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36
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 2070 (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.
Polygonization of Implicit Surfaces
, 1988
"... This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track ..."
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Cited by 373 (3 self)
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This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from the octree.
Octrees for faster isosurface generation
 IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2000
"... The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within ..."
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Cited by 274 (3 self)
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The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within the volume. This paper discusses research into the use of the octree hierarchical data structure when the regions of current interest can vary during the application, and are not known a priori. Octrees are well suited to the sixsided cell structure of many volumes. A new spaceefficient design is introduced for octree representations of volumes whose resolutions are not conveniently a power of two; octrees following this design are called branchonneed octrees (BONOs). Also, a caching method is described that essentially passes information between octree neighbors whose visitation times may be quite different, then discards it when its useful life is over. Using the application of octrees to isosurface generation as a focus, space and time comparisons for octreebased versus more traditional "marching" methods are presented.
Optical Models for Direct Volume Rendering
, 1995
"... This tutorial survey paper reviews several different models for light interaction with volume densities of absorbing, glowing, reflecting, and/or scattering material. They are, in order of increasing realism, absorption only, emission only, emission and absorption combined, single scattering of exte ..."
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Cited by 242 (6 self)
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This tutorial survey paper reviews several different models for light interaction with volume densities of absorbing, glowing, reflecting, and/or scattering material. They are, in order of increasing realism, absorption only, emission only, emission and absorption combined, single scattering of external illumination without shadows, single scattering with shadows, and multiple scattering. For each model I give the physical assumptions, describe the applications for which it is appropriate, derive the differential or integral equations for light transport, present calculations methods for solving them, and show output images for a data set representing a cloud. Special attention is given to calculation methods for the multiple scattering model.
Fast Isocontouring for Improved Interactivity
 In Proceedings of 1996 Symposium on Volume Visualization
, 1996
"... We present an isocontouringalgorithm which is nearoptimal for realtime interaction and modification of isovalues in large datasets. A preprocessing step selects a subset S of the cells which are considered as seed cells. Given a particular isovalue, all cells in S which intersect the given isocont ..."
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Cited by 120 (30 self)
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We present an isocontouringalgorithm which is nearoptimal for realtime interaction and modification of isovalues in large datasets. A preprocessing step selects a subset S of the cells which are considered as seed cells. Given a particular isovalue, all cells in S which intersect the given isocontour are extracted using a highperformance range search. Each connected component is swept out using a fast isocontour propagation algorithm. The computational complexity for the repeated action of seed point selection and isocontour propagation is O(logn 0 + k), where n 0 is the size of S and k is the size of the output. In the worst case, n 0 = O(n), where n is the number of cells, while in practical cases, n 0 is smaller than n by one to two orders of magnitude. The general case of seed set construction for a convex complex of cells is described, in addition to a specialized algorithm suitable for meshes of regular topology, including rectilinear and curvilinear meshes. Keyword...
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.
On Reliable Surface Reconstruction from Multiple Range Images
, 1996
"... This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topo ..."
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Cited by 96 (11 self)
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This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topology is recognised as a fundamental step in building 3D models. Model optimization can then be performed to fit the data to the desired accuracy with an efficient representation. A novel integration algorithm is presented that is based on local reconstruction of surface topology using operations in 3D space. A new continuous implicit surface function is proposed which merges the connectivity information inherent in the individual sampled range images. This enables the construction of a single triangulated model using a standard method. The algorithm is guaranteed to reconstruct the correct topology of surface features larger than the range image sampling resolution. Reconstruction of triangu...
Adaptive Marching Cubes
 THE VISUAL COMPUTER
, 1995
"... The Marching Cubes algorithm (MC) is a powerful surface rendering technique which can produce very high quality images. However, it is not suitable for interactive manipulation of the 3D surfaces constructed from high resolution volume data sets in terms of both space and time. In this paper, we pre ..."
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Cited by 30 (0 self)
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The Marching Cubes algorithm (MC) is a powerful surface rendering technique which can produce very high quality images. However, it is not suitable for interactive manipulation of the 3D surfaces constructed from high resolution volume data sets in terms of both space and time. In this paper, we present an adaptive version of MC called Adaptive Marching Cubes (AMC). It significantly reduces the number of triangles representing the surface by adapting the size of the triangles to the shape of the surface. This improves the performance of the manipulation of the 3D surfaces. A typical example with the volume data set of size shows that the number of triangles is reduced by 55%. The quality of images produced by AMC is similar to that of MC. One of the fundamental problems encountered with adaptive algorithms is the crack problem. Cracks may be created between two neighboring cubes processed with different levels of subdivision. We solve the crack problem by patching the cracks using polygons of the same shape as those of the cracks. We propose a simple but complete method by first abstracting 22 basic configurations of arbitrary sized cracks and then reducing the handling of these configurations to a simple rule. It requires only O(n²) working memory for a volume data set.
Topological manipulation of isosurfaces
, 2004
"... In this thesis, I show how to use the topological information encoded in an abstraction called the contour tree to enable interactive manipulation of individual contour surfaces in an isosurface scene, using an interface called the flexible isosurface. Underpinning this interface are several improve ..."
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Cited by 15 (2 self)
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In this thesis, I show how to use the topological information encoded in an abstraction called the contour tree to enable interactive manipulation of individual contour surfaces in an isosurface scene, using an interface called the flexible isosurface. Underpinning this interface are several improvements and extensions to existing work on the contour tree. The first, and most critical, extension, is the path seed: a new method of generating seeds from the contour tree for isosurface extraction. The second extension is to compute geometric information called local spatial measures for contours and store this information in the contour tree. The third extension is to use local spatial measures to simplify both the contour tree and isosurface displays. This simplification can also be used for noise removal. Lastly, this thesis extends work with contour trees from simplicial meshes to arbitrary meshes, interpolants, and tessellation cases. ii Contents ii
On the topology of grid continua
 SPIE VISION GEOMETRY VII
, 1998
"... Onedimensional and twodimensional continua belong to the basic notions of settheoretical topology and represent a subfield of the theory of dimensions developed by P. Urysohn and K. Menger. In this paper basic definitions and properties of grid continua in R² and R³ are summarised. Particularly, s ..."
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Cited by 13 (6 self)
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Onedimensional and twodimensional continua belong to the basic notions of settheoretical topology and represent a subfield of the theory of dimensions developed by P. Urysohn and K. Menger. In this paper basic definitions and properties of grid continua in R² and R³ are summarised. Particularly, simple onedimensional grid continua in R² and in R³, and simple closed twodimensional grid continua in R³ are emphasised. Concepts for measuring the length of onedimensional grid continua, or the surface area of twodimensional grid continua are introduced and discussed.