基于LIC的矢量场纹理生成与局部一维滤波

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本文主要探讨了利用线积分卷积（Line Integral Convolution, LIC）技术在图像处理和科学领域中对矢量场进行可视化的有效方法。LIC方法起源于对矢量方向相关性的深入理解，它旨在通过一种局部且一维的滤波方式，从噪声纹理中提取出与矢量场结构相关的特征。这种方法区别于传统的纹理生成和滤波技术，如[8,9,11,14,15,17,23]中的方法，因为它独立于预定义的几何结构或纹理信息，使得算法适应性强，能够处理任意二维和三维矢量场。 LIC的核心步骤包括：首先，对每个像素点，沿着矢量的正向和反向进行线积分，形成流线轨迹；然后，沿这些流线路径上的每个像素点，应用一个卷积核对输入噪声纹理进行卷积操作；最后，这个卷积的结果就构成了输出的纹理，其像素值反映了流线上矢量场的强度和方向信息。这种算法设计使得并行实现成为可能，从而提高了效率，特别适合大规模数据处理。值得注意的是，LIC的曲线滤波特性使其在处理复杂精细的矢量场时，能够保持细节清晰。当与诸如周期运动滤波等其他渲染和图像处理技术结合时，可以产生丰富信息且视觉冲击力强的效果。此外，LIC技术还能够用于创造新颖的特效，拓宽了其在艺术和视觉表达中的应用范围。本文的贡献在于提供了一种创新的矢量场成像技术，它凭借其高效性和灵活性，在计算机图形学的多个类别中，如图像生成（I.3.3）和三维图形的真实感（I.3.7）方面展现了其独特价值。通过LIC，研究人员和艺术家们能够更加直观地理解和展示复杂的矢量场，推动了相关领域的科研进展和艺术创新。

ABSTRACT

Imaging vector ﬁelds has applications in science, art, image pro-

cessing and special effects. An effective new approach is to use

linear and curvilinear ﬁltering techniques to locally blur textures

along a vector ﬁeld. This approach builds on several previous tex-

ture generation and ﬁltering techniques[8, 9, 11, 14, 15, 17, 23]. It

is, however, unique because it is local, one-dimensional and inde-

pendent of any predeﬁned geometry or texture. The technique is

general and capable of imaging arbitrary two- and three-dimen-

sional vector ﬁelds. The local one-dimensional nature of the algo-

rithm lends itself to highly parallel and efﬁcient implementations.

Furthermore, the curvilinear ﬁlter is capable of rendering detail on

very intricate vector ﬁelds. Combining this technique with other

rendering and image processing techniques — like periodic motion

ﬁltering — results in richly informative and striking images. The

technique can also produce novel special effects.

CR categories and subject descriptors: I.3.3 [Computer

Graphics]: Picture/Image generation; I.3.7 [Computer Graphics]:

Three-Dimensional Graphics and Realism; I.4.3 [Image Process-

ing]: Enhancement.

Keywords: convolution, ﬁltering, rendering, visualization, tex-

ture synthesis, ﬂow ﬁelds, special effects, periodic motion ﬁltering.

1. INTRODUCTION

Upon ﬁrst inspection, imaging vector ﬁelds appears to have lim-

ited application — conﬁned primarily to scientiﬁc visualization.

However, much of the form and shape in our environment is a

function of not only image intensity and color, but also of direc-

tional information such as edges. Painters, sculptors, photogra-

phers, image processors[16] and computer graphics researchers[9]

have recognized the importance of direction in the process of

image creation and form. Hence, algorithms that can image such

directional information have wide application across both scien-

tiﬁc and artistic domains.

Such algorithms should possess a number of desirable and

sometimes conﬂicting properties including: accuracy, locality of

calculation, simplicity, controllability and generality. Line Integral

Convolution (LIC) is a new technique that possesses many of these

properties. Its generality allows for the introduction of a com-

pletely new family of periodic motion ﬁlters which have wide

application (see section 4.1). It represents a conﬂuence of signal

and image processing and a variety of previous work done in com-

puter graphics and scientiﬁc visualization.

2. BACKGROUND

There are currently few techniques which image vector ﬁelds in

a general manner. These techniques can be quite effective for visu-

alizing vector data. However, they break down when operating on

very dense ﬁelds and do not generalize to other applications. In

particular, large vector ﬁelds (512x512 or greater) strain existing

algorithms.

Most vector visualization algorithms use spatial resolution to

represent the vector ﬁeld. These include sampling the ﬁeld, such as

with stream lines[12] or particle traces, and using icons[19] at

every vector ﬁeld coordinate. Stream lines and particle tracing

techniques depend critically on the placement of the “streamers” or

the particle sources. Depending on their placement, eddies or cur-

rents in the data ﬁeld can be missed. Icons, on the other hand, do

not miss data, but use up a considerable amount of spatial resolu-

tion limiting their usefulness to small vector ﬁelds.

Another general approach is to generate textures via a vector

ﬁeld. Van Wijk’s spot noise algorithm[23] uses a vector ﬁeld to

control the generation of bandlimited noise. The time complexity

of the two types of implementation techniques presented by Van

Wijk are relatively high. Furthermore the technique, by deﬁnition,

depends heavily on the form of the texture (spot noise) itself. Spe-

ciﬁcally, it does not easily generalize to other forms of textures that

might be better suited to a particular class of vector data (such as

ﬂuid ﬂow versus electromagnetic).

Reaction diffusion techniques[20, 24] also provide an avenue

for visualizing vector ﬁelds since the controlling differential equa-

tions are inherently vector in nature. It is possible to map vector

data onto these differential equations to come up with a vector

visualization technique. Here too however, the time complexity of

these algorithms limit their general usefulness.

Three-dimensional vector ﬁelds can be visualized by three-

dimensional texture generation techniques such as texels and

hypertextures described in [11, 15]. Both techniques take a texture

on a geometrically deﬁned surface and project the texture out some

distance from the surface. By deﬁnition these techniques are bound

to the surface and do not compute an image for the entire ﬁeld as is

done by Van Wijk[23]. This is limiting in that it requires a priori

knowledge to place the surface. Like particle streams and vector

streamers these visualization techniques are critically dependent

on the placement of the sampling surface.

The technique presented by Haeberli[9] for algorithmicly gener-

ating “paintings” via vector-like brush strokes can also be thought

of as a vector visualization technique. Crawﬁs and Max[5]

Imaging Vector Fields Using Line Integral Convolution

Brian Cabral

Leith (Casey) Leedom*

Lawrence Livermore National Laboratory

* Authors’ current e-mail addresses are: cabral@llnl.gov and

casey@gauss.llnl.gov.

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