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33
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.
Display of Surfaces from Volume Data
, 1988
"... The application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is explored. Fitting of geometric primitives to the sampled data is not required. Images are formed by directly shading each sample and projecting it onto the picture p ..."
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Cited by 724 (10 self)
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The application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is explored. Fitting of geometric primitives to the sampled data is not required. Images are formed by directly shading each sample and projecting it onto the picture plane. Surface shading calculations are performed at every voxel with local gradient vectors serving as surface normals. In a separate step, surface classification operators are applied to obtain a partial opacity for every voxel. Operators that detect isovalue contour surfaces and region boundary surfaces are presented. Independence of shading and classification calculations insures an undistorted visualization of 3D shape. Nonbinary classification operators insure that small or poorly defined features are not lost. The resulting colors and opacities are composited from back to front along viewing rays to form an image. The technique is simple and fast, yet displays surfaces exhibiting smooth silhouettes and few other aliasing artifacts. The use of selective blurring and supersampling to further improve image quality is also described. Examples from two applications are given: molecular graphics and medical imaging.
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.
Gradient Estimation in Volume Data using 4D Linear Regression
, 2000
"... . In this paper a new gradient estimation method is presented which is based on linear regression. Previous contextual shading techniques try to fit an approximate function to a set of surface points in the neighborhood of a given voxel. Therefore, a system of linear equations has to be solved u ..."
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Cited by 32 (4 self)
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. In this paper a new gradient estimation method is presented which is based on linear regression. Previous contextual shading techniques try to fit an approximate function to a set of surface points in the neighborhood of a given voxel. Therefore, a system of linear equations has to be solved using the computationally expensive Gaussian elimination. In contrast, our method approximates the density function itself in a local neighborhood with a 3D regression hyperplane. This approach also leads to a system of linear equations but we will show that it can be solved with an efficient convolution. Our method provides at each voxel location the normal vector and the translation of the regression hyperplane which are considered as a gradient and a filtered density value respectively. Therefore, this technique can be used for surface smoothing and gradient estimation at the same time. 1 Introduction In direct volume rendering the quality of the generated image is strongly influ...
Volume rendering: display of surfaces from volume data
 Computer Graphics and Applications
, 1988
"... In this article we will explore the application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions. It is not necessary to fit geometric primitives to the sampled data. Images are formed by directly shading each sample and projecting i ..."
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Cited by 28 (0 self)
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In this article we will explore the application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions. It is not necessary to fit geometric primitives to the sampled data. Images are formed by directly shading each sample and projecting it onto the picture plane. Surfaceshading calculations are performed at every voxel with local gradient vectors serving as surface normals. In a separate step, surface classification operators are applied to compute a partial opacity for every voxel. We will look at operators that detect isovalue contour surfaces and region boundary surfaces. Independence of shading and classification calculations ensure an undistorted visualization of 3D shape. Nonbinary
Efficient FeedForward Volume Rendering Techniques for Vector and Parallel Processors
, 1993
"... Rendering volumes represented as a 3D grid of voxels requires an overwhelming amount of processing power. In this paper we investigate efficient techniques for rendering semitransparent volumes on vector and parallel processors. Parallelism inherent in a regular grid is obtained by decomposing the ..."
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Cited by 24 (12 self)
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Rendering volumes represented as a 3D grid of voxels requires an overwhelming amount of processing power. In this paper we investigate efficient techniques for rendering semitransparent volumes on vector and parallel processors. Parallelism inherent in a regular grid is obtained by decomposing the volume into geometric primitives called beams, slices and slabs of voxels. By using the adjacency properties of voxels in beams and slices, efficient incremental transformation schemes are developed. The slab decomposition of the volume allows the implementation of an efficient parallel feedforward renderer which includes the splatting technique for image reconstruction and a backtofront method for creating images. We report the implementation of this feedforward volume renderer on a hierarchical shared memory machine with individual pipelined processors. 1: Introduction Representation by spatialoccupancy enumeration methods allows a simple yet versatile method for the generation and ...
Cube3: A RealTime Architecture for HighResolution Volume Visualization
 IN PROCEEDINGS OF THE 8TH EUROGRAPHICS WORKSHOP ON GRAPHICS HARDWARE '93
, 1994
"... This paper describes a highperformance specialpurpose system, Cube3, for displaying and manipulating highresolution volumetric datasets in realtime. A primary goal of Cube3 is to render 512³, 16bit per voxel, datasets at about 30 frames per second. Cube3 implements a raycasting algorithm in ..."
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Cited by 23 (10 self)
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This paper describes a highperformance specialpurpose system, Cube3, for displaying and manipulating highresolution volumetric datasets in realtime. A primary goal of Cube3 is to render 512³, 16bit per voxel, datasets at about 30 frames per second. Cube3 implements a raycasting algorithm in a highlyparallel and pipelined architecture, using a 3D skewed volume memory, a modular fast bus, 2D skewed buffers, 3D interpolation and shading units, and a ray projection cone. Cube3 will allow users to interactively visualize and investigate in realtime static (3D) and dynamic (4D) highresolution volumetric datasets.
Normal Estimation in 3D Discrete Space
, 1992
"... Stony Brook, New York 117944400 hreedimensional voxelbased objects are inherently discrete and do not l f maintain any notion of a continuous surface or normal values, which are crucia or the simulation of light behavior. Thus in volume rendering, the normal s vector of the displayed surfaces mus ..."
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Cited by 11 (2 self)
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Stony Brook, New York 117944400 hreedimensional voxelbased objects are inherently discrete and do not l f maintain any notion of a continuous surface or normal values, which are crucia or the simulation of light behavior. Thus in volume rendering, the normal s vector of the displayed surfaces must be estimated prior to rendering. We urvey several methods for normal estimation and analyze their performance. s One unique method, the context sensitive approach, employs segmentation and egmentbounded operators that are based on object and slope discontinuities in c o order to achieve high fidelity normal estimation for rendering volumetri bjects. Key Words: discrete shading, volume rendering, filtering, segmentation, volume visualization. 2T 1. INTRODUCTION he use of volume representation in graphics and imaging has seen great , m progress in the last decade. The availability of multidimensional scanners ainly in the biomedical fields, coupled with enhanced computing power for t ...
Sheared Interpolation and Gradient Estimation for RealTime Volume Rendering
 IN PROCEEDINGS OF THE 9TH EUROGRAPHICS WORKSHOP ON GRAPHICS HARDWARE '94 [EUR94
, 1994
"... In this paper we present a technique for the interactive control and display of static and dynamic 3D datasets. We describe novel ways of trilinear interpolation and gradient estimation for a realtime volume rendering system, using coherency between rays. We show simulation results that compare th ..."
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Cited by 10 (7 self)
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In this paper we present a technique for the interactive control and display of static and dynamic 3D datasets. We describe novel ways of trilinear interpolation and gradient estimation for a realtime volume rendering system, using coherency between rays. We show simulation results that compare the proposed methods to traditional algorithms and present them in the context of Cube3, a specialpurpose architecturecapable of rendering 512³ 16bit per voxel datasets at over 20 frames per second.
A hardware architecture for video rate smooth shading of Volume data
 in Eurographics Hardware Workshop
, 1994
"... This paper describes a new architecture for generating smoothly shaded two dimensional images of volume data. This architecture fits into an image synthesis pipeline and uses only simple arithmetic operations and a lookup table to generate two dimensional images in real time. The shading algorithm ..."
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Cited by 10 (4 self)
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This paper describes a new architecture for generating smoothly shaded two dimensional images of volume data. This architecture fits into an image synthesis pipeline and uses only simple arithmetic operations and a lookup table to generate two dimensional images in real time. The shading algorithm is an extension of the greylevel gradient algorithm for shading volume data. The shading technique produces smooth images for voxelized geometrical data and sampled volume data. Image synthesis from volume data in real time is an important technique in visualization and graphics systems. Additional Key Words and Phrases: realtime shading, volume visualization, graphics hardware, image generation 1 Introduction The generation of two dimensional (2D) images from volumetric data sets containing either measured data or voxelized geometrical primitives is creating a new alternative for image synthesis techniques [8]. The ability to synthesize 2D images in real time, that is at video presentat...