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13
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.
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 o ..."
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Cited by 93 (13 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...
An Efficient 3D Visualization Technique for Finite Element Models and Other Coarse Volumes
, 1989
"... We have developed a technique that extends existing 3D result visualization methods for use with discretized volumes such as finite element models, where result values are only available at coarsely spaced points throughout the volume. It represents results as smooth isosurfaces within the volume f ..."
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Cited by 20 (0 self)
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We have developed a technique that extends existing 3D result visualization methods for use with discretized volumes such as finite element models, where result values are only available at coarsely spaced points throughout the volume. It represents results as smooth isosurfaces within the volume for one or more result values, using visually continuous, bicubic polynomials. At each of the points where results are available, result gradients are calculated by a finite difference procedure. The result values and result gradients are used to obtain the location of and the tangents to the isosurfaces on lines connecting the result points. Continuous doubly curved surfaces and surface normals are constructed separately between these discrete isosurface points using bicubic polynomials. The isosurfaces are rendered with standard lightsource shading and optional levels of translucency, surrounded by translucent free faces of the structure. The method generates isosurfaces on an elementbyelement basis, without reference at display time to the behavior of neighboring elements. It is intended for high speed displaytime processing of either static or varying isosurface values.
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 7 (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.
Volume Viewing Algorithms: Survey
 IN INTERNATIONAL SPRING SCHOOL ON VISUALIZATION
"... The task of the rendering process is to display the primitives used to represent the 3D volumetric scene onto a 2D screen. Rendering is composed of a viewing process which is the subject of this paper, b and the shading process. The projection process determines, for each screen pixel, which object ..."
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Cited by 2 (0 self)
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The task of the rendering process is to display the primitives used to represent the 3D volumetric scene onto a 2D screen. Rendering is composed of a viewing process which is the subject of this paper, b and the shading process. The projection process determines, for each screen pixel, which objects are seen y the sight ray cast from this pixel into the scene. The viewing algorithm is heavily dependent on the e e display primitives used to represent the volume and whether volume rendering or surface rendering ar mployed. Conventional viewing algorithms and graphics engines can be utilized to display geometric d primitives, typically employing surface rendering. However, when volume primitives are displayed irectly, a special volume viewing algorithm should be employed. This algorithm should capture the conp tents of the voxels on the surface as well as the inside of the volumetric object being visualized. This aper surveys and compares previous work in the field of direct volum...
Classification and Survey of Algorithms for Volume Viewing
 ACM Transactions on graphics
, 1996
"... c s The task of the rendering process is to display the primitives used to represent the 3D volumetri cene onto a 2D screen. Rendering is composed of a viewing process which is the subject of this paper, b and the shading process. The projection process determines, for each screen pixel, which objec ..."
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c s The task of the rendering process is to display the primitives used to represent the 3D volumetri cene onto a 2D screen. Rendering is composed of a viewing process which is the subject of this paper, b and the shading process. The projection process determines, for each screen pixel, which objects are seen y the sight ray cast from this pixel into the scene. The viewing algorithm is heavily dependent on the e e display primitives used to represent the volume and whether volume rendering or surface rendering ar mployed. Conventional viewing algorithms and graphics engines can be utilized to display geometric d primitives, typically employing surface rendering. However, when volume primitives are displayed irectly, a special volume viewing algorithm should be employed. This algorithm should capture the conp tents of the voxels on the surface as well as the inside of the volumetric object being visualized. This aper surveys and compares previous work in the field of direct volume vie...
Shape Recovery Of Volume Data With Deformable BSpline Models
, 1996
"... In many fields today such as radiology, images of interesting structures are obtained. From these images the physician or scientist attempts to make decisions using a variety of techniques. The existing techniques for representing and analyzing particular structures include volume rendering, and sur ..."
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Cited by 1 (0 self)
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In many fields today such as radiology, images of interesting structures are obtained. From these images the physician or scientist attempts to make decisions using a variety of techniques. The existing techniques for representing and analyzing particular structures include volume rendering, and surface renderings from contours, freeform surfaces and geometric primitives. Several of these techniques are inadequate for accurate representations and studying changes in the structure over time. Further, some of these techniques have large data requirements that prevent interactive viewing. It is believed that if the structures of interest can be extracted from the image background, viewed and analyzed in an interactive setting, more accurate decisions can be made. The research described in this dissertation explores a new technique for shape recovery with deformable models using Bspline surfaces. The current literature shows that there have been many successful attempts to create deform...
Rendering of invivo Organs through Laparoscopybased Sampling of BRDF
"... Fig. 1. An image of a human liver captured during a laparoscopy as the input of our method (left). Approximation to organ geometry, the camera path and light position (middle). Global illumination rendering of a liver, based on the BRDF estimated by our method (right). Abstract—While improved visual ..."
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Fig. 1. An image of a human liver captured during a laparoscopy as the input of our method (left). Approximation to organ geometry, the camera path and light position (middle). Global illumination rendering of a liver, based on the BRDF estimated by our method (right). Abstract—While improved visual realism is known to enhance training effectiveness in virtual surgery simulators, the advances on realistic rendering for these simulators is slower than similar simulations for man made scenes. Among the various reasons for this, in vivo data is hard to gather and process. In this paper we propose the analysis of videolaparoscopy data to compute the BRDF of living organs and therefore provide plausible physicsbased rendering of the biological tissue. Based on the interplay between light and organic matter recorded in video images, we propose the definition of a process capable of establishing the BRDF for insidethebody organic surfaces. We present a case study around the liver with a full rendering pipeline, including global illumination simulations. Results show that despite the limited range of motion allowed within the body, the computed BRDF presents a highcoverage of the sampled regions. Keywordsorganic BRDF; highcoverage sampling; surgery simulation; patient specific; laparoscopic surgery; 1 I.
unknown title
"... 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 ..."
Abstract
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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.