体积渲染技术：消除锯齿与量化艺术的图像呈现

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本文是一篇关于"体积渲染"的经典论文，发表于1988年的《计算机图形学》(Computer Graphics)第22卷第4期，其影响力在Google学术上超过1500次引用。作者包括来自皮克斯(Pixar)的Robert A. Drebin、Loren Carpenter和Pat Hanrahan，他们探讨了一种处理混合材料的三维体积成像技术。体积渲染是一种关键的计算机图形技术，它允许对包含不同材料的立体结构进行视觉呈现，不仅能够展示材料内部的细节，还能呈现出材料之间的边界色彩。核心思想是通过模拟光线沿路径穿过体积的过程，观察光的吸收情况来生成图像。这种方法强调了消除图像中的锯齿效应（aliasing）和量化误差（quantization），确保渲染结果的精度和真实性。文章的关键算法设计旨在减少这些视觉缺陷，使得在图像计算机上实现高效且无损的渲染成为可能。体积渲染的应用广泛，文中展示了多个领域的实例，如医学影像（如计算机断层扫描CT和磁共振成像MRI）、非破坏性评估（NDE）以及科学研究中的可视化和图像处理。该技术涉及计算机图形学的多个子领域，如： 1. 计算几何与对象建模 - 关注曲线、表面、实体和对象的表示，这是构建三维模型的基础。 2. 三维图形与真实感 - 探讨颜色、阴影、纹理以及可见线和表面算法，这些对于创建逼真的视觉效果至关重要。这篇论文不仅介绍了体积渲染的技术原理，还提供了如何将其应用于实际场景的技术细节和解决方案，对于理解三维图形的计算方法和应用具有重要价值。

~ 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

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

Permission to copy without fee

all

or part of this material is granted

provided that the copies are not made or distributed for direct

commercial advantage, the ACM copyright notice and

the title of the

publication and its date appear, and notice is given that copying is by

permission of the Association for Computing Machinery. To copy

otherwise, or to republish, requires a fee and/or specific permission.

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

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