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115
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 2675 (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.
Volume Rendering
, 1988
"... A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The ..."
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Cited by 446 (2 self)
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A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.
A physically based approach to 2D shape blending
 Computer Graphics
, 1992
"... This paper presents a new afgorithm for smoothly blending between two 2D polygonal shapes. The algorithm is based on a physical model wherein one of the shapes is considered to be constructed of wire, and a solution is found whereby the first shape can be bent and/or stretched into the second shape ..."
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Cited by 153 (3 self)
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This paper presents a new afgorithm for smoothly blending between two 2D polygonal shapes. The algorithm is based on a physical model wherein one of the shapes is considered to be constructed of wire, and a solution is found whereby the first shape can be bent and/or stretched into the second shape with a minimum amount of work. The resulting solution tends to associate regions on the two shapes which look alike. If the two polYgons have m and n vertices respectively, the afgorithm is O(mn). The algorithm avoids local shape inversions in whkh intermediate
Arbitrary topology shape reconstruction from planar cross sections
 Graphical Models and Image Processing
, 1996
"... In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalarvalued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the directio ..."
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Cited by 85 (12 self)
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In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalarvalued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the direction orthogonal to the slices leads to two problems known as the correspondence problem and the tiling problem. A third problem, known as the branching problem, arises because of the structure of the objects being imaged in these applications. Existing reconstruction algorithms typically address only one or two of these problems. In this paper, we approach all three of these problems simultaneously. This is accomplished by imposing a set of three constraints on the reconstructed surface and then deriving precise correspondence and tiling rules from these constraints. The constraints ensure that the regions tiled by these rules obey physical constructs and have a natural appearance. Regions which cannot be tiled by these rules without breaking one or more constraints are tiled with their medial axis (edge Voronoi diagram). Our implementation of the above approach generates triangles of 3D isosurfaces from input which is either a set of contour data or a volume of image slices. Results obtained with synthetic and actual medical data are presented. There are still speci c cases in which our new approach can generate distorted results, but these cases are much less likely to occur than those which cause distortions in other tiling approaches. 2 1
PiecewiseLinear Interpolation between Polygonal Slices
 Computer Vision and Image Understanding
, 1994
"... In this paper we present a new technique for piecewiselinear surface reconstruction from a series of parallel polygonal crosssections. This is an important problem in medical imaging, surface reconstruction from topographic data, and other applications. We reduce the problem, as in most previous wo ..."
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Cited by 75 (12 self)
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In this paper we present a new technique for piecewiselinear surface reconstruction from a series of parallel polygonal crosssections. This is an important problem in medical imaging, surface reconstruction from topographic data, and other applications. We reduce the problem, as in most previous works, to a series of problems of piecewiselinear interpolation between each pair of successive slices. Our algorithm uses a partial curve matching technique for matching parts of the contours, an optimal triangulation of 3D polygons for resolving the unmatched parts, and a minimum spanning tree heuristic for interpolating between non simply connected regions. Unlike previous attempts at solving this problem, our algorithm seems to handle successfully any kind of data. It allows multiple contours in each slice, with any hierarchy of contour nesting, and avoids the introduction of counterintuitive bridges between contours, proposed in some earlier papers to handle interpolation between multi...
Computational methods for reconstructing and unfolding the cerebral cortex
 Cerb. Cortex
"... We describe computational methods for constructing threedimensional models and unfolded, twodimensional maps of the cerebral cortex. These methods consist of four procedures, including (1) sampling of a surface within the cortex, (2) reconstruction of a threedimensional model of that surface, (3 ..."
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Cited by 41 (0 self)
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We describe computational methods for constructing threedimensional models and unfolded, twodimensional maps of the cerebral cortex. These methods consist of four procedures, including (1) sampling of a surface within the cortex, (2) reconstruction of a threedimensional model of that surface, (3) unfolding of the surface to generate a twodimensional cortical map, and (4) visualization of data on the model and the map. These methods produce structurally accurate representations of tile cortex and have practical advantages over previous manual and automated approaches for flattening the cortex. We illustrate the application of these methods to neuroanatomical data obtained from histological sections of cerebral cortex in the macaque monkey. The approach should be equally useful for structural and functional studies in other species, including humans. In many mammalian species, the cerebral cortex occupies a sufficiently large surface area that it must be extensively fold
Geometric Methods for Vessel Visualization and Quantification  A Survey
 IN GEOMETRIC MODELLING FOR SCIENTIFIC VISUALIZATION
, 2002
"... ... This paper surveys several geometric methods to solve basic visualization and quantification problems like centerline computation, boundary detection, projection techniques, and geometric model generation. ..."
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Cited by 35 (1 self)
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... This paper surveys several geometric methods to solve basic visualization and quantification problems like centerline computation, boundary detection, projection techniques, and geometric model generation.
The Interpretation of Fuzziness
 IEEE Transactions on Systems, Man, and Cybernetics
, 1996
"... From laserscanned data to feature human model: a system based on ..."
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Cited by 32 (14 self)
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From laserscanned data to feature human model: a system based on