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39
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 2085 (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.
Modeling the Mighty Maple
"... A method is presented for representing botanical trees, given threedimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A freeform surface connects branching limbs. "Blobby" techniques are used to model the tree tru ..."
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Cited by 88 (1 self)
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A method is presented for representing botanical trees, given threedimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A freeform surface connects branching limbs. "Blobby" techniques are used to model the tree trunk as a series of noncircular cross sections. Bark is simulated with a bump map digitized from real world bark; leaves are textures mapped onto simple surfaces.
Function Representation of Solids Reconstructed from Scattered Surface Points and Contours
 Computer Graphics Forum
, 1995
"... This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of sca ..."
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Cited by 83 (11 self)
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This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from crosssections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces. 1. Introduction There are a number of applied problems that require interpolation or smoothing of large arrays of randomly measured points of a surface. The main sources of such data are physical measurements taken by scanning an object from different viewing directions. Scattered points arise also in mathematical simulation, for examp...
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 68 (10 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 65 (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...
Filling Gaps in the Boundary of a Polyhedron
 Computer Aided Geometric Design
, 1993
"... In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. These defects, usually caused by problems in CAD software, consist of small gaps bounded by edges that are incident to only one polyhedron face. The algorithm uses a partial curve matching t ..."
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Cited by 38 (4 self)
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In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. These defects, usually caused by problems in CAD software, consist of small gaps bounded by edges that are incident to only one polyhedron face. The algorithm uses a partial curve matching technique for matching parts of the defects, and an optimal triangulation of 3D polygons for resolving the unmatched parts. It is also shown that finding a consistent set of partial curve matches with maximum score, a subproblem which is related to our repairing process, is NPHard. Experimental results on several polyhedra are presented. Keywords: CAD, polyhedra, gap filling, curve matching, geometric hashing, triangulation. 1 Introduction The problem studied in this paper is the detection and repair of "gaps" in the boundary of a polyhedron. This problem usually appears in polyhedral approximations of CAD objects, whose boundaries are described using curved entities of higher leve...
Interactive Maximum Projection Volume Rendering
 In Proceedings Visualization '95
, 1995
"... 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 ren ..."
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Cited by 28 (1 self)
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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...
A Review of Medical Image Registration
 Interactive imageguided neurosurgery
, 1993
"... Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergist ..."
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Cited by 24 (0 self)
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Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergistic (i.e. the combination of information provides useful extra information). For example, Xray computed tomography (CT) and magnetic resonance (MR) imaging exquisitely demonstrate brain anatomy but provide little functional information. Positron emission tomography (PET) and single photon emission computed tomography (SPECT) scans display aspects of brain function and allow metabolic measurements but poorly delineate anatomy. Furthermore, CT and MR images describe complementary morphologic features. For example, bone and calcifications are best seen on CT images, while softtissue structures are better differentiated by MR imaging. Clinical diagnosis and therapy planning and evaluatio
Improved Constructions of Delaunay Based Contour Surfaces
 Proc. ACM Sympos. Solid Modeling and Applications 99
, 1999
"... Surface reconstruction from parallel slices is a well researched problem in solid modeling and computer graphics. The importance of the problem stems from its wide applicability such as in medical imaging for organ modeling, and in topography for terrain modeling. As pointed out in earlier literatur ..."
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Cited by 14 (0 self)
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Surface reconstruction from parallel slices is a well researched problem in solid modeling and computer graphics. The importance of the problem stems from its wide applicability such as in medical imaging for organ modeling, and in topography for terrain modeling. As pointed out in earlier literature, the three major issues for such surface reconstruction are tiling problem, correspondence problem and branching problem. Many of the earlier approaches concentrated primarily on the tiling problem, where the main concern is to generate a non selfintersecting surface connecting two contours with certain optimization. Lately, a few approaches take a more wholistic view to address all of them. In this paper we revisit one such method based on Delaunay triangulations. This method seems more promising and appropriate in handling correspondence and branching problem due to the inherent ability of Delaunay triangulations to capture proximity. Further, a non selfintersecting tiling is automatic...