The software implementation is described of an emerging standard for the lossy compression of continuous tone still images. This software program can be used to compress planetary images and other 2-D instrument data. It provides a high compression image coding capability that preserves image fidelity at compression rates competitive or superior to most known techniques. This software implementation confirms the usefulness of such data compression and allows its performance to be compared with other schemes used in deep space missions and for data based storage

Arnold, S.

Pollara, F.

English

NASA Technical Reports Server

/TDA Progress Report 42-104 February 15, 1991
N91-18317 J1(; "_
Emerging Standards for Still Image Compression:
A Software Implementation
and Simulation Study
F. Pollara and S. Arnold
Communications Systems Research Section
This article describes the software implementation of an emerging standard for
the lossy compression of continuous-tone still images. This software program can be
used to compress planetary images and other two-dimensional instrument data. It
provides a high-compression image-coding capability that preserves image fidelity at
compression rates competitive or superior to most known techniques. This software
implementation confirms the usefulness of such data compression and allows its
performance to be compared with other schemes used in deep-space missions and
for database storage.
I. Introduction
The Joint Photographic Experts Group of the Interna-
tional Standards Organization, together with the Interna-
tional Consultative Committee for Telephone and Tele-
graph, is in the process of developing an international
standard for still image compression with both transmis-
sion and storage applications [1]. In its baseline version,
the proposed algorithm consists of an 8 × 8 discrete co-
sine transform (DCT), coefficient quantization, and en-
tropy coding (Huffman or arithmetic). The complete en-
coder/decoder system is illustrated by the block diagram
in Fig. 1. This scheme provides a lossy high-compression
image coding capability that preserves image fidelity at
compression rates competitive or superior to most known
techniques [2]. Its software implementation is discussed in
the following section.
II. Structure of the Software Implementation
Image samples, or pixels, are read from the original
image file and sent to a two-dimensional DCT module,
which produces 64 coefficients that are independently and
uniformly quantized with a different step-size for each co-
efficient. Then a one-dimensional array is formed by read-
ing the 8 x 8 matrix of quantized coefficients in a zig-zag
fashion. The sequence of direct current (dc) components--
the first coefficient of each block--is differentially encoded,
while the alternating current (ac) components are run-
length encoded. Finally, some of the most significant bits
of each code are fllrther encoded with a variable-length
code; the remaining bits are transmitted essentially intact.
Flow diagrams of the software encoder and decoder
structures with IIuffman coding are shown in Figs. 2 and 3.
98
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Eachof theoperationsdescribedin thefollowingsections
hasbeenimplementedasa separatesoftwaremoduleto
allowforfuturetestingof modifiedmodules.
A. Discrete Cosine Transform Module
The forward and inverse two-dimensional DCTs used
in this software implementation are defined by
F(u, v) = C(u)C(v)_
7 7
EE:(,,.I
x----Oy=O
X COS
(2x + 1)urr (2y + 1)vrr
COS
16 16
and
7 71
= r_, F_,C(u)C(v)F(u,v)
u=0 v=0
X COS
(2x + 1)u_r (2y + 1)wr
COS
16 16
where C(k) = 1/V_ if k = 0, and C(k) = 1 if k # 0.
This definition is efficiently implemented by using row-
column decomposition [3]. First, the 8 x 1 DCT of each
data column is computed; then the transpose of the re-
sulting matrix is stored as an intermediate result. Finally,
the 8 x 1 DCT of each data row is computed to yield
the desired two-dimensional DCT. This method has the
advantage of considerably reducing the total number of
operations required and of limiting to (2P - 1)(P - 1)
(105 for P = 8) the number of cosine entries to be stored
permanently for a P x P transform. A fast very large-
scale integration (VLSI) of this method is described in [3].
In this article, the software implementation uses floating-
point representation but reduced precision versions have
also been considered. Another approach to reducing the
computational complexity of this step is to consider other
transforms such as the Hadamard transform [4] that. can
be performed using integer operations with only a slight
performance degradation [2].
B. Quantization Module
The 64 coefficients produced by the forward DCT mod-
ule are quantized by a uniform or constant step-size quan-
tizer, where the fixed step size may vary from coefficient
to coefficient. This is accomplished by a predefined 8 x 8
matrix specifying the step size Q(u, v) for each coefficient.
The DCT of 8-bit input pixelQ produces output coeffi-
cients with an 8-times-larger range corresponding to a to-
tal of 11 bits. The quantization matrix can, of course, be
adapted to satisfy different subjective quality measures or
different instrument nonlinearities.
C. Coefficient Modeling Module
Besides using two different Iluffman codes for the de
coefficient--the first term in the 8 x 8 matrix of coef-
ficients-and the ac coefficients, these two classes are also
differently pre-encoded or modeled.
1. DC Modeling. The quantized dc coefficient is
differentially pre-encoded by computing its difference with
the dc term in the previous block. These differences will
then be entropy coded. Their dynamic range has now
increased to 12 bits.
Two-dimensional dc prediction, which uses both the
previous block's de term and that of the block above, has
also been suggested to take greater advantage of pixel cor-
relation. This feature has not yet been implemented, but
it will be included in future revisions of the software.
The prediction residual is then assigned to one of 12
categories Ci (i = 0,...,11) defined by the base-2 loga-
rithm of the residual's absolute value. The resulting 4-bit
categories are later Huffman encoded. The remaining in-
formation about residual values and sign is encoded by a
simple variable-length-integer (VLI) code, in which each
eodeword is Ci bits long [1].
2. AC Modeling. As a first step, the 63 ac coefficients
are reordered into a one-dimensional array by reading the
8 x 8 matrix according to a predefined zig-zag scan path.
This reordering ranks the coefficients in approximate order
of decreasing magnitude.
The one-dimensional array of ac coefficients is modeled
by run-length coding. When a nonzero coefficient is en-
countered, the number of zeros preceding it and its 4-bit
category (one of 11) are concatenated and stored into an
8-bit word for further Ituffman coding. The remaining in-
formation about the run-length/nonzero ae pair is encoded
with the same VLI code discussed above. Since only 4 bits
are reserved to represent a run length, only runs up to
15 consecutive zeros can be modeled. Longer runs are ar-
tificially broken by transmitting a special code for a run
i The software implementation described in tiffs article is designed
for easy extension to higher input data precision, up to 12 bits per
sample.
99
length of 16 zeros. Another special code is reserved to sig-
nal the end of a block, which also prevents the propagation
of eventual channel errors to subsequent blocks.
D. Entropy-Coding Module
Entropy coding is the process that actually performs
the compaction of the data by reducing statistical redun-
dancy. Either IIuffman or arithmetic coding can be used
as an entropy-coding method.
1. Huffman Coding. The dc category and ac run-
length/category pairs are Huffman coded using two differ-
ent codes. These two codes are not a disjoint partition of a
larger prefix code since they contain common codewords.
Itowever, they can be decoded by their relative position
in the serial stream of codewords, which is known on tile
receiver side since an end-of-block is always followed by a
dc code, which may then be followed by ac codes or by
an end-of-block code. This solution allows more efficient
encoding with smaller average codeword length at the ex-
pense of a slightly more complex synchronization scheme.
The present software implementation uses two default
look-up tables for the two Huffman codes. The dc table
contains 12 codewords, one for each possible category; the
ac table contains 162 codewords, one for each combination
of 16 run lengths and 10 categories 2 plus the two special
codewords for end-of-block and run-length 16. The maxi-
mum length of ac codewords is constrained to 16 bits.
The dc code tables are specified by an array of 12 bytes,
which contains a properly ordered list of categories corre-
sponding to a lexicographically ordered list of codewords
belonging to a prefix code, and by an array of 16 en-
tries representing the number of codewords of each length.
The ac code tables are similarly specified by an array of
162 bytes, which contains a properly ordered list of run-
length/category pairs corresponding to a lexicographically
ordered list of codewords of a prefix code, and by an ar-
ray of 16 entries representing the number of codewords of
each length. These four arrays completely specify the two
codes and can be used to send code information to the de-
coder or to specify custom tables adapted to the particular
2 The number of categories that can actually occur is 11 {for g-bit
data plus 3-bit expansion due to DCT), but category 0 is unused
since only nonzero ac coefficients need to be encoded.
source of interest. This software implementation can also
be used to perform a two-pass encoding in which specific
codes for the image to be transmitted are created by the
encoder during the first pass.
2. Arithmetic Coding. As a higher performance al-
ternative to Huffman coding, arithmetic coding has also
been included in the standard's specification [1]. Arith-
metic coding provides a one-pass scheme that dynamically
adapts to image statistics. For this reason, it has a gener-
ally superior performance [2] to the nonadaptive ][uffman
coding chosen for the standard that requires image sl.atis-
tics information before coding. Furthermore, unlike lluff-
man coding, arithmetic coding does not always require at.
least one bit per data sample.
III. Conclusions
This article described a software implementation of a
DCT-based lossy compression algorithm suitable for trans-
mitting images from deep space and for storing images in
databases. This software is now available for testing and
for measuring compression and reproduction-quality per-
formance on various instrument sources of interest. The
compression procedure is executed by running the encoder
program, which reads tile original raster-scanned image--
with 8-bit-per-pixel gray-scale resolution--to produce a
compressed binary-file image and to compute the compres-
sion ratio. Different compression ratios can be obtained by
changing the quantization table or the arrays specifying
the tluffman codes. The decoder program, in turn, reads
the compressed image and produces the reconstructed im-
age in the same format as the original. Very satisfying re-
production quality has been obtained in preliminary tests
described in [2].
In the standard considered in this article, practical
hardware realization issues have been carefiflly evaluated
to yield designs suitable for VLSI implementation. A com-
mercial VLSI chip set based on this algorithm is already
available [5]. Beyond improvements in performance or re-
ductions in complexity that may be possible for specific
deep-space instrument applications, the main challenge
will be to demonstrate that this algorithm can be realized
in a space-qualified version.
lOO
Acknowledgments
The authors acknowledge the useful suggestions of K.-M. Cheung, S. J. Dolinar,
and I. Onyszehuk during the development of this software.
References
[1] JPEG Draft Technical Specification (Rev. 5), International Standards Orga-
nization/International Consultative Committee for Telephone and Telegraph
(ISO/CCITT), Washington, D.C., January 15, 1990.
[2] S. J. Dolinar, K.-M. Cheung, I. Onyszchuk, S. Arnold, and F. Pollara, "Com-
pressed/Reconstructed Test Images for CRAF/Cassini," TDA Progress Report
4e-104 (this issue), vol. October-December 1990, Jet Propulsion Laboratory,
Pasadena, California, pp. 88-97, February 15, 1991.
[3] M. Sun, T. Chert, and A. Gottlieb, "VLSI Implementation of a 16 x 16 Discrete
Cosine Transform," IEEE Trans. on Circuits and Systems, vol. 36, no. 4, pp. 610-
617, April 1989.
[4] W. K. Pratt, Digital Image Processing, New York: Wiley & Sons, 1978.
[5] Technical Specification Catalog, LSI Logic Corporation, Milpitas, California, June
1990.
lOl
ORIGINAL COMPRESSED
IMAGE IMAGE
FORWARD I _'_
DISCRETE ENTROPY
m, COSINE QUANTIZER ENCODER
TRANSFORM
NOISELESS 1
CHANNEL
  OO St UOZ OJIMAGE DISCRETE DEQUANTIZER ENTROPYCOSINE DECODERTRANSFORM
Fig. 1. Block diagram of compression system.
t
DC MODELING
(DIFFERENCES)
DC ENCODING
IMAGE FILE
READ Px NBUFFER 9
EXTRACT
Px P BLOCK _-
2D DCT
QUANTIZER
Z l G -ZAG
REORDERING
AC MODELING
(RUN LENGTH)
AC ENCODING
I IT
COMPRESSED
FILE
NO
NO
Fig. 2. Baseline compressor for Huffman coding.
COMPRESSED FILE
EXTRACT
CODEWORD
i
DIFFERENTIAL DECODER I RUN LENGTH DECODER
I I
INVERSE ZIG-ZAG
DEQUANTIZER
2D INVERSE DCT
RECONSTRUCTED
FILE
Fig. 3. Baseline decompressor for Huffman coding.
102


Emerging standards for still image compression: A software implementation and simulation study

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