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ISO/IEC JTC 1/SC 29/WG 1 N 2412

Date: September 1, 2001

ISO/IEC JTC 1/SC 29/WG 1

(ITU-T SG8)

Coding of Still Pictures

JBIG JPEG

Joint Bi-level Image Joint Photographic

Experts Group Experts Group

TITLE: The JPEG-2000 Still Image Compression

Standard

SOURCE: Michael D. Adams

Dept. of Electrical and Computer Engineering

University of British Columbia

Vancouver, BC, Canada V6T 1Z4

E-mail: mdadams@ece.ubc.ca

PROJECT: JPEG 2000

STATUS:

REQUESTED ACTION:

DISTRIBUTION: Public

Contact:

ISO/IEC JTC1/SC29/WG1 Convener—Dr. Daniel Lee

Yahoo!, 3420 Central Expressway, Santa Clara, California 95051, USA

Tel: +1 408 992 7051, Fax: +1 253 830 0372, E-mail: dlee@yahoo-inc.com

The JPEG-2000 Still Image Compression Standard

∗

(Last Revised: September 1, 2001)

Michael D. Adams

Dept. of Elec. and Comp. Engineering, University of British Columbia

Vancouver, BC, Canada V6T 1Z4

mailto:mdadams@ieee.org http://www.ece.ubc.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

Digital imagery is pervasive in our world today. Conse-

quently, standards for the efﬁcient representation and inter-

change 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, 2] and JPEG-LS [3] standards were born

from the work of the JPEG committee. For the last few years,

the JPEG committee has been working towards the establish-

ment of a new standard known as JPEG 2000 (i.e., ISO/IEC

15444). The fruits of these labors are now coming to bear, as

JPEG-2000 Part 1 (i.e., ISO/IEC 15444-1 [4]) has recently been

approved as a new international standard.

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 [4] before attempting an

implementation. The JPEG-2000 codec realization in the JasPer

software [5–7] may also serve as a practical guide for imple-

mentors. (See Appendix A for more information about JasPer.)

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-

marks in Section IV. Throughout our presentation, a basic un-

derstanding of image coding is assumed.

∗

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).

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 [8] 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 re-

gion of interest coding, and a more ﬂexible ﬁle format, 4) avoid

excessive computational and memory complexity. Undoubtedly,

much of the success of the original JPEG standard can be at-

tributed to its royalty-free nature. Consequently, considerable

effort has been made to ensure that minimally-compliant JPEG-

2000 codec can be implemented free of royalties

B. Structure of the Standard

The JPEG-2000 standard is comprised of numerous parts,

several of which are listed in Table I. For convenience, we will

refer to the codec deﬁned in Part 1 of the standard as the baseline

codec. The baseline codec is simply the core (or minimal func-

tionality) coding system for the JPEG-2000 standard. Parts 2

and 3 describe extensions to the baseline codec that are useful

for certain speciﬁc applications such as intraframe-style video

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.

compression. In this paper, we will, for the most part, limit our

discussion to the baseline codec. Some of the extensions pro-

posed for inclusion in Part 2 will 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 [9,10]. It handles both lossy and lossless compression us-

ing the same transform-based framework, and borrows heavily

on ideas from the embedded block coding with optimized trun-

cation (EBCOT) scheme [11,12]. In order to facilitate both lossy

and lossless coding in an efﬁcient manner, reversible integer-

to-integer [13, 14] 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 [15] is used—more speciﬁ-

cally, the MQ coder from the JBIG2 standard [16]. 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 fol-

lowed, 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 extensions proposed for inclusion 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

), 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

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

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.

(Xsiz−1,Ysiz−1)

(XOsiz,YOsiz)

Xsiz−XOsiz

Image Area

(0,0)

Xsiz

Ysiz−YOsiz

Ysiz

XOsiz

YOsiz

Fig. 2. Reference grid.

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

− 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-

TABLE I

PARTS OF THE STANDARD

Part Title Purpose

1 Core coding system Speciﬁes the core (or minimum functionality) codec for the JPEG-2000 family of standards.

2 Extensions Speciﬁes additional functionalities that are useful in some applications but need not be supported

by all codecs.

3 Motion JPEG-2000 Speciﬁes extensions to JPEG-2000 for intraframe-style video compression.

4 Conformance testing Speciﬁes the procedure to be employed for compliance testing.

5 Reference software Provides sample software implementations of the standard to serve as a guide for implementors.

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-

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 combinations

of the Xsiz, Ysiz, XOsiz, and YOsiz parameters can be chosen to

obtain an image area with the same size. Thus, one might won-

der 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 chang-

ing the XOsiz and YOsiz parameters (while keeping the size of

the image area constant). Such changes affect codec behavior in

several important ways, as will be described later. This behavior

allows a number of basic operations to be performed efﬁciently

on coded images, such as cropping, horizontal/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

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 parti-

tioning of the components themselves is obtained. For example,

suppose that a tile has an upper left corner and lower right corner

with coordinates (tx

, ty

) and (tx

− 1, ty

− 1), respectively.

Then, in the coordinate space of a particular component, the tile

would have an upper left corner and lower right corner with co-

ordinates (tcx

, tcy

) and (tcx

−1, tcy

−1), respectively, where

(XOsiz,YOsiz)

(0,0)

(XTOsiz,YTOsiz)

XTOsiz XTsiz XTsiz XTsiz

YTsiz

YTOsiz

Ysiz

Xsiz

Fig. 3. Tiling on the reference grid.

tcx

tcy

tcx

tcy

(0,0)

Tile−Component Data

( , )

( −1, −1)

Fig. 4. Tile-component coordinate system.

(tcx

, tcy

) = (dtx

/XRsize , dty

/YRsize) (1a)

(tcx

, tcy

) = (dtx

/XRsize , dty

/YRsize) . (1b)

These equations correspond to the illustration in Fig. 4. The por-

tion of a component that corresponds to a single tile is referred

to as a tile-component. Although the tiling grid is regular with

respect to the reference grid, it is important to note that the grid

may not necessarily be regular with respect to the coordinate

systems of the components.

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kapoyegou

2021-04-02

资源确实是jpeg2000的，是adams的会议论文，就是我要找的。人家也没说是官方标准啊。。
Ihatec2s3d4n5

2011-10-07

不是jpeg2000标准就别在那里浪费别人的时间了-100

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