多维度数字信号处理：图像、视频与编码详解

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"《多维数字信号处理：图像、视频与编码》是由约翰·W·伍兹（John W. Woods）所著的一本国外研究生教材，着重探讨了二维、多维数字信号在图像和视频处理领域的理论与实践。该书是学术出版社艾塞尔维尔（Elsevier）的Academic Press分社出版，封面设计巧妙，展示了作者的宠物狗海蒂（Heidi）在后院奔跑的简短序列，通过30帧每秒的DV摄像机捕捉，尽管此处展示的帧率较低，主要用于封面艺术展示。书中涵盖了广泛的内容，包括但不限于多维信号的基础概念，如信号的空间和时间特性，以及它们在图像和视频处理中的重要性。读者可以学习到如何分析和处理来自各种传感器的数据，如摄像头、雷达或声纳，以提取有用的信息，如图像特征、运动估计、压缩编码等。此外，书中还会介绍数字信号处理的算法和技术，如傅立叶变换、小波分析、滤波器设计，以及现代编码标准，如JPEG、H.264等在视频压缩中的应用。作者约翰·W·伍兹，作为Rensselaer Polytechnic Institute的教授，将丰富的理论知识与实践经验相结合，使得本书成为理解多维数字信号处理的权威参考书籍。书中强调版权保护，所有复制或传播行为必须得到书面许可，以尊重作者的知识产权。《多维数字信号处理》不仅适合对信号处理感兴趣的研究生和研究人员，也是工程师、计算机科学家和图像/视频处理专业技术人员的实用工具，它提供了深入理解复杂多媒体数据处理流程的宝贵资源。通过阅读这本书，读者能够掌握处理高维信号的策略，应对现代科技发展中日益增长的数据处理需求。"

started out on my book-writing project while teaching from the textbook

Two-

Dimensional Digital

lmage Processing

by Jae Lim, and readers familiar with that

book will certainly see a similarity to mine, especially in the first four chapters.

Thanks Jae. Thanks to colleagues Janusz Konrad and Aggelos Katsaggelos with

Eren

Soyak, for providing some key examples in Chapters

and 12, respectively.

Thanks also to Peisong Chen, Seung-Jong Choi, Allesandro Dutra, Soo-Chul Han,

Shih-Ta Hsiang, Fure-Ching

Jeng, Jaemin Kim, Ju-Hong Lee, Anil Murching, T.

Naveen, Yufeng Shan, Yongjun Wu, and Jie Zou, who through their research,

have helped me to provide many examples all through the book. Special thanks

to former student Ivan Bajic for writing Section 12.2 on robust

subbandlwavelet

video packetizing for wired networks. Additional thanks go out to colleagues

Maya Bystrom and Shiv Kalayanaraman, who provided valuable feedback on

Chapter 12. Thanks also to Tobias Lutz and Christoph Schmid for finding errors

in a prior draft version of the text. If you find any further errors, please bring

them to my attention via

email woods@ecse.rpi.edu. Finally, thanks to my wife

Harriet who has cheerfully put up with my book writing for many years now.

CHAPTER

TWO-DIMENSIONAL SIGNALS AND SYSTEMS

This chapter sets forth the main concepts of two-dimensional

(2-D)

signals and

systems as extensions of the linear systems concepts of

l-D

signals and systems.

We concentrate on the discrete-space case of digital data, including the corre-

sponding

2-D

Fourier transform. We also introduce the continuous-space Fourier

transform to deal with angular rotations and prove the celebrated projection-slice

theorem of computer tomography. Also, later we will find that the central role of

motion compensation in image sequences and video, where motion is often not

an exact number of pixels, makes the interplay of discrete and continuous para-

meters quite important. While this first chapter is all discrete space, Chapter

focuses on sampling of

2-D

continuous-space functions.

A scalar

2-D

signal s(n1, n2) is mathematically a complex bi-sequence, or a map-

ping of the

2-D

integers into the complex plane. Our convention is that the signal s

is defined for all finite values of its integer arguments

nl, nz using zero padding as

necessary. Occasionally we will deal with finite-extent signals, but will clearly say

so. We will adopt the simplified term sequence over the more correct bi-sequence.

A simple example of a

2-D

signal is the impulse 6(nl, nz), defined as follows:

for (nl,nz)=(O,O)

6(n1, nz)

for (n1, nz)

(0, O),

a portion of which is plotted in Figure 1.1.

MATLAB

plot of

2-0

spatial impulse bi-sequence

6(nl. n2)

Section of the unit impulse line

6(nl

n2)

45'

general

2-D

signal can be written as an infinite sum over shifted impulses,

which will be found useful later:

where the summation is taken over all integer pairs

(kl, k2). By the definition of

the

2-D

impulse, for each point (nl, n2), there is exactly one term on the right side

that is nonzero, the term

x(nl, nr) . 1, and hence (1.1-1) is correct. This equality

is called the shifting representation of the signal

Another basic

2-D

signal is the impulse line, e.g., a straight line at

45",

nl=nz

6(nl

n2)

0, else,

as sketched in Figure

1.2.

We can also consider line impulses at 0°, 90°, and

-4.5"

in discrete space, but other angles give "gaps in the line." Toward the end of this

chapter, when we look at continuous-space signals, there the line impulse can be

at any angle.

Apart from impulses, a basic

2-D

signal class is step functions, perhaps the

most common of which is the first-quadrant unit step function

u(n1, n2), defined

CHAPTER

TWO-DIMENSIONAL SIGNALS AND SYSTEMS

This chapter sets forth the main concepts of two-dimensional

(2-D)

signals and

systems as extensions of the linear systems concepts of

l-D

signals and systems.

We concentrate on the discrete-space case of digital data, including the corre-

sponding

2-D

Fourier transform. We also introduce the continuous-space Fourier

transform to deal with angular rotations and prove the celebrated projection-slice

theorem of computer tomography. Also, later we will find that the central role of

motion compensation in image sequences and video, where motion is often not

an exact number of pixels, makes the interplay of discrete and continuous para-

meters quite important. While this first chapter is all discrete space, Chapter

focuses on sampling of

2-D

continuous-space functions.

A scalar

2-D

signal s(n1, n2) is mathematically a complex bi-sequence, or a map-

ping of the

2-D

integers into the complex plane. Our convention is that the signal s

is defined for all finite values of its integer arguments

nl, nz using zero padding as

necessary. Occasionally we will deal with finite-extent signals, but will clearly say

so. We will adopt the simplified term sequence over the more correct bi-sequence.

A simple example of a

2-D

signal is the impulse 6(nl, nz), defined as follows:

for (nl,nz)=(O,O)

6(n1, nz)

for (n1, nz)

(0, O),

a portion of which is plotted in Figure 1.1.

MATLAB

plot of

2-0

spatial impulse bi-sequence

6(nl. n2)

Section of the unit impulse line

6(nl

n2)

45'

general

2-D

signal can be written as an infinite sum over shifted impulses,

which will be found useful later:

where the summation is taken over all integer pairs

(kl, k2). By the definition of

the

2-D

impulse, for each point (nl, n2), there is exactly one term on the right side

that is nonzero, the term

x(nl, nr) . 1, and hence (1.1-1) is correct. This equality

is called the shifting representation of the signal

Another basic

2-D

signal is the impulse line, e.g., a straight line at

45",

nl=nz

6(nl

n2)

0, else,

as sketched in Figure

1.2.

We can also consider line impulses at 0°, 90°, and

-4.5"

in discrete space, but other angles give "gaps in the line." Toward the end of this

chapter, when we look at continuous-space signals, there the line impulse can be

at any angle.

Apart from impulses, a basic

2-D

signal class is step functions, perhaps the

most common of which is the first-quadrant unit step function

u(n1, n2), defined

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