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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 2261 (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.
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.
3D visualization of unsteady 2D airplane wake vortices
 IN PROCEEDINGS OF VISUALIZATION'94
, 1994
"... Air flowing around the wing tips of an airplane forms horizontal tornadolike vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be im ..."
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Cited by 16 (0 self)
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Air flowing around the wing tips of an airplane forms horizontal tornadolike vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be improved. In this paper, we introduce threedimensional techniques for visualizing timedependent, twodimensional wake vortex computations, and the hazard strength of such vortices near the ground. We describe a vortex core tracing algorithm and a local tiling method to visualize the vortex evolution. The tiling method converts timedependent, twodimensional vortex cores into threedimensional vortex tubes. Finally, a novel approach calculates the induced rolling moment on the following airplane at each grid point within a region near the vortex tubes and thus allows threedimensional visualization of the hazard strength of the vortices. We also suggest ways of combining multiple visualization methods to present more information simultaneously.
Reconstruction of 3D medical images: A nonlinear interpolation technique for reconstruction of 3D medical images
 Computer Vision, Graphics, and Image Processing 53(4):382391
, 1991
"... Threedimensional medical images reconstructed from a series of twodimensional images produced by computerized tomography, magnetic resonance imaging, etc., present a valuable tool for modem medicine. Usually, the interresolution between two cross sections is less than the intraresolution within e ..."
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Cited by 5 (0 self)
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Threedimensional medical images reconstructed from a series of twodimensional images produced by computerized tomography, magnetic resonance imaging, etc., present a valuable tool for modem medicine. Usually, the interresolution between two cross sections is less than the intraresolution within each cross section. Therefore, interpolations are required to create a 3D visualization. Many techniques, including voxelbased and patch tiling methods, apply linear interpolations between two cross sections. Although those techniques using linear interpolations are economical in computation, they need much crosssectional data and are unable to enlarge because of aliasmg. Hence, the techniques that apply twodimensional nonlinear interpolation functions among cross sections were proposed. In this paper, we introduce the curvature sampling of the contour of a medical object in a CT (computerized tomography) image. Those sampled contour points are the candidates for the control points of Hermite surfaces between each pair of cross sections. Then, a nearestneighbor mapping of control points between every two cross sections is used for surface formation. The time complexity of our mapping algorithm is O(m + n), where m and II are the numbers of control points of two cross sections. It is much faster than Kehtamavaz and De Figueiredo’s merge method, whose time complexity is O(n’m~). 0 1991 Academic Press, Inc. 1.
Scanline Surfacing: Building Separating Surfaces from Planar Contours
, 2000
"... A standard way to segment medical imaging datasets is by tracing contours around regions of interest in parallel planar slices. Unfortunately, the standard methods for reconstructing three dimensional surfaces from those planar contours tend to be either complicated or not very robust. Furthermore, ..."
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Cited by 5 (1 self)
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A standard way to segment medical imaging datasets is by tracing contours around regions of interest in parallel planar slices. Unfortunately, the standard methods for reconstructing three dimensional surfaces from those planar contours tend to be either complicated or not very robust. Furthermore, they fail to consistently mesh abutting structures which share portions of contours. In this paper we present a novel, straightforward algorithm for accurately and automatically reconstructing surfaces from planar contours. Our algorithm is based on scanline rendering and separating surface extraction. By rendering the contours as distinctly colored polygons and reading back each rendered slice into a segmented volume, we reduce the complex problem of building a surface from planar contours to the much simpler problem of extracting separating surfaces from a classified volume. Our scanline surfacing algorithm robustly handles complex surface topologies such as bifurcations, embedded features, and abutting surfaces.
EDWARD I. FARRELL ET AL.
"... 3D color display of multiplevariable data: Application to semiconductor design ..."
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3D color display of multiplevariable data: Application to semiconductor design
Reconstruction of Surfaces From Planar Contours
, 1994
"... Reconstruction of Surfaces From Planar Contours by David Meyers Chairperson of the Supervisory Committee: Professor Anthony DeRose Department of Computer Science and Engineering This dissertation is concerned with the problem of reconstructing the surfaces of threedimensional objects from a collec ..."
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Reconstruction of Surfaces From Planar Contours by David Meyers Chairperson of the Supervisory Committee: Professor Anthony DeRose Department of Computer Science and Engineering This dissertation is concerned with the problem of reconstructing the surfaces of threedimensional objects from a collection of planar contours representing cross sections through the objects. This problem has important applications in diverse fields, including biomedical research and instruction, solid modeling, geology, archaeology, oceanography and industrial inspection. The problem can be broken into four subproblems, the correspondence problem, the tiling problem, the branching problem, and the surface fitting problem. This dissertation is concerned with improving the quality of automated solutions to the tiling and branching problems. A new method for solving the tiling problem is developed that makes use of multiresolution analysis to improve performance of an optimizing tiling algorithm both in term...
Accurate SamplingBased Algorithms for Surface Extraction and Motion Planning
, 2005
"... Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. Their applications include computeraided design, numericallycontrolled machining, tolerance verification, packing, assembly planning, and dyna ..."
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Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. Their applications include computeraided design, numericallycontrolled machining, tolerance verification, packing, assembly planning, and dynamic simulation. Prior algorithms for solving these problems can be classified into exact and approximate approaches. The exact approaches are difficult to implement and are prone to robustness problems. Current approximate approaches may not solve these problems accurately. Our work aims to bridge this gap between exact and approximate approaches. We present a samplingbased approach to solve these geometric problems. Our approach
MARCHING CUBES: A H IGH RESOLUTION 3D SURFACE CONSTRUCTION ALGORITHM
"... 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 ..."
Abstract
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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.