计算机图形学经典论文计算机图形学经典论文
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~ Computer Graphics, Volume 22, Number 4, August 1988
i uu DRill li i •
Volume Rendering
Robert A. Drebin, Loren Carpenter, Pat Hanrahan
Pixar
San Rafael, CA
Abstract
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.
CR Categories: 1.3.3 [Computer Graphics] Computational
Geometry and Object Modeling - Curve, surface, solid, and
object representations. 1.3.5 [Computer Graphics] Three-
Dimensional Graphics and Realism - Color, shading, shadow-
ing and texture; Visible line/surface algorithms.
Additional Keywords and
Phrases: Medical imaging, com-
puted tomography (CT), magnetic resonance imaging (MRI),
non-destructive
evaluation (NDE), scientific visualization,
image processing.
Introduction
Three-dimensional arrays of digital data representing spa-
tial volumes arise in many scientific applications. Computed
tomography (CT) and magnetic resonance (MR) scanners can
be used to create a volume by imaging a series of cross sec-
tions. These techniques have found extensive use in medicine,
and more recently, in non-destructive evaluation (NDE).
Astrophysical, meteorological and geophysical measurements,
and computer simulations using finite element models of stress,
fluid flow, etc., also quite naturally generate a volume data set.
Given the current advances in imaging devices and computer
processing power, more and more applications will generate
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volumetric data in the future. Unfortunately, it is difficult to
see the three-dimensional structure of the interior of volumes
by viewing individual slices. To effectively visualize volumes,
it is important to be able to image them from different
viewpoints, and to shade them in a manner which brings out
surfaces and subtle variations in density or opacity.
Most previous approaches to visualizing volumes capital-
ize on computer graphics techniques that have been developed
to display surfaces by reducing the volume array to only the
boundaries between materials. Two-dimensional contours
from individual slices can be manually traced (Mazziotta,
1976) or automatically extracted (Vannier, 1983) and con-
nected to contours in adjacent slices to form triangle strips
(Keppel,
1975,Fuehs,
1977, Christianson, 1978, Ganapathy,
1982) or higher order surface patches (Sunguruff, 1978).
These techniques have problems with branching structures,
particularly if the distance between serial sections is large rela-
tive to the size of the volume elements or
voxels.
Other surface
techniques output polygons at every voxel. The
cuberille
tech-
nique first sets a threshold representing the transition between
two materials and then creates a binary volume indicating
where a particular material is present. Each solid voxel is then
treated as a small cube and the faces of this cube are output as
small square polygons (Herman, 1979). Adjacent cubes can be
merged to form an oct-tree; this representation compresses the
original voxel array and reduces the subsequent processing
requirements (Meagher, 1982). The
marching cubes
technique
places the sample values at the vertices of the cube and esti-
mates where the surface cuts through the cube (Lorensen,
1987). A variation of this technique, called the
dividing cubes
algorithm, approximates the polygon with points (Cline, 1988).
These techniques are analogous to algorithms used to extract
surfaces from implicit functions (Norton, 1982, Bloomenthal,
1987,Wyvill, 1986), or to produce three-dimensional contour
maps (Wright, 1979).
Several researchers have developed methods which
directly image the volume of data. The
additive reprojection
technique computes an image by averaging the intensities of
voxels along parallel rays from the rotated volume to the image
plane (Harris, 1978,Hoehne, 1987). This has the effect of
simulating an x-ray image. The
source-attenuation reprojec-
tion
technique assigns a source strength and attenuation
coefficient to each voxel which allows for object obscuration
(Jaffey, 1982, Schlusselberg, 1986). Attenuation coefficients
are often referred to as
opacities.
Depth shading algorithms
trace rays through the volume array until they hit a surface and
65
资源评论
zheng4909073652013-06-03好东西，不过需要仔细研究一下~- yj5277049542013-02-27不错，渲染的，受用
- 012huang2013-08-16感谢分享，是要找的文章
ddrmsdos2014-11-09不错，很久之前下载的，现在正需要。
chchpd2011-11-19不错，讲渲染的，文档也清晰
