around an object of interest. The evolution of the contour was controlled by a simulated annealing process which caused the contour to settle into the global minimum of an imagederived “energy ” function. The nonparametric energy function was derived from the statistical properties of previously segmented images, thereby incorporating prior experience. Since the method was based on a state space search for the contour with the best global properties, it was stable in the presence of image errors which confound segmentation techniques based on local criteria, such as connectivity. Unlike “snakes ” and other active contour approaches, the new method could handle arbitrarily irregular contours in which each interpixel crack represented an independent degree of freedom. Furthermore, since the contour evolved toward the global minimum of the energy, the method was more suitable for fully automatic applications than the snake algorithm, which frequently has to be reinitialized when the contour becomes trapped in local energy minima. High computational complexity was avoided by efficiently introducing a random local perturbation in a time independent of contour length, providing control over the size of the perturbation, and assuring that resulting shape changes were unbiased. The method was illustrated by using it to find the brain surface in magnetic resonance head images and to track blood vessels in angiograms. Additional information is available from
Interactive maximum projection volume rendering
 In Proceedings of IEEE Visualization
, 1995
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Automatic morphologybased brain segmentation (MBRASE) from MRIT1 data
 NeuroImage
, 2000
"... A method called morphologybased brain segmentation (MBRASE) has been developed for fully automatic segmentation of the brain from T1weighted MR image data. The starting point is a supervised segmentation technique, which has proven highly effective and accurate for quantitation and visualization p ..."
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Cited by 7 (0 self)
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A method called morphologybased brain segmentation (MBRASE) has been developed for fully automatic segmentation of the brain from T1weighted MR image data. The starting point is a supervised segmentation technique, which has proven highly effective and accurate for quantitation and visualization purposes. The proposed method automates the required user interaction, i.e., defining a seed point and a threshold range, and is based on the simple operations thresholding, erosion, and geodesic dilation. The thresholds are detected in a region growing process and are defined by connections of the brain to other tissues. The method is first evaluated on three computer simulated datasets by comparing the automated segmentations with the original distributions. The second evaluation is done on a total of 30 patient datasets, by comparing the automated segmentations with supervised segmentations carried out by a neuroanatomy expert. The comparison between two binary segmentations is performed both quantitatively and qualitatively. The automated segmentations are found to be accurate and robust. Consequently, the proposed method can be used as a default segmentation for quantitation and visualization of the human brain from T1weighted MR images in routine clinical procedures. © 2000 Academic Press Key Words: segmentation; MRI; brain imaging; mathematical
A QueueBased Region Growing Algorithm for Accurate Segmentation of MultiDimensional Digital Images
, 1997
"... An algorithm for automatic and accurate segmentation of multidimensional 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 watershedlike region growing with a very simpl ..."
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Cited by 6 (2 self)
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An algorithm for automatic and accurate segmentation of multidimensional 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 watershedlike 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.
Operational research techniques in medical treatment and Diagnosis: A Review
, 2000
"... Many modern techniques for the diagnosis of pathological states in humans and for their subsequent treatment can be posed as nonlinear identification problems of essentially nonlinear dynamic systems or as nonlinear optimal control problems. It can be shown that the linearised versions of such model ..."
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Many modern techniques for the diagnosis of pathological states in humans and for their subsequent treatment can be posed as nonlinear identification problems of essentially nonlinear dynamic systems or as nonlinear optimal control problems. It can be shown that the linearised versions of such models are inadequate and do not represent at all well the complexity of the problem. Thus, nonlinear estimation and control techniques are required for progress to be made in this field. The aim of this review is to examine some models suggested in the medical literature for the modelling of certain medical treatments and diagnoses. Then examine how these models can be enriched by using Operational Research techniques so that a better control is provided on the diagnosis and the treatment, as well as the formulation of more precise models of the phenomenon. The review will present some applications both therapeutic and diagnostic that have appeared in the literature. Special interest will be bestowed on hyperthermic systems in oncological treatment and glucoseinsulin dynamics for diabetic patients, while heart dynamics and magnetic resonance imaging will also receive attention. These applications are good examples to show the advantages of Operational Research methods in this field of endeavour. The outline of the paper is the following. After the introduction, in section two a brief description of nonlinear