[其它] Multiscale Vector Volumes

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发表于 2011-12-28 11:20:20 |只看该作者 |倒序浏览

Multiscale Vector Volumes

Lvdi Wang Yizhou Yu Kun Zhou Baining Guo

Tsinghua University University of Illinois at Urbana-Champaign Zhejiang University Microsoft Research Asia

The University of Hong Kong Tsinghua University

Abstract

We introduce multiscale vector volumes, a compact vector repre-

sentation for volumetric objects with complex internal structures

spanning a wide range of scales. With our representation, an object

is decomposed into components and each component is modeled as

an SDF tree, a novel data structure that uses multiple signed dis-

tance functions (SDFs) to further decompose the volumetric com-

ponent into regions. Multiple signed distance functions collectively

can represent non-manifold surfaces and deliver a powerful vector

representation for complex volumetric features. We use multiscale

embedding to combine object components at different scales into

one complex volumetric object. As a result, regions with dramat-

ically different scales and complexities can co-exist in an object.

To facilitate volumetric object authoring and editing, we have also

developed a scripting language and a GUI prototype. With the help

of a recursively deﬁned spatial indexing structure, our vector repre-

sentation supports fast random access, and arbitrary cross sections

of complex volumetric objects can be visualized in real time.

Keywords: volumetric modeling, multiscale representations

1 Introduction

Most natural organisms and materials, such as the human body,

fruits and sedimentary rocks, have rich and complex volumetric

structures, patterns and color variations. Constructing high-quality

digital models for such natural organisms and materials is of vital

importance because they exist everywhere, and literally everything

we see is either a living being, a natural material or something made

from these two. Since volumetric models allow us to visualize the

internal structure of an object, they are valuable graphical contents

that can be used in biomedical research, scientiﬁc visualization as

well as educational and training activities.

Nevertheless, constructing high-quality digital models of natural or-

ganisms and materials with complex volumetric properties is an ex-

tremely challenging task. First, how can we compactly represent

volumetric structures and patterns spanning a wide range of scales?

Taking the human body as an example, it has a skeleton, organs

and tissues at the macroscopic scale, cellular structures and neu-

ronal ﬁbers at an intermediate scale as well as proteins and genes at

the molecular scale. Second, how can we represent high-frequency

features in a resolution-independent way? Physical and appearance

properties (e.g. color) change abruptly across different materials or

volumetric components. Such discontinuities typically form thin

surface sheets, which may join or split following an irregular pat-

tern, giving rise to a non-manifold structure (Figure 2). To prevent

visual artifacts when zooming into these high-frequency structures,

a resolution-independent vector representation is desired. A volu-

metric object representation not only needs to depict complex mul-

tiscale structures, but also should be easy to use, which means it

should be easy to create novel objects and easy to view existing ob-

jects in this representation. Thus, a volumetric object representation

should have the following desired properties:

Expressiveness: It should be able to represent volumetric

objects with spatial structures spanning a wide range of

scales and including complex non-manifold features. High-

frequency features should remain sharp during magniﬁcation.

Ease of editing: It should be easy and intuitive to create novel

objects and edit existing ones using this representation.

Random access: To be able to provide a timely response to

user interactions, fast visualization is required, which further

demands efﬁcient random access to the volumetric content.

Compactness: Given the limited memory on current graphics

cards, the representation should be as compact as possible.

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