优化的Shear-Warp快速体渲染技术

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"Fast Volume Rendering 使用Shear-Warp算法进行快速体绘制" 在计算机图形学领域，体绘制（Volume Rendering）是一种用于可视化三维数据集的技术，它能够呈现数据内部的结构和细节。本资源主要关注的是“Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation”，这是一种提高体绘制效率的算法，由Philippe Lacroute和Marc Levoy于1994年在斯坦福大学的研究中提出。体绘制通常涉及到对大量三维数据（如医学扫描、流体动力学模拟或天文学图像）的处理，以生成二维的透视视图。这个过程通常包括多个步骤，包括数据采样、光照计算和颜色映射等。而Shear-Warp算法则通过将视角变换分解为三个部分来优化这一流程：三维切变（3D shear）、平行投影（projection）以及二维扭曲（2D warp）。 Shear-Warp算法的独特之处在于它能保持体积数据切片与中间扭曲图像的像素行对齐，这意味着数据中的连续体（voxel rows）与中间图像的像素行一致。这一特性使得算法可以利用空间一致性，即相邻的体素在视觉上通常是连续的，从而提高渲染速度。在实现这一算法时，研究者们采用了基于运行长度编码（Run-Length Encoding）的空间数据结构。运行长度编码是一种压缩技术，特别适合于处理具有长串连续相同值的数据。在体绘制中，这种方法可以减少处理大量重复或相似数据时的计算量，进一步提升渲染效率。通过同步遍历体积数据和中间图像的扫描线算法，可以有效地利用这种空间一致性，减少不必要的计算，并保持较高的图像质量。 Shear-Warp算法通过巧妙地分解视角变换，结合高效的数据结构和同步遍历策略，实现了快速的体绘制。这种算法对于需要实时或高分辨率体渲染的应用，如医学成像、科学可视化和虚拟现实等领域，具有显著的优势。由于其兼顾速度和质量，该算法在当时的计算机图形学领域是一个重要的进步，至今仍对相关研究和应用产生着深远的影响。

COMPUTER GRAPHICS Proceedings, Annual Conference Series, 1994

Fast Volume Rendering Using a Shear-Warp Factorization

of the Viewing Transformation

Philippe Lacroute

Computer Systems Laboratory

Stanford University

Marc Levoy

Computer Science Department

Stanford University

Abstract

Several existing volume rendering algorithms operate by factor-

ing the viewing transformation into a 3D shear parallel to the data

slices, a projection to form an intermediate but distorted image,

and a 2D warp to form an undistorted final image. We extend

this class of algorithms in three ways. First, we describe a new

object-order rendering algorithm based on the factorization that is

significantly faster than published algorithms with minimal loss

of image quality. Shear-warp factorizations have the property that

rows of voxels in the volume are aligned with rows of pixels in the

intermediate image. We use this fact to construct a scanline-based

algorithm that traverses the volume and the intermediate image in

synchrony, taking advantage of the spatial coherence present in

both. We use spatial data structures based on run-length encoding

for both the volume and the intermediate image. Our implemen-

tation running on an SGI Indigo workstation renders a 2563 voxel

medical data set in one second. Our second extension is a shear-

warp factorization for perspective viewing transformations, and

we show how our rendering algorithm can support this extension.

Third, we introduce a data structure for encoding spatial coherence

in unclassified volumes (i.e. scalar fields with no precomputed

opacity). When combined with our shear-warp rendering algo-

rithm this data structure allows us to classify and render a 2563

voxel volume in three seconds. The method extends to support

mixed volumes and geometry and is parallelizable.

CR Categories:

1.3.7 [Computer Graphics]: Three-Dimensional

Graphics and Realism; 1.3.3 [Computer Graphics]: Picture/Image

Generation--Display Algorithms.

Additional Keywords:

Volume rendering, Coherence, Scientific

visualization, Medical imaging.

1 Introduction

Volume rendering is a flexible technique for visualizing scalar

fields with widespread applicability in medical imaging and sci-

entific visualization, but its use has been limited because it is

Authors' Address: Center for Integrated Systems, Stanford University,

Stanford, CA 94305-4070

E-mail: lacroute@weevil.stanford.edu, levoy@cs.stanford.edu

Word Wide Web: http://www-graphics.stanford.edu/

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.

computationally expensive. Interactive rendering rates have been

reported using large parallel processors [17] [19] and using algo-

rithms that trade off image quality for speed [10] [8], but high-

quality images take tens of seconds or minutes to generate on

current workstations. In this paper we present a new algorithm

which achieves near-interactive rendering rates on a workstation

without significantly sacrificing quality.

Many researchers have proposed methods that reduce render-

ing cost without affecting image quality by exploiting coherence

in the data set. These methods rely on spatial data structures that

encode the presence or absence of high-opacity voxels so that

computation can be omitted in transparent regions of the volume.

These data structures are built during a preprocessing step from a

classified

volume: a volume to which an opacity transfer function

has been applied. Such spatial data structures include octrees and

pyramids [13] [12] [8] [3], k-d trees [18] and distance transforms

[23]. Although this type of optimization is data-dependent, re-

searchers have reported that in typical classified volumes 70-95%

of the voxels are transparent [12] [18].

Algorithms that use spatial data structures can be divided into

two categories according to the order in which the data structures

are traversed: image-order or object-order. Image-order algo-

rithms operate by casting rays from each image pixel and pro-

cessing the voxels along each ray [9]. This processing order has

the disadvantage that the spatial data structure must be traversed

once for every ray, resulting in redundant computation (e.g. mul-

tiple descents of an octree). In contrast, object-order algorithms

operate by splatting voxels into the image while streaming through

the volume data in storage order [20] [8]. However, this process-

ing order makes it difficult to implement early ray termination, an

effective optimization in ray-casting algorithms [12].

In this paper we describe a new algorithm which combines

the advantages of image-order and object-order algorithms. The

method is based on a factorization of the viewing matrix into a 3D

shear parallel to the slices of the volume data, a projection to form

a distorted intermediate image, and a 2D warp to produce the final

image. Shear-warp factorizations are not new. They have been

used to simplify data communication patterns in volume rendering

algorithms for SIMD parallel processors [1] [17] and to simplify

the generation of paths through a volume in a serial image-order

algorithm [22]. The advantage of shear-warp factorizations is that

scanlines of tlae volume data and scanlines of the intermediate im-

age are always aligned. In previous efforts this property has been

used to develop SIMD volume rendering algorithms. We exploit

the property for a different reason: it allows efficient, synchro-

nized access to data structures that separately encode coherence

in the volume and the image.

The factorization also makes efficient, high-quality resampling

possible in an object-order algorithm. In our algorithm the re-

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