ISO/IEC JTC 1/SC 29/WG 1 N 2412
Date: 2005-12-03
ISO/IEC JTC 1/SC 29/WG 1
(ITU-T SG 16)
Coding of Still Pictures
JBIG JPEG
Joint Bi-level Image Joint Photographic
Experts Group Experts Group
TITLE: The JPEG-2000 Still Image Compression Standard
(Last Revised: 2005-12-03)
SOURCE: Michael D. Adams
Assistant Professor
Dept. of Electrical and Computer Engineering
University of Victoria
P. O. Box 3055 STN CSC, Victoria, BC, V8W 3P6, CANADA
E-mail:
mdadams@ece.uvic.ca
Web:
www.ece.uvic.ca/˜mdadams
PROJECT: JPEG 2000
STATUS:
REQUESTED ACTION: None
DISTRIBUTION: Public
Contact:
ISO/IEC JTC 1/SC 29/WG 1 Convener—Dr. Daniel T. Lee
Yahoo! Asia, Sunning Plaza, Rm 2802, 10 Hysan Avenue, Causeway Bay, Hong Kong
Yahoo! Inc, 701 First Avenue, Sunnyvale, California 94089, USA
Tel: +1 408 349 7051/+852 2882 3898, Fax: +1 253 830 0372, E-mail:
dlee@yahoo-inc.com
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Copyright
c
2002–2005 Michael D. Adams 1
The JPEG-2000 Still Image Compression Standard
∗
(Last Revised: 2005-12-03)
Michael D. Adams
Dept. of Electrical and Computer Engineering, University of Victoria
P. O. Box 3055 STN CSC, Victoria, BC, V8W 3P6, CANADA
E-mail:
mdadams@ece.uvic.ca
Web:
www.ece.uvic.ca/˜mdadams
Abstract—JPEG 2000, a new international standard for still image com-
pression, is discussed at length. A high-level introduction to the JPEG-2000
standard is given, followed by a detailed technical description of the JPEG-
2000 Part-1 codec.
Keywords—JPEG 2000, still image compression/coding, standards.
I. INTRODUCTION
D
IGITAL IMAGERY is pervasive in our world today. Con-
sequently, standards for the efficient representation and
interchange of digital images are essential. To date, some of
the most successful still image compression standards have re-
sulted from the ongoing work of the Joint Photographic Experts
Group (JPEG). This group operates under the auspices of Joint
Technical Committee 1, Subcommittee 29, Working Group 1
(JTC 1/SC 29/WG 1), a collaborative effort between the In-
ternational Organization for Standardization (ISO) and Interna-
tional Telecommunication Union Standardization Sector (ITU-
T). Both the JPEG [1–3] and JPEG-LS [4–6] standards were
born from the work of the JPEG committee. For the last few
years, the JPEG committee has been working towards the estab-
lishment of a new standard known as JPEG 2000 (i.e., ISO/IEC
15444). The fruits of these labors are now coming to bear, as
several parts of this multipart standard have recently been rati-
fied including JPEG-2000 Part 1 (i.e., ISO/IEC 15444-1 [7]).
In this paper, we provide a detailed technical description of
the JPEG-2000 Part-1 codec, in addition to a brief overview of
the JPEG-2000 standard. This exposition is intended to serve as
a reader-friendly starting point for those interested in learning
about JPEG 2000. Although many details are included in our
presentation, some details are necessarily omitted. The reader
should, therefore, refer to the standard [7] before attempting
an implementation. The JPEG-2000 codec realization in the
JasPer software [8–10] (developed by the author of this paper)
may also serve as a practical guide for implementors. (See Ap-
pendix A for more information about JasPer.) The reader may
also find [11–13] to be useful sources of information on the
JPEG-2000 standard.
The remainder of this paper is structured as follows. Sec-
tion II begins with a overview of the JPEG-2000 standard. This
is followed, in Section III, by a detailed description of the JPEG-
2000 Part-1 codec. Finally, we conclude with some closing re-
∗
This document is a revised version of the JPEG-2000 tutorial that I wrote
which appeared in the JPEG working group document WG1N1734. The original
tutorial contained numerous inaccuracies, some of which were introduced by
changes in the evolving draft standard while others were due to typographical
errors. Hopefully, most of these inaccuracies have been corrected in this revised
document. In any case, this document will probably continue to evolve over
time. Subsequent versions of this document will be made available from my
home page (the URL for which is provided with my contact information).
marks in Section IV. Throughout our presentation, a basic un-
derstanding of image coding is assumed.
II. JPEG 2000
The JPEG-2000 standard supports lossy and lossless com-
pression of single-component (e.g., grayscale) and multi-
component (e.g., color) imagery. In addition to this basic com-
pression functionality, however, numerous other features are
provided, including: 1) progressive recovery of an image by fi-
delity or resolution; 2) region of interest coding, whereby differ-
ent parts of an image can be coded with differing fidelity; 3) ran-
dom access to particular regions of an image without needing to
decode the entire code stream; 4) a flexible file format with pro-
visions for specifying opacity information and image sequences;
and 5) good error resilience. Due to its excellent coding per-
formance and many attractive features, JPEG 2000 has a very
large potential application base. Some possible application ar-
eas include: image archiving, Internet, web browsing, document
imaging, digital photography, medical imaging, remote sensing,
and desktop publishing.
A. Why JPEG 2000?
Work on the JPEG-2000 standard commenced with an initial
call for contributions [14] in March 1997. The purpose of having
a new standard was twofold. First, it would address a number
of weaknesses in the existing JPEG standard. Second, it would
provide a number of new features not available in the JPEG stan-
dard. The preceding points led to several key objectives for the
new standard, namely that it should: 1) allow efficient lossy and
lossless compression within a single unified coding framework,
2) provide superior image quality, both objectively and subjec-
tively, at low bit rates, 3) support additional features such as rate
and resolution scalability, region of interest coding, and a more
flexible file format, 4) avoid excessive computational and mem-
ory complexity. Undoubtedly, much of the success of the orig-
inal JPEG standard can be attributed to its royalty-free nature.
Consequently, considerable effort has been made to ensure that
a minimally-compliant JPEG-2000 codec can be implemented
free of royalties
1
.
B. Structure of the Standard
The JPEG-2000 standard is comprised of numerous parts,
with the parts listed in Table I being defined at the time of this
writing. For convenience, we will refer to the codec defined in
1
Whether these efforts ultimately prove successful remains to be seen, how-
ever, as there are still some unresolved intellectual property issues at the time of
this writing.
2 Copyright
c
2002–2005 Michael D. Adams
Part 1 (i.e., [7]) of the standard as the baseline codec. The base-
line codec is simply the core (or minimal functionality) JPEG-
2000 coding system. Part 2 (i.e., [15]) describes extensions to
the baseline codec that are useful for certain “niche” applica-
tions, while Part 3 (i.e., [16]) defines extensions for intraframe-
style video compression. Part 5 (i.e., [17]) provides two refer-
ence software implementations of the Part-1 codec, and Part 4
(i.e., [18]) provides a methodology for testing implementations
for compliance with the standard. In this paper, we will, for the
most part, limit our discussion to the baseline codec. Some of
the extensions included in Part 2 will also be discussed briefly.
Unless otherwise indicated, our exposition considers only the
baseline system.
For the most part, the JPEG-2000 standard is written from the
point of view of the decoder. That is, the decoder is defined quite
precisely with many details being normative in nature (i.e., re-
quired for compliance), while many parts of the encoder are less
rigidly specified. Obviously, implementors must make a very
clear distinction between normative and informative clauses in
the standard. For the purposes of our discussion, however, we
will only make such distinctions when absolutely necessary.
III. JPEG-2000 CODEC
Having briefly introduced the JPEG-2000 standard, we are
now in a position to begin examining the JPEG-2000 codec in
detail. The codec is based on wavelet/subband coding tech-
niques [21, 22]. It handles both lossy and lossless compres-
sion using the same transform-based framework, and borrows
heavily on ideas from the embedded block coding with opti-
mized truncation (EBCOT) scheme [23–25]. In order to fa-
cilitate both lossy and lossless coding in an efficient manner,
reversible integer-to-integer [26–28] and nonreversible real-to-
real transforms are employed. To code transform data, the codec
makes use of bit-plane coding techniques. For entropy coding,
a context-based adaptive binary arithmetic coder [29] is used—
more specifically, the MQ coder from the JBIG2 standard [30].
Two levels of syntax are employed to represent the coded image:
a code stream and file format syntax. The code stream syntax is
similar in spirit to that used in the JPEG standard.
The remainder of Section III is structured as follows. First,
Sections III-A to III-C, discuss the source image model and
how an image is internally represented by the codec. Next, Sec-
tion III-D examines the basic structure of the codec. This is
followed, in Sections III-E to III-M by a detailed explanation of
the coding engine itself. Next, Sections III-N and III-O explain
the syntax used to represent a coded image. Finally, Section III-
P briefly describes some of the extensions included in Part 2 of
the standard.
A. Source Image Model
Before examining the internals of the codec, it is important to
understand the image model that it employs. From the codec’s
point of view, an image is comprised of one or more compo-
nents (up to a limit of 2
14
), as shown in Fig. 1(a). As illustrated
in Fig. 1(b), each component consists of a rectangular array of
samples. The sample values for each component are integer val-
ued, and can be either signed or unsigned with a precision from
Component 1
Component 2
...
Component 0
Component N−1
(a)
Component i
...
...
...
(b)
Fig. 1. Source image model. (a) An image with N components. (b) Individual
component.
1 to 38 bits/sample. The signedness and precision of the sample
data are specified on a per-component basis.
All of the components are associated with the same spatial ex-
tent in the source image, but represent different spectral or aux-
iliary information. For example, a RGB color image has three
components with one component representing each of the red,
green, and blue color planes. In the simple case of a grayscale
image, there is only one component, corresponding to the lu-
minance plane. The various components of an image need not
be sampled at the same resolution. Consequently, the compo-
nents themselves can have different sizes. For example, when
color images are represented in a luminance-chrominance color
space, the luminance information is often more finely sampled
than the chrominance data.
B. Reference Grid
Given an image, the codec describes the geometry of the var-
ious components in terms of a rectangular grid called the ref-
erence grid. The reference grid has the general form shown
in Fig. 2. The grid is of size Xsiz × Ysiz with the origin lo-
cated at its top-left corner. The region with its top-left corner at
(XOsiz,YOsiz) and bottom-right corner at (Xsiz− 1, Ysiz − 1)
is called the image area, and corresponds to the picture data to
be represented. The width and height of the reference grid can-
not exceed 2
32
− 1 units, imposing an upper bound on the size
of an image that can be handled by the codec.
All of the components are mapped onto the image area of
the reference grid. Since components need not be sampled at
the full resolution of the reference grid, additional information
is required in order to establish this mapping. For each com-
ponent, we indicate the horizontal and vertical sampling period
in units of the reference grid, denoted as XRsiz and YRsiz, re-
spectively. These two parameters uniquely specify a (rectangu-
lar) sampling grid consisting of all points whose horizontal and
vertical positions are integer multiples of XRsiz and YRsiz, re-
spectively. All such points that fall within the image area, con-
Copyright
c
2002–2005 Michael D. Adams 3
TABLE I
PARTS OF THE STANDARD
Part Title Purpose Document
1 Core coding system Specifies the core (or minimal functionality) JPEG-2000 codec. [7]
2 Extensions Specifies additional functionalities that are useful in some applications but need not be supported
by all codecs.
[15]
3 Motion JPEG 2000 Specifies extensions to JPEG-2000 for intraframe-style video compression. [16]
4 Conformance testing Specifies the procedure to be employed for compliance testing. [18]
5 Reference software Provides sample software implementations of the standard to serve as a guide for implementors. [17]
6 Compound image file format Defines a file format for compound documents. [19]
8 Secure JPEG 2000 Defines mechanisms for conditional access, integrity/authentication, and intellectual property
rights protection.
∗
9 Interactivity tools, APIs and pro-
tocols
Specifies a client-server protocol for efficiently communicating JPEG-2000 image data over net-
works.
∗
10 3D and floating-point data Provides extensions for handling 3D (e.g., volumetric) and floating-point data.
∗
11 Wireless Provides channel coding and error protection tools for wireless applications.
∗
12 ISO base media file format Defines a common media file format used by Motion JPEG 2000 and MPEG 4. [20]
13 Entry-level JPEG 2000 encoder Specifies an entry-level JPEG-2000 encoder.
∗
∗
This part of the standard is still under development at the time of this writing.
(Xsiz−1,Ysiz−1)
(XOsiz,YOsiz)
Xsiz−XOsiz
Image Area
(0,0)
Xsiz
Ysiz−YOsiz
Ysiz
XOsiz
YOsiz
Fig. 2. Reference grid.
stitute samples of the component in question. Thus, in terms
of its own coordinate system, a component will have the size
Xsiz
XRsiz
−
XOsiz
XRsiz
×
Ysiz
YRsiz
−
YOsiz
YRsiz
and its top-left sam-
ple will correspond to the point
XOsiz
XRsiz
,
YOsiz
YRsiz
. Note that
the reference grid also imposes a particular alignment of sam-
ples from the various components relative to one another.
From the diagram, the size of the image area is (Xsiz −
XOsiz) × (Ysiz − YOsiz). For a given image, many combina-
tions of the Xsiz, Ysiz, XOsiz, and YOsiz parameters can be
chosen to obtain an image area with the same size. Thus, one
might wonder why the XOsiz and YOsiz parameters are not
fixed at zero while the Xsiz and Ysiz parameters are set to the
size of the image. As it turns out, there are subtle implications
to changing the XOsiz and YOsiz parameters (while keeping the
size of the image area constant). Such changes affect codec be-
havior in several important ways, as will be described later. This
behavior allows a number of basic operations to be performed
more efficiently on coded images, such as cropping, horizon-
tal/vertical flipping, and rotation by an integer multiple of 90
degrees.
C. Tiling
In some situations, an image may be quite large in compar-
ison to the amount of memory available to the codec. Conse-
quently, it is not always feasible to code the entire image as a
T
7
T
0
T
1
T
2
T
3
T
4
T
5
T
6
T
8
(XOsiz,YOsiz)
(0,0)
(XTOsiz,YTOsiz)
XTOsiz XTsiz XTsiz XTsiz
YTsiz
YTsiz
YTsiz
YTOsiz
Ysiz
Xsiz
Fig. 3. Tiling on the reference grid.
single atomic unit. To solve this problem, the codec allows an
image to be broken into smaller pieces, each of which is inde-
pendently coded. More specifically, an image is partitioned into
one or more disjoint rectangular regions called tiles. As shown
in Fig. 3, this partitioning is performed with respect to the ref-
erence grid by overlaying the reference grid with a rectangu-
lar tiling grid having horizontal and vertical spacings of XTsiz
and YTsiz, respectively. The origin of the tiling grid is aligned
with the point (XTOsiz,YTOsiz). Tiles have a nominal size of
XTsiz × YTsiz, but those bordering on the edges of the image
area may have a size which differs from the nominal size. The
tiles are numbered in raster scan order (starting at zero).
By mapping the position of each tile from the reference grid
to the coordinate systems of the individual components, a par-
titioning of the components themselves is obtained. For exam-
ple, suppose that a tile has an upper left corner and lower right
corner with coordinates (tx
0
,ty
0
) and (tx
1
− 1,ty
1
− 1), respec-
tively. Then, in the coordinate space of a particular component,
the tile would have an upper left corner and lower right cor-
ner with coordinates (tcx
0
,tcy
0
) and (tcx
1
−1,tcy
1
−1), respec-
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