Appendix G. Sample Probit Analysis SAS Code. 103. Appendix H. ..... Yellow-BI. Luminance. 0.1. 0.3. 1. 3. 10. Spatial fr
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Color space selection for JPEG image compression Nathan Moroney
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Color Space Selection for JPEG Image Compression
Nathan Moroney B .S. Philadelphia College of Textiles and Science ( 1991)
A thesis submitted for partial fulfillment of the requirements for the degree of Master of Science in Color Science in the Center for Imaging Science on the College of Imaging Arts and Sciences of the Rochester Institute of Technology
December 1993
Nathan M. Moroney Signature of Author
Mark D. Fairchild Accepted by
College of Imaging Arts and Science Rochester Institute of Technology Rochester, New York
CERTIFICATE OF APPROVAL
M.S. DEGREE THESIS
The M.S. Degree Thesis of Nathan Moroney has been examined and approved by two members of the color science faculty as satisfactory for the thesis requirement for the Master of Science degree.
Mark D. Fairchild Dr. Mark Fairchild, Thesis Advisor
Roy Berns Dr. Roy Berns
Thesis Release Permission Form
Rochester Institute of Technology Center for Imaging Science
Title of Thesis Color Space Selection for JPEG Image Compression
1, Nathan M. Moroney, hereby grant permission to the Wallace Memorial Library of R.I.T. to reproduce my thesis in whole or in part Any reproduction will not be for commercial use or profit.
Date
_
l
d._,_;/l~b_,/"-4L.:!.)'----'
I
Color Space Selection for JPEG Image Compression
Nathan
Moloney
Submitted for partial fulfillment for the degree of Master of Science in Color Science in the Center for Imaging Science the Rochester Institute of Technology
of the requirements
at
ABSTRACT
The Joint Photographic Experts Group's image compression algorithm has been be a very efficient and powerful method of compressing images. However, there is litde substantive information about which color space should be utilized when implementing the JPEG algorithm. Currendy, the JPEG algorithm is set up for use with any three component color space. The objective of this research was to determine whether or not the color space selected will significandy improve image compression capabilities. The RGB, XYZ, YIQ, CIELAB, CIELUV, and CIELAB LCh color spaces were examined and compared. Both numerical measures and psychophysical techniques were used to assess the results. The final results indicate that the device space, RGB, is the worst color space to compress images. In comparison, the nonlinear transforms of the device space, CIELAB and CIELUV, are the best color spaces to compress images. The XYZ, YIQ, and CIELAB LCh color spaces resulted in intermediate levels of shown to
compression.
Acknowledgments
I
would
received as
I
like
to thank the
following people for all of the help
and assistance that
I
the Munsell
Lab, for providing the support and environment that made all of this possible, Mark Fairchild, for suggesting such a terrific research topic and for overseeing the entire process, Mike Stokes, for getting carried out
my thesis
research:
everything started by patiendy helping me to debug and implement my JPEG code, Tim Kohler, for coundess programming tips, software details, and trivia, and Eli, for her hope and love.
"Learning
changes us;
'preserve'
-as
it does what all nourishment does which also does not merely down' know. But at the bottom of us, really 'deep there is, of
physiologists
course, something unteachable, some granite
of spiritual
fatum,
of predetermined
decision and answer to predetermined selected questions. Whenever a cardinal problem is at stake, there speaks an unchangeable 'this is T; about man and woman, for example, a thinker cannot relearn but only finish learning -only discover ultimately how this is At times we find certain solutions of problems that inspire strong faith in 'settled in him.'
'convictions.'
Later -we see them only as steps to us; some call them henceforth their problem we are, -rather, to the great stupidity we are, to self-knowledge, signposts to the down.' " our spiritual fatum, to what is unteachable very 'deep Friedrich Nietzsche Beyond Good and Evil
Table
Table List
of
of
List List 1
.
2
.
4
.
i iii
Figures
iv vi
Introduction
1
Background
3
Baseline
JPEG
2.1.1.
The
2.1.2.
Quantization
2.1.3.
Huffman
2.1.4.
Measures
2.2.
.
Contents
Tables
2.1.
3
Contents
Images of
of
of
Color
FDCT
3 IDCT
and
and
Dequantization
5 of the
Encoding and Decoding of
Image Compression
Spaces
DCT Coefficients
8 12 17
19
2.2.1.
Device Color Spaces
2.2.2.
Linear Transforms
2.2.3.
Nonlinear Transforms
2.2.4.
CRT Gamut Transforms
of
Device Space of
Device Space
Color Spaces
2.3.
JPEG Quantization
2.4.
Computational Example
of
20 21 22 25 26
29 33
Experimental
3.1.
Environment
33
3.2.
Experiment One
38
3.3.
Experiment
Results
4.1.
Two
40
Discussion
42
Experiment One
42
and
4.1.1.
Probit Analysis
of Data
43
Table
4.2.
.
Contents
(continued)
Two
49
4.2.1.
Analysis
4.2.2.
Image
4.2.3.
Colorimetric Measures
4.2.4.
Error Images
4.3.
5
Experiment
of
of
the
Logistically
Processing
Transformed Data
Measures
of
Error
of Error
51 54
58 61
Analysis
62
4.3.1.
Channel
4.3.2.
Perceptual
4.3.3
Quantization
4.3.4.
Improvement Over RGB Compression
66
Redundancy L*
67
Polar hab Information
69
Uniformity of of
Conclusions
70 74
References
77
Appendix A. Huffman Encoding Tables for AC Terms
80
Appendix B. JPEG
86
C
Code
Appendix C. Inverse Color Space Transformations
95
Appendix D. CRT Calibration
97
Appendix E.
Preliminary Psychophysics
Experiment
100
Appendix F. Observer Instructions
102
Appendix G. Sample Probit Analysis SAS Code
103
Appendix H. Bits/Min2 Calculations
1 05
ii
List
of
Images
Image 3.1 Birds
34
Image 3.2 Fruit
34
Image 3.3 Musicians
35
Image 3.4 Pasture
35
Image 4.1 CIELAB
Fruit Error
63
Image
Image 4.2 CIELAB LCh Fruit Error Image
63
Image 4.3 CIELUV Fruit Error Image
64
Image 4.4 RGB Fruit Error Image
64
Image 4.5 XYZ Fruit Error Image
65
Image 4.6
65
YIQ Fruit Error Image
in
List
Figures
of
Fig. 2.1
Flowchart for Baseline JPEG Algorithm
4
Fig. 2.2
The 64 DCT Basis Functions
7
Fig. 2.3
Human Luminance
7
Fig. 2.4
Example Luminance
Fig. 2.5
Quantization Scaled DCT Basis Functions
11
Fig. 2.6
The
14
Fig. 2.7
CRT Gamut in RGB Space
27
Fig. 2.8
CRT
Gamut
in
XYZ
27
Fig. 2.9
CRT
Gamut
in
YIQ Space
Fig. 2.10
CRT Gamut in CIELAB Space
28
Fig. 2.11
CRT Gamut in CIELUV Space
28
Fig. 2.12
Example
Fig. 2.13
Example
Fig. 3.1
Experimental Electronic
Fig. 3.2
Observer
Fig. 4. 1
Sample Probit Analysis
Fig. 4.2
Visually
Fig. 4.3
Visually Lossless
Thresholds
of
Compression for Fruit Image
46
Fig. 4.4
Visually Lossless
Thresholds
of
Compression for Musicians Image
46
Fig. 4.5
Visually Lossless
Thresholds
of
Compression for Pasture Image
47
Fig. 4.6
Visually Lossless Thresholds
of
Compression Averaged for All Images
47
Fig. 4.7
Image
Fig. 4.8
Overall Image
Fig. 4.9
L*
and
Chrominance CSFs
and
Chrominance Q-Tables
Zig-Zag Ordering of the Quantized DCT coefficients
of
of
Space
27
Color Space Transformations
JPEG Compression
and
Decompression
Imaging
System
32
37
43
Lossless Thresholds
of
Scales Derived
Quality
30
37
Viewing Conditions
Quality
9
Compression for Birds Image
Using
Scale Derived
Logistic Analysis
Using
Logistic Analysis
45
53 53
68
Transform Jones Diagram
iv
List
of
Figures
Fig. 4.10
Example hab Compression
Fig. H.l
Basic Experimental
Fig. H.2
Simplified Experimental
and
(continued)
Decompression
Viewing Geometry Viewing Geometry
71 105 105
List
of
Tables
Table 2.1
Categorization Table for AC
Table 2.2
Baseline entropy encoding table for DC terms
15
Table 2.3
Quantization Schemes Used for Different Color Spaces
29
Table 3.1
List
39
Table 3.2
List
Table 4. 1
Visually lossless Thresholds for Compression in Bits/Pixel
48
Table 4.2
Two Standard Errors in Bits/Pixel for the Thresholds in Table 4.1
48
Table 4.3
Frequency
Table 4.4
Proportionality Matrix for Birds Using 25
Table 4.5
Matrix
Table 4.6
Logit interval
Table 4.7
Image
Processing Error Metrics Averaged for Each of the Color Spaces
Table 4.8
Image
Processing
Table 4.9
Colorimetric Error Metrics Averaged for Each
of
Images
of
used
Images
of
and
DC Coefficients
for Experiment One
used
for Experiment Two
Matrix for Birds Image
Using
scales
derived for
Table 4.12 Percent Improvement
Table A.2
Huffman
50
Encoding
of the
of the
51
images
52
of
the Images
RGB Compression
Table for Luminance AC Terms
Encoding Table for Chrominance AC Term
vi
Images
Color Spaces
Channels for Fruit Image
over
observers
each of the color spaces and
Error Metrics Averaged for Each
of
50
Observers
Logistically Transformed Data for Birds using 25
Table 4. 1 1 Standard Deviations
Huffman
41
25 Observers
Table 4. 10 Colorimetric Error Metrics Averaged for Each
Table A.l
15
58 58
60 61 67 72
80 83
1.
Any
by
given scene viewed
million receptors.
This
be transmitted
the one million
human
by
visual system
seven to one
visual
a
human
observer
of years.
achieves a
routinely
visually lossless level
(Granrath 1981). It is encouraging to
One
has been possible
of the most
Baseline JPEG
widely
with
Group
CCITT
up to study
industry
formulating, revising
its
and
color
image
is
of compression
decade that the
of thousands
same
level
of
originally
used to
compression.
about to approve as an
has been developed is the
an acronym
The
standard compression algorithm which
and
levels
images.
JPEG is
name was
that it can
means that the
for hundreds
used and successful methods that
Photographic Experts
the
color
compression algorithm.
committee set
under our noses
This
seven
of compression of about
realize that such
within the past
digital
compressed so
to the brain.
or so optic neurons
However, it has only been
compression
is detected using roughly
information is then automatically
information have been occurring right
of visual
identify
Introduction
standing for the Joint
identify
name
is
the joint
ISO /
now also used to
the committee has been
international
standard
(Mitchell
and
Pennebaker 1991). Image
information ways and
compression refers to
needed to represent a
JPEG
utilizes
techniques involves as
spatial, temporal
any
class of
techniques used to reduce the amount of
digital image. This
two of the
can
most common
methods which attempt
be done in
approaches.
a number of
The first group
to reduce any redundancies
or spectral correlations.
The
second
different
in the image,
of
such
group involves systematically
throwing out less visually significant information from the image (Limb 1976). The JPEG
algorithm
technologies. These advances
an
in
imaging science are opening entire new regions for future
development. Currently, JPEG is
images in
important
is
being
an electronic environment.
used
This
part of
the rapidly
growing
compression
to improve the storage capacity for digital
means
that storing and
communicating digital
images is will
be
now
for
vital
and
less
At the be
future, JPEG
high definition television,
there is little substantive
time,
implementing
Some
authors
have
and related
color
faxes,
(Leger, Omachi
information
technologies
video
and
telephones
Wallace 1991).
about which color space
the JPEG algorithm (Wallace 1988).
the RGB device space is
shown that
compression space.
near
storage and retrieval systems
utilized when
has
research
present
In the
expensive.
such products as
high-end image
and other
should
faster
a poor choice
suggested that the
for
Previous
a color
image
NTSC YIQ, NTSC YCbCr,
or
the CIE XYZ tristimulus space should be used when compressing color images (Pratt 1971 and
Ylakoski
and
Ronngren 1992). These
from providing any would
be
concrete
optimal
details
for JPEG
psychophysics which
results provide a
point
but they
are
far
about which of the multitude of color spaces available
compression.
have been
starting
In addition, there is
published on this
issue. This thesis
minimal
research
reported
investigates
this topic and will provide numerical and psychophysical assessment of which color space should
be
used with
The selected
significant
for
algorithm are
compression.
image
differences in the
use with the
differences in the
color
the JPEG algorithm.
just
JPEG
perceptual
a
few
This thesis
compression.
of
various color spaces suggest that the color space
algorithm will affect the
resulting
compression.
The
uniformity, channel redundancy, and compatibility with the
the
variables
that could affect the efficiency of the resulting
research also attempts to
determine how these factors influence
2.
The
following
sections
Background
discuss the details
of
the Baseline JPEG
the specifics of each of the color spaces used in this research
is
computational example
from
original
RGB
This
presented.
form,
example
follows
Finally,
are reviewed.
a sample
Then
algorithm.
8x8 block
a
of pixels
through the color space transformations, through the
compression steps and then
back
illustrates the discussions
the JPEG algorithm and the color space transformations.
of
out
through the decompression steps.
Moreover, the example provides a useful reference for the Results
2.1.
Discussion
of
the major objectives of the JPEG committee
compression technique
with all of
To
use throughout
Additional
individual
users
implemented be
industry. A and software
changes could then
be
made
was
noted that
in
This
algorithm was
compression
compatible
to the Baseline algorithm according to
accept
the term pixel
would
8 bits
is
be universally
per pixel
images.
loosely
to mean
used
The
either a single monochrome pixel or a single channel of a color pixel.
terminology is specified, the green or
used
in this thesis
word pixel will
blue
be
and
the reader
should
be
aware
that,
same
unless otherwise
synonymous with a single pixel channel or an
individual
pixel component.
The Baseline JPEG
algorithm
is
composed of three major compression steps and
three major decompression steps. This is
following page.
image
developed the Baseline JPEG
designed to
literature,
be
that would be performing
preferences, but only the Baseline algorithm
and utilized.
basic
to establish a
method that would
accomplish this goal the committee
algorithm.
should
for
the various types of hardware
compression.
red,
section.
Baseline JPEG
One
It
and
This further
The first step in the
shown
process
in flowchart form in Fig. 2.1
is to break the
original
on
the
image down into
eight
Original Digital Image 3 Channels 8 Bits / Channel 8x8 Image Block III
jr
Color Space Conversion
Image Compression
V Forward Discrete
Huffman
Quantization
Encoding
Storage
or
Transmission
of
-^r
Cosine Transform
Image
Y Huffman -^
De-Quantization
Decoding
Invserse Discrete
Cosine Transform
Image Decompression
Reconstructed 8x8 Image Block
HI
50 t/>
c 0) CO
to ?0 a i
c
o
O
10
03
0.1
Spatial
3
1
0.3
10
frequency (cycles/degree)
Fig. 2.3. Human Luminance (From Mitchell
and
and
Chrominance CSF's
Pennebaker 1993).
100
f(x,y)
=
^ 4
i2.
v
X u
=
0v
=
rv
\rv \t_. C(u)C(v)F(u,v)cos
(2x + l)uTC
(2y + l)vTC i
.
(2.2)
cos
16
0
16
where:
The
variables u, v,
output of
the IDCT
adding 2(n~l)
-
1 to
and the
concentrates a
Woods 1990). As compact
2.1.2.
it
-jLforu,v =
V2
1
otherwise.
back from in
IDCT
0,
in the IDCT
a signed
order to get
integer to
as
an unsigned
essentially lossless. A lossless transform is
are
portion of
result, the DCT does
integer
the signal in the not
by
the original values.
information is lost. This transform is
large
in the FDCT. The
actually
a crucial
step in JPEG
lower frequencies (Gonzalez
compress the
one
and
information but it does
significantly.
Quantization
The
step
a
=
shifted
which none of the original
because it
C(u),C(v)
all of the values
Both the FDCT
in
be
=
perform the same roles
x, and y must
C(u),C(v)
Dequantization
step in the flow
next
compresses
and
the image
quantizing the DCT the DCT terms are
by
chart
is the
selectively
coefficients attempts
quantized
of
the DCT Coefficients
quantization of
discarding
to
model
the FDCT coefficients.
information. The JPEG
the human visual system.
according to their visual
This
scheme
for
Specifically,
significance.
Early on the JPEG committee recognized that color information could be quantized differently than monochrome information. color
information
could
(Hunt 1988). This
be
quantized more
scheme was
based
To illustrate, the human luminance
on
The largest difference
was that chrominance or
coarsely than the luminance
the
or
physiological properties of
and chrominance contrast
tone information
the visual system.
sensitivity functions
are
shown
in Fig. 2.3. This figure
roughly bell sensitivity The
shaped and peaks around
7
chrominance
sensitive to
sensitivity is
frequencies.
luminance
1991). The JPEG
luminance
cycles per
function, in comparison, is plateau
maximum
of the
shows that the
contrast
sensitivity function is
degree. The
chrominance contrast
shaped and peaks at a
lower
frequency level.
higher for the luminance information than for the
also
This demonstrates that the human
visual system
is
more
frequency changes than chrominance frequency changes (Schreiber
quantization scheme attempts to model this relationship, as well as some
details. The JPEG
committee
has
not provided
any
quantization
tables,
Q-Tables, for use
or
in Fig. 2.4, for
as standards.
They have provided two example tables,
algorithm and
this research utilized these two tables. One table is for quantizing luminance
information
and the other
is for
shown
chrominance quantization.
It has been
there are some irregularities in these two tables (Klein 1992). concepts of
and of
quantizing
varying the
valid and
chrominance
information
rate of quantization
have been
based
more
on the
by experimental results
supported
use with
commented
Nevertheless,
the
that
the basic
coarsely than luminance information
frequency
of the
basis functions
are
(Lohscheller 1984).
JPEG Chrominance O-Table
JPEG Luminance O-Table 16
11
10
16
24
40
51
61
17
18
24
47
99
99
99
99
12
12
14
19
26
58
60
55
18
21
26
66
99
99
99
99
14
13
16
24
40
57
69
56
24
26
56
99
99
99
99
99
18
22
37
56
68
109
103
77
47
99
99
99
99
99
99
99
24
35
55
64
81
104
113
92
99
99
99
99
99
99
99
99
49
64
78
87
103
121
120
101
99
99
99
99
99
99
99
99
72
92
95
98
112
100
103
99
99
99
99
99
99
99
99
99
Fig. 2.4 Example Luminance
and
Chrominance Q-Tables
Another way committee
is
shown
are shown with
particular
of
illustrating
the quantization scheme
The
sizes.
varying
will
be
size of
coarsely it
will
quantization
how
much
for
the basis functions is indicative
quantized
2.4. The larger the basis function, the will
more
using the luminance Q-Table
quantized and the more
each
block has been
smaller
information
scaled relative
larger the basis functions in the
of
how that
shown
in Fig.
finely the signal will be quantized and the less
be discarded. In comparison, the be
the JPEG
by
in Fig. 2.5. In this figure, the 64 DCT basis functions from Fig. 2.2
DCT basis function
information
proposed
upper
left
the basis function the more
will
to each blocks portion of
The
be lost.
the
amount of
relative size.
figure
Notice
are compared
to
the other basis functions.
The
actual equation
corresponding nearest
integer
quantization
the
follows:
indices
used
are the
=
Integer Round
to locate the
FDCT
this the
case
quantization
the Q-Table
coefficient
is then
rounded
fF(u,v) l
specific elements
coefficients and
Q(u,v)
operation of
are
the
by
the
to the
(2.3)
l.Q(u,v)
The dequantization is the inverse the same two
FDCT
the entire operation can be expressed as
Q-Table, F(u,v)
uses
each
number
in the Quantization Table.
Fq(u,v)
where u and v are
is to divide This
element
and
for
in the 8x8 FDCT block
and
the Q-Table values.
quantization process.
This step
tables as are used for quantizing the FDCT coefficients.
values are multiplied
by the IDCT coefficients.
This
can
be
written
In in
following form:
Fc? (u, v)
where
IDCT
u, v,
and
Q(u,v)
=
(2.4)
Fq(u, v) Q(u, v)
are the same variables as specified
coefficients.
10
previously
and
Fq(u,v)
are the
il______i
i"
'1.
.._'___
SiSllllSl|l|liSll MM
r
'I JBh
1 1
I
10*1
4
'
will 4
ii rr
IH
m fcW
__OCI
il IBEHSSBS
Mi .
SSf
lliili
a__-_______-aa^|"*^1t^^
Fig. 2.5 Quantization Scaled DCT Basis Functions.
11
The Q-Tables of compression
much an
image
all of
scaling
instance,
are a vital part of
achieved, but because will
be
the elements in the Q-Tables
a constant greater
more
decrease
be
compression.
be
no
compression
in
possible
Q-Table
values should
finely,
be larger
all of the Q-
Multiplying all of the elements by
deals
with
and
with
data
its
lossy as
Basically,
this
step
is
image is
compression
visually lossless
no round-off
referred to as
error
free, it is
minimal.
lossless
not used
Therefore,
most
lossy compression. lossy
which there
is
algorithm.
no perceptible
compression and results
compression occurs with no
in
a
distortion in the image
experiment performed
for visually lossless JPEG
for this
compression.
Decoding
algorithm
according to image works
is
step, is a
in
Walowit 1990). The first
and
assuming
often referred to as
quantization
The final step in the Baseline JPEG coefficients and to encode them
is completely
what
determining levels
Encoding
of compression
compression of the
to perform
which a maximum
Huffman
space.
by
discard less information.
discards information in
quality (Gentile, Allebach, research
values.
compression
degradation in the image. This is known compression
the
to quantize the signal more
information lost. This type
Although lossless
Nevertheless, it is
of
be determined
factor (Wallace 1990). For
coefficients are not quantized at all,
The JPEG Baseline algorithm,
less
some constant
default
and will
extensively because the resulting
2.1.3.
of compression can
how
determining
Multiplying all of the elements by a constant less than one will
the Q-Table values
will
for
of the amount
than one will increase all of the Q-Table values and will, consequently,
information.
all of
error, there
thesis
by
hand,
smaller than their
However, if the DCT
image
provide a mechanism
to quantize the signal more coarsely, all
values should
discard
they
The level
compressed.
than their default values. On the other
Table
the JPEG algorithm, not only because
by
giving the
12
is take the
statistics so
most
that
quantized
they
will
FDCT
take up even
commonly occurring
sequences
of quantized
occurring
FDCT
sequences of quantized
Huffman encoding
English language letter like A be
assigns
This step is
coefficients.
might
coefficients the shortest code words.
or
E
might
a unique
similar
occur more
be
of
study known
Before the reorganized
in
actual
order
to
coefficients are given the
binary
taking
advantage of the
given a code word of
as
the least commonly
longest
code words.
codeword to each sequence of
frequently than others.
given a code word of
larger field
FDCT
Likewise,
010
fact that
For example, or
11
and a
a
letters in the
some
commonly occurring
less frequent letter like
1001 1 10 (Raisbeck 1965). These techniques
Q
are a part of a
information theory.
encoding
sequence
to take advantage of the
begins,
the quantized DCT coefficients are
compaction of
15
information that
*16
28
occurs
*"29
P// / / / / \/ / / / / / A 3
5
S
14
17
27
30
43
A
9
13
15
26
31
42
44
/////// \/ // / // A 10
12
19
25
32
41
45
54
11
20
24
33
40
46
53
55
/////// \/ / // //A / // ///P
21
23
34
39
47
52
56
61
22
35
36
46
51
57
60
62
36
^37
49
*"5Q
58
59
63
**64
Fig. 2.6 The
FDCT
Zig-Zag Ordering of the Quantized DCT coefficients.
13
following the DCT.
This
new
ordering is
shown
the upper left corner to the lower right comer.
lower
frequency
zeros after
values to
value
be
64
first. The higher
zig-zagging from the
sequence allows all of
frequencies,
which are
usually
all
encoded all at once.
coefficients
between neighboring DC
as an arrow
This encoding
to be encoded is the DC term and this
average value of the
correlation
encoded
can then
quantization,
The first
be
in Fig. 2.5
in that block. As
coefficients.
a
coefficient
a measure of the
there is a
Generally, result, the
is
amplitude of
fairly
high
the DC term
to be encoded is the current DC coefficient minus the previous coefficient.
The two category
values
and the amplitude of the term.
within
and can
or
is
converted to a category.
be both
MSB,
of
positive and negative.
The
range
category is the
DC
codelength and
shows
intervals
The total
categories.
Table 2.2 lists these in
images
is just
the JPEG committee.
luminance
and the chrominance
Next, LSB is
the least
calculated
amplitude of the
5.
56
by taking
DC term
and the previous
Using Table 2.1,
FDCT
significant
the combined for the final was
by
bits
either
analyzed
DC
or
LSB
written
most significant
how the MSB bits to
bits,
of the
encode a given
This table is based
a previous study.
on
the
Once again, this table
are separate tables
of the codeword must
difference
minus
To illustrate, if the
be
51,
1. The MSB
current
for the
computed.
The
and the
luminance DC
LSB
can
coefficient
the difference value or amplitude would
5 is in category 3. The MSB
the difference between 100000 and 101 is Oil. The final then be
on the powers of two
the positive difference between the MSB and the
coefficient was
a value of
based
number of
There
which
range that an amplitude
shows
values.
the
coefficients.
or the negative
codeword.
are
Table 2.2
statistical properties of a set of
a sample provided
how the
The category determines the
the codeword to be assigned.
codewords are assigned to the
are
The category is determined according to
falls in. Table 2. 1
the amplitude
range of values
falls
that are then used to assign the DC coefficient's code word
100011.
14
of
be
category 3 terms is 100
and
for this DC term
can
codeword
Table 2.1 Categorization Table for AC Range 0 1 -1,
I
-3,-2, -7,
...,
-4,
-15,
...,
-8,
-31,
...,
-16,
-63,
...,
-32,
-127,
...,
-64,
-255,
...,
-128,
-511,
...,
-256,
-1023,
...,
-512,
-2047,
...,
-1024,
-4095,
...,
-2048,
-8191,
...,
-4096,
-16383,
...,
-8192,
-32767,
Category 0 1
...,
-16384,
and
DC
DC Coefficients
Category AC Category 0
N/A
1
1
2,3
2
2
7 4, 15 8, 31 16, 63 32, 127 64, 255 128, 511 256, 1023 512, 2047 1024, 4095 2048, 8191 4096, 16383 8192, 32767 16384,
3 4
4
5
5
...,
...,
...,
3
6
6
7 8
7
9
9 10
...,
10 11 12
...,
13
13
...,
14
14
15
N/A
...,
...,
...,
...,
...,
...,
...,
8
11
!
12
Table 2.2 Baseline entropy encoding table for DC terms. Luminance Luminance Chrominance Chrominance Codelength MSB of Codelength MSB of Codeword Codeword 2 00 2 00 4
010
3
011
4
10
100
4
5 6 7
5
8
110
110 1110 11110
6
10
1110
6 8 10 12
111110
7
12
11110
14
1111110
8
14
111110
16 18
11111110
2
3
101
9
16
1111110
10
18
11111110
11
20
111111110
The 63 AC terms
are encoded
the amplitude and category encoded.
information,
This is done because,
quantized a
majority
of
using
as was
number of zeros
previously stated,
1111111110 11111111110
scheme, but in addition to
proceeding that term is
once
j
111111110
20 22
a somewhat similar
the
01
also
the DCT terms have been
the AC coefficients are now zero. This variable length encoding
uses the number of zeros
proceeding the term,
or runlength, and the
15
category
of the
AC
determine the
coefficient to
AC
coefficient
is just the
The
coefficients.
preceding the category the
runlength can
runlength and
There
amplitude
depending JPEG
0
or
differential encoding is
by
of the
coefficient
EOB
category
two other
remaining
simply counting the
AC term is determined
falls in. The
on whether
has
values would
15
process
be
used
special code words.
The
in the block
is based
One
15. Once again, there
are
15
by of
AC term
on the same
possible sizes of
This is known
is for
for
encoded
details to
other operations
but this level
of
the negative difference
bits from the Huffman
At this
attend
of
point the
suffices
use with
minus
The
the JPEG algorithm. Due
The LSB
can
of the
and the
1.
encoded
DC
and
image is maximally
for this
of
AC terms
compacted.
are joined
There
format, byte-stuffing,
are
and
research.
Image Compression
When the final bit string has been
has
AC term
two different tables to be used
to such as establishing a storage
detail
the
as
they are listed in Appendix A for reference. These tables
or as
numerous other
Measures
an
by taking either the positive difference between the MSB
together into one bit string.
compression that
which
the special code words
are zero.
other special code word
provided two example tables
determined
From here the
2.1.4.
number of zeros
by finding
then be used to determine the MSB of the AC coefficients code word.
amplitude of the
for the AC
the block contains luminance or chrominance information.
to the size of these two tables,
codeword are
used
of the
to look up the MSB of the
possible runlengths
coefficients
codeword.
and a runlength of
committee
computed
consists of
are also
signifies that all of the
block
no
the code word. The amplitude
of
determining the DC categories and is also shown in Table 2.1.
This table
code word.
be
AC
bits
that term;
The category
amplitude of the
Then the
end of
value of
coefficient.
table used for the
codewords.
most significant
assembled
occurred as a result of the
16
it is
JPEG
possible
to determine the amount
algorithm.
For this research, four
different are
measures were used to assess
the final bit size of the
image,
compressed
The final memory
and
computed
image
These
compression.
measures
image, the compression ratio, the number of bits per pixel for the
the number of bits per minute squared for the
compressed
the compressed image is nothing more than the
size of
in bits that the
measured
the resulting
compressed
image took
The
up.
size
in
image. computer
compression ratio was
by dividing the number of bits in the original image by the number of bits in the image. The is
compressed
can
be formulated
Compression Ratio
as
follows:
=
-
(2.5)
-
Bits in Compressed Image
The resulting of
value can range
4 to 10. No
Likewise
an
one to some
in the image
compression
image
from
compressed to
half the
large
positive
would correspond
size of
number, usually in the range
to a compression ratio of one.
the original would result in
a compression
ratio of two.
The bits
1990). To
per pixel measure of compression
compute
image is divided
the
number of
,.
.
channels.
as was
The
,
original
compression
monitor.
the
=
image has
bits
from
a
eight
(Rabbani
the number of bits in the compressed
This
can
be
written:
little
number of
refers
per pixel and
after
under one
that avoids the ambiguities of
(2.6)
actually
pixels
bits
per minute squared
In this case, the
another simple quotient
Bits in Compressed Image ^ Number of Pixels
previously mentioned,
values can range anywhere
Lastly,
per pixel
by the number of pixels in the image.
Bits / Pixel
Remember,
bits
is
to
about
has been
17
by
JPEG
two and a
compression the
half.
suggested as a measure of
pixel size and
bits is divided
to the individual pixel
the
distance
of observer
image
from the
number of pixels as was
done
for the bits
per pixel computations.
This
minutes squared.
can
be
Then,
this value is multiplied
by the size of one pixel in
expressed as:
Bits/Mlule==!^E^p.e|s.e.MBfcl
Number
This
image
measure of
compression
This is important because the conditions
but only
image
an
original size and still
is independent
perceived
quality
of
of pixel size and
viewing distance.
the image is dependent on the viewing
be
can
compressed anywhere
be visualy indistinguishable from the
from a quarter to original.
an eighth of the
Further
compression
is
by sacrificing image quality. Therefore, a compression of 2 bits/pixel can
usually be
achieved with
image
is
size
Pixels
(Klein 1992).
Typically,
possible
of
one of
little
or no
loss
of
image fidelity. This dramatic
reduction
the major reasons that JPEG is used so extensively in many
in
imaging
applications.
2.2. Color Spaces
The JPEG committee, space
for
use with
JPEG
previously stated, did
Initially,
the algorithm.
as a standard color
was used as the
as was
the YCbCr color space was considered
space, but this idea was abandoned.
default
color space
not select a standard color
for much
However,
for
use
the YCbCr color space
of the experimental research carried out
by the
committee.
There has been affects the
a
limited
compressibility
amount of research on
of color
images. Although,
how the
given the
use of other color spaces
drastic differences among
the various ways of representing color, it seems unlikely that there would be no
among the
color spaces.
better than the RGB
In fact, the XYZ
color space
for image
and
YCbCr
color spaces
compression
18
(Ylakoski
have been
and
differences
shown to
Ronngren 1992
be
and
Peterson, Peng, Morgan, been
shown to
Allenbach,
be
and
and
Pennebaker 1991). Moreover, the CIELUV
a good color space
Walowit 1990).
for the
quantization of color
Therefore,
selection of a given color space would
the initial
have
color space
has
information (Gentile,
hypothesis
was made
a significant effect on the
that the
resulting
compression.
The
various color spaces
These divisions
categories.
and non-linear
spaces,
disadvantages for computational
also
are
currently device
transforms
of
color
device
spaces, linear transforms
and visual
The
uniformity (Kasson
main
and
the additional considerations of channel redundancy and
The
six color spaces selected
CIELAB LCh, color spaces
these
and
is the
for this
international
sections provide some
background
transformations to each of these color
brevity,
the inverse
An
trade-offs are between
Plouffe 1990). There
reasons
are
for selecting these
these color spaces.
on each of these color spaces.
spaces are also
be
In addition,
The forward
For the
presented.
sake of
in Appendix C.
the device color space for the CRT is the RGB or
In this
defining the color image. interface
space
are advantages and
the currently available color spaces. The
color space transformations are given
example of
color space.
space.
color
Device Color Spaces
2.2.1.
Blue
use of all of
device
RGB, XYZ, YIQ, CIELAB,
the CIELUV color spaces. One of the main widespread
of
ease of sub-band coding.
research are the
six spaces provide a good cross-section of
following
There
color spaces.
each of these three categories.
complexity
be divided into three different
available can
color
This
space, the RGB
color space
is
values are
used as an
simply the digital
input to the CRT
and therefore no additional computations are needed to
In comparison, any
before it
can
other color space will
be displayed. Regardless
signal
and
counts
processing
display an image in RGB
have to be transformed back into RGB
of this advantage, the
19
Red, Green,
RGB
color space
is
not
very visually do
space
uniform.
means that equivalent steps
in different
not correspond to equivalent perceived changes
is very
color space
three channels
correlated and there
(Limb, Rubenstein
device dependent color
This
and cannot
be
and
is
a considerable
in
RGB
areas of the
Likewise,
color.
redundancy
of
the RGB
information in the
Thompson 1977). Lastly, the RGB
directly displayed on any other device
color
color space
without
is
altering the
fidelity of the original image. The RGB
monitor corrected
counts used to
CRT, like the space
is
correct
now
RGB
drive the
a
and
gamma,
RGB
on color
spaces, the raw RGB
2.2.2.
color space will
remainder of
be the
one that
raw
spaces,
RGB
account certain
space can
CRT
are
digital
features
of the
be derived. This RGB
values.
derived
The terms when
and
color
needed
to
the monitor
is
this section on color spaces, the monitor
is
color space will
Although
being utilized. be the
is
one that
after
this section
meant when the
RGB
mentioned.
Linear Transforms
An
RGB
a new
other
color space consists of the actual
and gamma of the
corrected
is
RGB
linear transform away from tristimulus
(Motta 1991). For the
color space
raw
However, by taking into
monitor.
gain, offset,
only
The
space.
for the gain, offset,
calibrated
be further divided into two
color space can
example of a
of
Device Space
linear transform
of
the device color space is the CIE XYZ or
tristimulus color space. Extensive research has shown that the human visual system uses
three different types of cones to perceive color. sensitivities
has
proven
to be an
Direct
measurement of
matching functions. These themselves,
are a
color
matching functions,
linear transform
for determining if two
Therefore, in
elusive and problematic goal.
several elaborate psychophysical experiments were conducted
while not
of the cone sensitivities
colors match or not.
Essentially,
20
these three cone
in
order
the 1930s
to derive the color
the actual cone sensitivities
This
color space
is very
useful
the products of a given spectral
power
distribution for
matching functions Previous
can
illuminant,
an
be integrated to
for
a reflectance curve
yield three
values, the
has demonstrated that the CIE XYZ
research
the CRT's monitor corrected RGB space (Motta 1991).
necessary to
convert
from RGB to XYZ
calibrating the CRT. This and the method and
transform derived
The R, G,
and
B
between 0
and
1
in lux. The 3x3 RGB
space.
the RGB
A
be
3x3
17.50
Y
9.68
35.36
4.82
Z
0.71
5.36
62.90
linear transform
a
exact
used
linear transform
by
colorimetrically
for this thesis
research
in Appendix D. The form
of
of
actual
the transform is:
(2.8)
green, and blue digital counts for a given
pixel normalized
the units for the XYZ values listed inside of the matrix are measured
matrix shown above can then
The XYZ
space
is
second example of a
This
expressed as a
be inverted to transform from XYZ back to
somewhat more
color space
is
3x3
matrix
linear transform used
visually
computing the
computed
beginning
going from
uniform and
matrix transform used
is
as
of
less
color space
is very closely
this section.
space
The
NTSC RGB
YIQ
redundant
than
is the NTSC
YIQ
to
follows:
21
since
related
to the YCbCr
color space can
space
(Buchsbaum 1987).
However,
method was used
device
and
a standardized
same values.
the second
of a
for television
3x3 transform going from XYZ to YIQ
been
is
is determined
matrix and the equation
18.78
color space mentioned at the
means of
The
are outlined
X
are the red,
space
for the CRT
process was carried out
written as
again
X, Y and Z values.
space.
color space.
a
back
the results of the calibration
can
and
and
sample, and the color
a
to
YIQ
Both
be
space or as
are equivalent
the CIE XYZ values had already
compute
the
YIQ
values.
The
exact
3x3
Y I
0.000 1.000 1.389 0.827 0.453 0.938 1.195 0.233
Q
The inverse
of the above matrix will go
space, the
color
YIQ
redundant.
The
band
for transmission
coded
2.2.3.
YIQ
color space
The CIELAB
space
However, it is
CIELAB
color space are
a given color
given color
in
and a negative
a*
is
L*,
bluish
first be in XYZ
space
visually
additional
back to XYZ. Like the XYZ considerably less
meaningful and
feature that it
can
be efficiently
sub-
Device Space
an example of a nonlinear
is among the
a*
a*
and
visually
Likewise,
The
uniform color spaces
The three
axis or
L*
currently
coordinates of the
represents
how light
coordinates are rectangular coordinates that
lightness. A
In
transform of the device color
complex.
b*. The lightness
b*
colors.
space.
most
computationally
and
greenish colors.
b*
of
somewhat
is. The
more
has the
a plane of constant
and a negative
should
little
YIQ
purposes.
color space
available.
dark
a
Nonlinear Transforms
The CIELAB space.
is
space
from the
(2.9)
positive
a positive
a*
b*
locate
a
corresponds to reddish colors
corresponds to yellowish colors
order to convert to the
following
or
CIELAB space, the
transformations will then yield
colors
CIELAB
coordinates:
1 L*
L*
=
=
I
i
-
VYnJ
0.008856
=
500
=
200 ,Yn>
22
(2.10)
0.008856
(2.11)
UnJ
(2.12)
Yn
KXnJ b*
>
7.787^1 + -^ for Xn VXny 116
=
.Xn,
(2.14)
Xn
0.008856
(2.16)
Yn
YA
for
+
KYnJ
116
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22 ,
'ftftftft
discussion be
should
be focused
in this
examined
RGB
improvement in
Channel
The issue color spaces.
RGB
and
redundancy
of
deviations for
hue information. Lastly, there
for
be
if a color
and the
of the
space of other than the
compression.
of channel
redundancy
was noted
this aspect of color spaces
color spaces performed so poorly.
information in the three
briefly
in the Background
one of the significant reasons that the
In
order to provide some measure of the
channels of each of the color spaces, the standard
each of the channels were computed
between 0
and
255. The
section on
is
separately for the fruit image. Before
this calculation was performed, the pixel values for all of the color normalized
L*
be brief discussion
will
attained
of
will
Redundancy
However,
XYZ
redundancy, the perceptual uniformity
compression that could
color space was used
4.3.1.
the specifics of the results. Three specific topics that
section are channel
problem of quantizing polar percent
on
standard
deviation
images
were
using the
usual
space
was then calculated
equation:
Standard Deviation
where
value
X is the
for that
mean pixel value
channel.
fruit image. The
This
value of
summed and each of the
converted the standard
percentages can
for
((lr\
a given channel and
calculation was repeated
the
standard
individual
deviation
HA2
X2J-(xf I
=
deviations for
standard
values
to
for
X
(7.11)
is the
each of
the three channels of the
each of the three channels was
deviations
was
divided
normalized percentages.
be found in Table 4.11.
66
mean squared pixel
by
this total.
then
This
The resulting list
of
Table 4.11 Normalized Standard Deviations for Each of the Individual Channels for the Different Color Space Representations of the Fruit Image. Channel Three Color Space Channel Two Channel One LAB
61.86%
17.69%
20.45%
LCh
40.31%
18.55%
41.14%
LUV
67.94%
17.69%
14.37%
RGB
28.50%
39.47%
32.03%
XYZ
35.38% 61.28%
35.33%
29.29%
28.08%
10.64%
YIQ
As
be
can
color space representations of the
XYZ
suggests
majority
of their
most of the
hab
is
that there
Future conversion.
large
as the
in
one channel.
and
The
L*
variation.
XYZ
and
YIQ
equal.
Y
have
a
channels contain
in that the
values are unusual
In this case, this large hab-
This
color space
color spaces
and
and
This
value
will
for the
be further
following section on quantizing hab. these
conversion
color spaces
is
(Pratt 1971).
This
space
to the Karhunen-Louve color
an orthogonal transformation
uncorrelated channels and an optimal
independence for
for the RGB
approximately
L*
as a result of the polar nature of
The Karhunen-Louve
channels
would
distribution provide
a
of
energy in
base level
that
results
each of
the
of channel
comparison purposes.
Uniformity
Perceptual
of the major
is the way in
true in the
concentrated
as
channels
redundancy in the RGB
research could also compare
in statistically
One
is
is occurring
demonstrated in the
spaces
are all about
information for these images. The CIELAB LCh
channel
4.3.2.
a considerable
deviation
channel variation
three
fruit image
In comparison, the CIELAB, CIELUV
representations.
hab
in Table 4.1 1, the deviations in the three
seen
expansion of
Eqns. 2.10
uniform than
Y. The
L*
differences between the
which
defining L*,
of
nonlinear color spaces and
transformed. the lightness information was
the darker
and
2.11,
extent of
regions or shadows of
were
derived
this transformation
67
so that
it
in terms
the
of
This is especially
images.
would
be
the other color
The
more
equations
perceptually
CRT luminances may to be
from those two
obvious
This figure counts to
from Y to L*.
shows the conversion
Y in the lower right L*
digital
counts
a normalized
expands
arrow
until
left
of equivalent
The
linear red, green,
right
upper
was generated
from
L*
digital
that the bottom 20% of the digital
128. This
over
means
at
will
in
100
51
on
more
a more
L*
scale.
the RGB axis and circling the
back to 51
be
normalized
on the
RGB
accurately
perceptually
This
axis.
quantized
count trio of
This is
origin
in
and the
shown
blue
51 transforms to count
triplets
in Fig. 4.9
lightness information
Transform Jones Diagram.
68
normalized
additional precision means
uniform manner.
L*
to
as an
a counter-clockwise manner
r
Fig. 4.9
blue digital
matched red, green, and
L*
a
in Fig. 4.9.
quadrant shows the conversion
the conversion from
quadrant shows the conversion
and
Notice that
comes
compressed
Jones diagram
quadrant shows
to occupy over 50% of the
shadows
a
directly to normalized L*.
starting
it
from trios
quadrant.
and the the upper
The lower left
Therefore,
equations.
that the will
be
4.3.3 Quantization
The
Polar
of
hab Information
CIELAB LCh
main reason that
CIELUV
color spaces was
generated
high frequencies in the data
image. One polar
b*
coordinates
represent
between the
quadrant of
0
between
alternate
into
of
hab-
did
not
do
as well as
This is because the
even when
there was
the CIELAB and
hab
polar nature of
none present
in the
original
that is easy to imagine is for reddish pixels that happened to fall along the
case
discontinuity
positive
because
space
a
the high
CIELAB
and
high
positive
frequency
would
shifts
frequency hab
-negative
Small
space.
360. This
a*
b*
quadrant and the positive
variations could would cause the
transform a low
frequency
in hab- Consequently, it
data than it
shifts
hab
to
in CIELAB
would take more
would to represent the
a*-
lower
bits to
frequency
CIELAB data.
However, it is likely 360
discontinuity
at
generation of
high
achromatics.
An
and
are
that blocks containing pixels on both sides of the
fairly
uncommon.
frequency hab
example of
pixels at the
of the
top
be
RGB
4. 10 is just the hue
RGB 8x8 blocks
compressions to
as a result of minor variations
This flowchart is
original source
of Fig.
at
more probable case would
this is illustrated using a flowchart
decompression in Fig. 4.10.
2.13 and, in fact, the
data
Another,
the
compared.
top It is
of
pixel
similar
block is the
angle plane of
evident the
hab
the
This is
also
representations of
This
shift
the
true
when
original
the
hab
plane
hab
compression
same.
The
hab
block
of
8x8
allows the results of the
two
the original
data
representation of
green, or blue pixel
compared
to the XYZ and CIELAB
RGB data in Fig. 2.12.
to higher frequencies is because the CIELAB coordinates of original near
achromatic triangles were scattered around
widely in
is
a region of near
to the one presented in Fig.
definitely exhibits higher frequencies than was present in original red, planes.
be the
the CIELAB LCh representation
This
Fig. 2.12.
of
in
hab
polar
the CIELAB origin.
order to represent these near achromatics.
69
This
Consequently,
the
made
the
hab
vary
final bit string for
85.6
85.6
85.6
85.6
85.6
85.6
85.6
-33.1
250.8 215.2 189.1 177.5 208.7 240.7 212.
85.6
85.6
85.6
85.6
85.6
85.6
-33.1
-33.1
191.0 231.3 208.5 213.7 222.6 212.5
92,
106.9
85.6
85.6
85.6
85.6
85.6
-33.1
-33.1
-33.1
210.3 165.3 231.6 255.6 232.8
69.0
73,
104.1
85.6
85.6
85.6
85.6
-33.1
-33.1
-33.1
-33.1
224.1 219.7 177.9 233.5
88.6
64.9
87
99.2
B5.6
85.6
85. 6
-115.1
-115.1
-33.1
-33.1
-33.1
240.5 229.9 221.1
28.3 104.2
91
108.7
85.6
B5.6
-115.1
-115.1
-115.1
-115.1
-33.1
-33.1
220.4 230.1
5.6
16.5
0.0
29.9 121
94.5
85.6
-115.1
-115.1
-115.1
-115.1
-115.1
-115.1
-33.1
191.8
0.0
38.8
6.2
9.3
26.1
23
78.4
-115.1
-115.1
-115.1
-115.1
-115.1
-115.1
-115.1
-115.1
0.0
49.4
0.0
5.6
29.9
27.0
17.5
Normalized
hab
128 Subtracted.
with
0.0
Reconstructed Block Normalized
hab
of
82.6
8x8
pixels.
?
FDCT
IDCT
\r
+
128
-54.5
270.0
91.4
28.4
0.1
8.6
6.6
2.2
-51
270
96
47
0
0
0
0
494.4
59.3
-192.8
0.0
-40.7
0.0
-10.6
0.0
486
63
-182
0
0
0
0
0
-91.3
-123.9
-100.3
70.2
37.7
13.8
-0.2
3.2
-96
-130
-112
99
0
0
0
0
34.9
0.1
151.3
59.3
-56.2
-0.1
-18.8
-0.1
47
0
198
99
-99
0
0
0
-0.1
-22.4
-37.9
-45.6
-100.3
30.6
15.9
4.5
0
0
0
0
-99
0
0
0
22.8
-0.2
9.1
0.0
83.2
59.6
-12.6
0.2
0
0
0
0
99
99
0
0
-6.4
-6.8
-8.7
-15.8
-19.5
-100.5
10.7
0
0
0
0
0
0
-99
..0
0
-3.6
0.2
17.0
-0.0
-8.1
-0.2
52.6
59.2
99
99
Decoded
Forward Discrete Cosine Transform Coefficients
Quantize
and
Dequantized Values
Dequantize 0
-3
15
4
1
0
0
0
27
3
-7
0
0
0
0
0
10011100000011100100101
-5
-2
1
0
0
0
0
10100111000110101000111
-4
1
0
2
1
-1
0
0
0
01000010100100111111011
0
0
0
0
-1
0
0
0
10111101011001011101111
0
0
0
0
1
1
0
0
11100101111010011110011 111010111110100110101011
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
1
1
Huffman Encoded Bit Stream
FDCT Coefficients Quantized
Using
Chrominance Q-Table
for the compression and decompression of a the same RGB blocks shown at the top of normalized 8x8 block of hab pixels based on the page and decompression Fig. 2.12. The compression steps are shown going down
Fig 4 10
Computational
steps are shown
0.0
example
going up the
page.
70
the
hab
compression shown
compression was
using the
4.3.4.
in Fig. 4.10 is
over
only 12 bits long. This is
120 bits long.
a clear
In comparison, the
demonstration
of the
inefficiency
b*
of
hab representation for JPEG compression.
Improvement Over RGB Compression
The
first
results of the
dependent algorithm, but is
experiment showed that not
also a color space
dependent
only is JPEG
algorithm.
image
an
The possibility
of
improving the JPEG compression based on color space selection was investigated using the visually lossless thresholds derived RGB
had the highest threshold.
compression
improvement in
during the first experiments.
compression will
be
Therefore,
made relative to the
The first step in comparing the different compressed the
Specifically,
the compressed threshold
image data
P
can
image. The
be
image
exact
can
This the
P is the
'Bits in
Compressed Image
the
for the RGB
of the other color spaces.
image
relative
original size
for
of the
expressed as a
is to determine how original
fraction
image.
or percentage
compute this percent reduction
in the
This
that the threshold
all of the
yielded a
images
(7.12)
,
images
difference in
71
for
all of
from
the
all of
compressed
color spaces.
the percentages
percent reduction over
space compression.
and also averaged
image has been
for
and
compression was subtracted
to the RGB color
differences for each
in
color compression.
100
=
percent of
cases, the
written:
calculation was performed
percentage
be
of
majority
all of the comparisons
color spaces
formula to
Bits in Original Image
where
a
threshold image for that color space was relative to the
of the size of the original
original
RGB
In
Table 4.12 lists
all of the color spaces.
to.
Next, for
all
the original
all of
these
Table 4.12 Percent Improvement over RGB Compression. Percent Percent Percent Percent Difference Difference Difference Difference for Birds for Fruit for for Pasture Musicians
Color Space
LAB
8.1%
14.2%
8.8%
13.2%
11.1%
LCh
7.5%
14.5%
3.8%
-2.9%
5.7%
LUV XYZ
9.8% 7.2% 7.7% 8.1%
13.1%
9.4% 3.4% 6.8% 6.4%
YIQ Average for Each Column
Based color spaces
CIELAB
the
on
did
at
RGB. The XYZ
11.0% 12.7% 13.1%
values
for the
the
color
YIQ
compression was
compression was
5% improvement. The last each of
and the
dependent
row
in forth
RGB
provided
It is
case, the images
Baseline JPEG
basis
10.2% 7.2%
9.6%
9.2%
7.1%
8.7%
color space
over
were
for JPEG
a close third with a
and the
CIELAB LCh
interesting
to note
musicians
all of
compression.
over
in fifth
with
space was
that,
on
over
RGB
averaged
the average, using a
compression
image. Of course these
according to the level
algorithm.
72
of
The
9% improvement
for the fruit
conclusions are
compression. of the comparisons and the conditions of the
were compared
the
10% better than the RGB
the most improvement in
least improvement for the
on the
in
8.4%
in Table 4.12 lists the improvement
the columns in the table.
color space other than
image
compressions
7.1%
differences in Table 4.12,
overall percentage
least 5% better than the RGB
CIELUV
and
compressions and
for
Overall Percent Difference
visually lossless
In this
compression
for
Conclusions
5.
The
results of both of the pyschophysical experiments and the numeric measures of
indicate that
error
compression.
Color
color spaces
tested.
CIELUV
YIQ
and
There
The device
color spaces were
for visually losseless
information
research
issues
some color spaces are
in
which
compression
Tables
in
to
customize
The
results of
could
plane.
be
by
used
this
Another
all
be
worst
the six and
for JPEG image The
and
CIELUV
of compression,
the XYZ
CIELAB
Finally, CIELAB LCh space.
as a result, the
interesting
addressed.
compression
First
was
very
The
hab
CIELAB LCh
than others.
Altering
results, but there are still a
of all, the
However,
possibly be
JPEG
as this research
Regardless,
enhanced
algorithm
is
has shown,
there are other
to be more conducive for
the Q-Tables or modifying the Huffman
be
made to the
JPEG
algorithm
specific color space.
research suggest
altering the
for
higher levels
efficiently and,
produced some
use as a color compression space.
compression
at
possible changes which could
it for a
of
bit.
algorithm could
two
the
a poor color compression
compress
a given color space.
are examples of
order
better for
was
and worse than
component color space.
the JPEG
in
However,
and problems to
designed for any three
ways
has
best
the RGB space produced intermediate results.
a good and
compression ranged varied quite a
multitude of
RGB,
space,
better than RGB
very difficult to
This thesis
color
performed the
difference between the CIELAB
than the RGB compression.
both
and was
was
of
compression.
color space was worse
inconsistent
CIELUV
and
was no significant
Linear transforms
XYZ
CIELAB
spaces such as
color spaces.
compression.
for JPEG image
nonlinear color spaces are the preferred color spaces
that tristimulus space
It may be
quantization scheme.
three planes or the
option would
be to
possible
very
efficient
for
For instance, the Luminance Q-Table
the tristimulus
73
not
to improve the tristimulus
chrominance plane could
convert
is
be
applied
data from XYZ to
to
just the Z
Yxy
and the
quantize the
Although, would
Luminance-Chrominance-Chrominance
a
the results do not indicate how much
have
yielded.
the XYZ scheme the
data according to
Yxy
It
used
seems
improvement these
of an
alternate schemes
likely though that these schemes could not be any worse than
for this thesis
and
any better than the
compression achieved
using
YIQ color space. The
compression
efficiency
of the
CIELAB LCh
changing the
hue
representation of
angle or
the other nonlinear color spaces.
hab
of the
first
hue information
as
pixel
AH*
Similarly, based
in
One
or the
altering the way in
possible method of
block
a given
and then
on observer
feedback
in the image is
supported
by the magnitude of chroma errors
could
gained
by
performing
chroma colors.
other color spaces although
transformation would
further
possible
b*
wider range of color spaces.
would produce results similar
research.
More
of
it is
for
be to
encode all the
level
of
encode
remaining
value.
would appear
that the loss
of chroma
is
also
listing the colorimetric errors
be
compression
the color channels
run
through a quadratic or
would assign a
could also
before
be
higher priority to
used with
any
of the
be necessary to determine if this
compression.
expanding the
testing.
It
to those of the
research
This
quantized.
this would
scope of the
investigation to include
For example, the OSA, HSL, YCbCr, YES
color spaces are also available
for this
This
This strategy
by
improvement in the
planes could
experiments would
truly improve the
Of course there is the topic
used
and
possibly be done
This dramatic loss
in the Table 4.9
look up table before compressing them.
maintaining the higher
it
some sort of transformation on
a*
by
compression to the
doing
and comments,
images. A
compressing them. For instance, the cubic
which
differentially
definitely a noticeable error.
second set of experimental
be
could
hue difference from the preceding hue
of chroma
for the
This
improve the CIELAB LCh
additional computational effort could
be improved
space could also
determining a method of quantizing the hue angle plane.
the
scheme.
seems
likely
74
support
many
other
that these other color spaces
device, linear,
is necessary to
and
a
and non-linear color spaces
this hypothesis.
Lastly, compression.
the study could be expanded to cover a wider visual range of image
The
differences in the This for
results of
compression
the XYZ compressions suggest that there may be
depending on the extent to which the image is compressed.
would then raise the question of which color space
all
levels
of
image
visual
compression.
75
is
optimal
for image
compression
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J. L. Mitchell, W. B. Pennebaker, "Evolving JPEG Color Data Compression Standards", Standardsfor Electronic Imaging Systems, SPIE Optical Engineering Press, Bellingham, Washington, 1991, pp 68-97. J. L.
Mitchell, W. B. Pennebaker, JPEG Still Image Compression Standard, Van Nostrand Reinhold, New York, (1993). R. J. Motta, "An Analytical Model for the Colorimetric Characterization of Color CRTs", MS Thesis, Rochester Institute of Technology, Center for Imaging Science, (1991).
H. A. Peterson, H. Peng, J. H. Morgan, W. B. Pennebaker, "Quantization of Color Images in the DCT Domain", SPIE 1453 Human Vision, Visual Processing, and Digital Display II, 210-222 (1991).
W. K. Pratt, 992 (1971).
"
Spatial Transform Coding", IEEE Trans,
on
Com. Tech. COM-19,
980-
M. Rabbani, Digital Image Compression, Short Course Notes, Rochester Institute Technology, (1990).
of
M. Rabbani, P. W. Jones, Digital Image Compression Techniques, SPIE Optical Press, Bellingham, Washington, 1991.
Engineering
G. Raisbeck, Information Theory: An Introduction for Scientists
Press,
and
Engineers, MIT
Cambridge, Massachusetts, 1965.
J. C. Russ, The Image Processing Handbook, CRC Press, Boca Raton, 232-233 (1992).
77
SAS/STAT Users's Guide, Version 6, Forth Ed., 1071-1126 (1990). W. F.
Schreiber, Fundamentals of Electronic Imaging Systems, Springer-Verlag, New York, 1991, pp 104-133, 198-207. C. S. Stein, A. B. Watson, L. E. Hitchner, "Psychophysical Rating of Image Compression Techniques", SPIE 1077, Human Vision, Visual Processing, and Digital Display, 198-207 (1989). M. D. Stokes, "Colorimetric Tolerances of Digital Images", MS Thesis, Rochester Institute of Technology, Center for Imaging Science (1991).
G. K. Wallace, "The JPEG Picture Compression Standard", IEEE Transactions Consumer Electronics, 38 xviii-xxxiv (1992). G. K. Wallace "Overview of the JPEG (ISO/CCITT) Still Image Compression SPIE 1244, Image Processing Algoritms and Techniques, 220-233 (1990).
on
Standard"
G. Wallace, R. Vivian, H. Poulsen, "Subjective Testing Results for Still Picture Compression Algorithms for International Standardization ",GLOBECOM 88 1022-1027 (1988). G. Wyszecki, W.S. Stiles, Color Science: Concepts Formulae, John Wiley and Sons, 1982.
and
I. Ylakoski, H. Ronngren, "CIE XYZ Colour Space Targa Proceedings, 139-151.
used
78
Methods, Qualitative Data
and
for Image Compression", 1992
Appendix A.
Tables H.l
H.2 list the
lengths
various zero run
using the
and
tables was copied
lengths
and coefficient sizes
or chrominance
directly out of the
is only the length, in bits, code word
is
for both the length
not
derived
until the
most significant and
and
adding the
for AC terms. These
least
length for
altogether.
These two tables
that simply converted
Code
0/0 0/1 0/2 0/3
(EOB)
significant
significant
length 1,
from run length
5 7 8 10
code
length
are computed.
bits
be
can
size
7 term
The total
computed
value.
code
length
by taking the MSB
For instance, using Table
would
look-up
be 16 tables
word
1010 00 01 100 1011 11010 1111000 11111000 1111110110 1111111110000010
16 16
1111111110000011
4
1100
5 7 9
1111001
1/5 1/6
11 16 16 16
1/8
for the
bits
1/1 1/2 1/3 1/4
1/7
text
or code word and that the complete
Code
2 2 3 4
two tables
plus
7
or
23 bits
in the JPEG C
and size straight to the total number of bits.
4
0/5 0/6 0/7 0/8 0/9 0/A
actual
Encoding Table for Luminance AC Terms
length
0/4
The
are
derived
bits
the coefficient to that
a run
assigned to
tables were
images. There
coefficients respectively.
were then used to create
Table A_ 1. Huffman
be
1990 ISO/CCITT DRAFT. Notice that the
least
size of
code word
Run/Size
AC
for AC Terms
and code words that would
of the most significant
H.l the total
program
code
Encoding Tables
average statistics of large collection of experimental
for either luminance
code
Huffman
11011 111110110 11111110110 1111111110000100
1111111110000101 1111111110000110
79
1/9
16
11111111 100001 1 1
VA
16
2/1
5 8 10 12 16
11111111 10001000 11100 11111001 1111110111
2/2 2/3 2/4
2/5 2/6
111111110100 1111111110001001 11111111 10001010
16
2/7
16
11111111 1000101 1
2/8
16
1111111110001100
2/9 2/A
16 16 6
1111111110001110
3/1
3/2 3/3 3/4
3/5 3/6 3/7
3/8 3/9 3/A 4/1
4/2
4/3 4/4
4/5 4/6 4/7
4/8
4/9 4/A
5/1
5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/A 6/1 6/2 6/3 6/4
6/5 6/6 6/7 6/8
6/9 6/A 7/1 7/2 7/3 7/4 7/5 7/6 7/7-
7/8 7/9 7/A 8/1
8/2 8/3 8/4
8/5 8/6 8/7
1111111110001101 111010
9 12 16 16 16 16
111 1 101 1 1
111111110101 11111111 10001 1 1 1
1111111110010000 1111111110010001
1111111110010010 1111111110010011 1111111110010100 1111111110010101
16 16 16 6
111011
1111111000 1111111110010110 1 1111111 10010 111 1111111110011000 1111111110011001
10 16 16
16 16 16 16 16 16 7 11 16 16 16 16 16 16 16 16 7 12 16 16 16 16 16 16
1111111110101011
16
1111111110101100
16 8
1111111110101101
12 16 16
111111110111
1111111110011010 1111111110011011
1111111110011100 1111111110011101
1111010 11111110111
1111111110011110 1111111110011111
1111111110100000 1111111110100001
1111111110100010 1111111110100011
1111111110100100 1111111110100101
1111011 111111110110
1111111110100110 1111111110100111 1111111110101000 1111111110101001
1111111110101010
11111010 1111111110101110 1111111110101111
1111111110110000
16 16 16 16 16
1111111110110001
1111111110110010 1111111110110011
1111111110110100 1111111110110101
16 9 15 16 16 16 16 16
111111000 111111111000000 1111111110110110 1111111110110111
1111111110111000 1111111110111001
1111111110111010
80
B/a
16
1111111110111011
8/9 8/A 9/1
16
1 1 1 1 111 110111 100
16
1111111110111101
9
9/2 9/3 9/4
9/5 9/6
11111 1001
16
1111111110111110
16 16
1111111110111111 111111111 1000000 111111111 1000001 111111111 1000010
16 16
9/7
16
9/8
16
9/9 9/A
16
111111111 100001 1 111111111 1000100
16
111111111 1000101 111111111 10001 10 11111 1010
A/1
9
A/2
16
A/3
16
111111111 10001 1 1 111111111 1001000
A/4
16
111111111 1001001
A/ 5
16
A/6
16 16
111111111 1001010 111111111 1001011 111111111 1001 100 111111111 1001 101
A/7
A/8
16
A/9
16
A/A
16 10
B/l
16 16 16
B/2
B/3 B/4
B/7
B/8
C/1
16 10
C/2 C/3
16
C/4
1111111111011100 1111111111011101
16 16
C/8 C/9 C/A D/1
D/2 D/3 D/4
D/5 D/6 D/7
D/8 D/9 D/A E/1 E/2 E/3 E/4
E/5. E/6 E/7 E/8
F/5
11111 11111011011
16 16
C/7
F/
1111111111011000 1111111010 1111111111011001 1111111111011010
16
C/5 C/6
F/2 F/3
111111 1111010110 11 1 111111101011 1
16
B/9 B/A
F/1
11111111 11010001 111111111 1010010 1111111111010011 111111111 1010100 111 1111111010101
16 16 16 16
B/5 B/6
E/9 E/A F/0
11 1 1 1 11 1 1 10011 10 111111111 1001111 1 1 111 1 1001 111111111 1010000
(ZRL)
1111111111011110 1111111111011111
16 16 16 11 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 11 16 16 16 16 16
1111111111100000 1111 111111100001 11111111000 1111111111100010 1111111111100011
1111111111100100 1T11111111100101 1.111111111100110 1111111111100111
1111111111101000 1111111111101001 1111111111101010 1111111111101011 1111111111101100 1111111111101101
1111111111101110 1111111111101111 1111111111110000 1111111111110001
1111111111110010 1111111111110011
1111111111110100 11111111001 1111111111110101
1111111111110110 1111111111110111
1111111111111000 1111111111111001
81
F/6
16
F/7
16
1111111111111010 1111111111111011
F/8
16
1111111111111100
F/9
16
1111111111111101
F/A
16
1111111111111110
Table A.2. Huffman Encoding Table for Chrominance AC Terms Run/Size 0/0 0/1
Code
(EOB)
0/2 0/3 0/4
0/5 0/6 0/7
length
Code
2 2 3
00 01
4
1010
5 5
11001
100
11000
6 7
1 11000 1111000 111110100 1111110110 111111110100
9
0/8 0/9 0/A
10
12
1/1
4
1/2 1/3
6 8 9
1/4
word
1011 111001
11110110 111110101 11111110110
11
1/5 1/6 1/7
12 16
111111110101
1/8
16
1111111110001001
1/9 1/A
16
1111111110001010
16
1111111110001011
2/1
5 8
2/2 2/3 2/4
2/5 2/6 2/7 2/8 2/9 2/A 3/1
4/4
4/5 4/6-
4/7 4/8
4/9 4/A 5/1 5/2 5/3 5/4
5/5 5/6 5/7
10
1111110111
12 15 16 16 16 16 16
111111110110 111111111000010 1111111110001100 1111111110001101
1111111110001110 1111111110001111
1111111110010000 11011
11111000 1111111000
10
"
4/1 4/2 4/3
11O10 11110111
5 8
3/2 3/3 3/4 3/5 3/6 3/7 3/8
3/9 3/A
1111111110001000
111111110111
12 16 16 16 16 16 16
1111111110010001
1111111110010010 1111111110010011 1111111110010100 1111111110010101 1111111110010110
6 9
111010 111110110 1111111110010111
16 16 16 16 16 16 16 16 6 10 16 16 16 16 16
1111111110011000 1111111110011001
1111111110011010 1111111110011011 1111111110011100 1111111110011101
1111111110011110
111011 1111111001 1111111110011111
1111111110100000 1111111110100001
1111111110100011
82
S/8 5/9 5/A 6/1
16
6/2 6/3
11
1111001 11111110111
16
1 111 1 1 1 1 101001 1 1
6/4
16
11111111 10101000
6/5 6/6 6/7 6/8 6/9 6/A
16 16
1111111110101001 1111111110101010 1111111110101011 1111111110101100 1111111110101101 1111111110101110 1111010 11111111000
7/2 7/3 7/4
7/5 7/6 7/7 7/8 7/9 7/A 8/1
8/2 8/3 8/4
8/5 8/6 8/7
8/8 8/9 8/A 9/1
9/2 9/3 9/4
9/5 9/6 9/7 9/8 9/9
9/A A/1
A/2 A/3 A/4
A/5 A/6 A/7
A/8 A/9 A/A B/1
B/2 B/3 B/4 B/5.
B/6 B/7 B/8 B/9 B/A C/1
C/2 C/3 C/4
C/5 C/6
11111111 10100100 111 1 11 1 1 10100101
16 16
7
1111111110100110 .
16
16 16
16 7
..
11
16 16 16 16 16 16 16 16 8 16 16 16 16 16 16 16 16 16 9 16 16 16 16 16 16 16 16 16 9 16 16 16 16 16 16 16 16 16
1111111110101111
1111111110110000 mm moi 10001
1111111110110010 1111111110110011 1111111110110100 1111111110110101 1111111110110110 11111001 1111111110110111
1111111110111000 1111111110111001
1111111110111010 1111111110111011
1111111110111100 1111111110111101 1111111110111110 1111111110111111 111110111 1111111111000000 1111111111000001 1111111111000010 1111111111000011
1111111111000100 1111111111000101 1111111111000110 1111111111000111
1111111111001000 111111000 1111111111001001
1111111111001010 1111111111001011 11.11111111001100 1111111111001101 1111111111001110 1111111111001111 1111111111010000 1111111111010001
9
111111001 1111111111010010 1111111111010011
16 16 16
1111111111010100 1111111111010101
16 16 16 16 16 16 9 16 16 16 16 16
1111111111010110 1111111111010111 1111111111011000 1111111111011001
1111111111011010
111111010 1111111111011011 1111111111011100 1111111111011101 1111111111011110 1111111111011111
83
C/7
16
11 1 111 111 1 100000
C/8
16
C/9
16
1111111111 100001 1111111111 100010
C/A
16
1 1 1 nm ii ioooii
D/1
1 1
1 1 1 1 m 1001
D/2
16
111 1 1 1 1 1 1 1 100100
D/3
16
mi mi n iooioi mini imoono
D/4
16
0/5
16
1111111111100111
D/6
16
111111111 1101000
0/7
D/8
16 16
1111111 111101010
D/9
16
11 11111111101011
D/A E/1
16
1 1 11 1 11 1 11101 100
14
11111111100000
E/2
16
1111111111 101 10,1
E/3
16 16 16
11111 111 1 11011 10 1111111111101111
16
11111111111 10001
E/4
E/S E/6
111111 1111101001
11111111111 10000
E/7
16
1111111111110010
E/8
16
11111111 1111001 1
E/9
16
nn immioioo
E/A F/0 F/1
16
1111111 111110101
10
111.1 1 1 1010
15 16
1111 1 in i mono
(ZRL)
F/2
111111 111000011
1111111111110111
F/5
16 16 16
111111111 1111001
F/6
16
111111111 1111010
F/7
16
1111111111111011
F/8
16
F/9
16 16
1111111111111100 1111111111111101
F/3 F/4
F/A
.
111111111 imooo
1111111111111110
84
Appendix B.
JPEG C Code
/A************************************* /* /* /*
*/ file:
cexec_jpeg.c
Nathan
author:
/*
*/
Moroney
Mike
and
Stokes
*/
1/27/93
Date:
*/
/*
Mike
/*
Munsell
/*
Center
/*
Rochester
/*
Stokes
(
[email protected])
Color
Science
*/
Laboratory (MCSL)
*/
for Imaging Science Institute
Rochester,
*/ */
Technology
of
14623
NY
*/
/*
*/
/*
description:
/*
Baseline
/*
Forward Discrete
/*
*/
JPEG Program
/* /*
F(u,v)
1/4
=
/*
C(u)C(v)
*/
cos[(2y+l)vPI]/16
/*
Inverse
/*
Calculations
/*
f(x,y)
are
1/4 [
=
based
*
F(u,v)
on
the
*/
following
cos[
(2x+l)uPI]/16
This three will
program
channels
(L*,
Y)
/*
both
addition,
of
color
*/
*
*/ 16
the
and
is RGB.
X&Z,
will
into
i&q)
Otherwise
*/
the program
*/
the
first
table
for
the
channel
*/
two
*/
other
*/
.
work
only
vertically
*/ for
all
table
for
table
quatization
x&y,
program
image
space
]
Quantization
Luminance
quantization
u*&v*,
this
horizontally
sampling
the
chrominance
(a*&b*,
components
In
if the
the
and
use
luminance
the
use
will
*/
equation:
C(u)C(v)*
cos[(2y+l)vPI]/
/*
/*
*/
SUM(u=0-7)SUM(v=0-7)
/*
/*
*/
]
Discrete Cosine Transform
/*
/*
*/
cos[(2x+l)uPI]/16*
/*
/*
f(x,y)*
[SUM(x=0-7)SUM(y=0-7)
/*
/*
*/
image is first broken down into 8 by 8 blocks. */ These blocks are shifted from unsigned to signed integers first.*/ Calculations are based on the following formula: */ Input
/*
/*
*/
Cosine Transform
multiples
images
for of
8
(due
that to
*/
are
*/
the
8x8 blocks.
*/
/*
*/
(.include
# define PIE 3.14159265 /* Eight levels of Quatization */ # define P 8 # define HALFSCL 128.0 /* 128 for 0 to 255 images * images /
and
0.5
for
.
int cexec_jpeg(crs, crsimg_ptr win_ptr
win,
xfcn_jpeg)
crs;
win;
xfcn_ptr
xfcn_jpeg;
{ register
int xb,
int xtmp, ytmp; int tmp2 , width, int index ; int plane,
xp,
yb,
yp,
xt,
yt;
height;
11;
int qtabl_fact[8] [8]
,
qtab2_fact
[8] [8]
85
,
qtab3_fact
[8] [8]
;
0
to
1
float dctbasis[64] [64] /*
source
float
is
source
the
integer array
[8] [8] [3]
/*
/*
/*
qtcof
is the array
[8] [8] [3] ; quantcof [64] [3]
for
of
the
temp,
,
source
basis,
8x8
sum[3]
,
CC;
image block */
;
dctcof is the array float dctcof [8] [8] [3] ;
int int
idctbasis [64] [64]
,
dct
of
of
coefficients.
quantized
dct
'/
coefficients.
*/
qtcof
zzag[64][3]
;
is the
rearranged
(flattened)
array of quantized dct coefficients. the bit rate can be computed. */
int zzag[64] [3] ; int zagorder[64]
=
{ 18, 13, 28, 36, 30, 59, 54,
1, 25, 20, 21, 43, 23, 60, 61,
2, 33, 27, 14, 50, 16, 53, 62,
9, 26, 34, 7, 57, 24, 46, 55,
This
step
must
be done before
17, 10, 3, 4, 11, 19, 12, 5, 6, 41, 49, 42, 35, 8, 15, 22, 29, 58, 51, 44, 37, 31, 38, 45, 52, 39, 32, 40, 47, }; 48, 56, 63, 64
int DCLbitlut
[12] = {2,3,3, 3,3,3,4,5,6,7,8,9}; [12] = {2,2,2, 3,4,5,6,7,8,9,10,11}; int DCbitlut [12] [3 ]; 10, 16, 16, int ACLbitlut [16] [ io] = { ; 7, 3, 4, 5, 2, 11 16 16 16 16, 16, 9, 5, 7, 4, 16 16 16 16, 16, 10, 12, 16 5, 8, 16 16 16 16, 16, 12, 16, 16 6, 9, 16 16 16 16, 16, 6, 10, 16, 16, 16 16 16 16 16, 16, 11, 16, 16, 16 7, 16 16 16 16, 16, 12, 16, 16, 16 7, 16 16 16 16, 16, 12, 16, 16, 16 8, 16 16 16 16, 16, 15, 16, 16, 16 9, 16 16 16 16, 16, 16, 16, 16, 16 9, 16 16 16 16, 16, 16, 16, 16, 16 9, 16 16 16 16 16, 16, 16, 10, 16, 16, 16 16 16 16, 16, 10, 16, 16, 16, 16 16 16 16 16, 16, 11, 16, 16, 16, 16 16 16 16 16, 16, 16, 16, 16, 16, 16 16 16 16 16, 16 }; 16, 16, 16, 16, 16 9 10, 12, 6, 7, 5, 5, 4, 3, int ACCbitlut [16] [10] = { 16 16 12 11 16, 16, 8, 9, 6, 4, 16 16 16 16, 16, 10, 12, 15 8, 5, 16 16 16 16 16, 16, 12, 10, 8, 5, 16 16 16 16, 16, 16, 16, 16 9, 6, 16 16 16, 16, 16 10, 16, 16, 16 6, 16 16 16, 16, 16 11, 16, 16, 16 7, 16 16 16 16, 16, 16 11, 16, 16, 7, 16 16 16 16, 16, 16 16, 16, 16, 8, 16 16 16 16, 16, 16, 16, 16, 16 9, 16 16 16, 16, 16 16, 16, 16, 16 9, 16 16 16 16, 16, 16 16, 16, 16, 9, 16 16 16 16, 16, 16 16, 16, 16, 9, 16 16 16, 16, 16 11, 16, 16, 16, 16 int DCCbitlut
.
,
.
86
16, 16,
14, 15, int int int int
16, 16,
16, 16,
16, 16,
16, 16,
16, 16,
16, 16,
16, 16,
16, 16
};
ACbitlut
[16] [10] [3] ; {0, 0, 0}; numbits[3] {0, 0, 0}; numzero[3] {0, 0, 0}; DCprev[3]
=
=
=
intDCcur[3],
category [3 ] abszzag[3] int xc, yc, zc, count, twopow, DCflag, ACflag; int order, rangemax, zcount, bits, cat; int totalbits 0; absDCcur[3],
,
stop[3],
,
eob[3] ;
=
/*
dqtcof
is the array
float dqtcof [8] [8] [3] /*
lqtab_fact is
de-quantized dct
of
2D array that
a
coefficients.
*/
;
will
the
contain
pre-calculated
values
of
luminance
the
qtable
times
the
factor
quantization
(QFACT)
.
Similarly, cqtab_fact of
is
2D array that
a
chrominance
qtable
float lqtable[8] [8]
16.0, 12.0, 14.0, 14.0, 18.0, 24.0, 49.0, 72.0, }; /*
will
the
contain
pre-calculated
values
the
A
11.0, 12.0, 13.0, 17.0, 22.0, 35.0, 64.0, 92.0,
sample
the
or
float
10.0, 14.0, 16.0, 22.0, 37.0, 55.0, 78.0, 95.0,
times
the
{ 16.0, 19.0, 24.0, 29.0, 56.0, 64.0, 87.0, 98.0,
24.0, 26.0, 40.0, 51.0, 68.0, 81.0, 103.0, 112.0,
factor.
for
table
channel
for
a
40.0, 51.0, 61.0, 58.0, 60.0, 55.0, 57.0, 69.0, 56.0, 87.0, 80.0, 62.0, 109.0, 103.0, 77.0, 104.0, 113.0, 92.0, 121.0, 120.0, 101.0, 100.0, 103.0, 99.0 a
monochrome
device-
signal
independent
17.0,
18.0,
[8] 24.0,
= { 47.0,
99.0,
99.0,
99.0,
99.0,
18
.0,
21.
26.
66
.0,
99
.0,
99,
99,
99,
24
.0,
26,
56.
99
.0,
99
.0,
99,
99,
.0,
99,
47,
66,
99,
99.
99,
99,
99,
.0,
99,
99,
99.
99,
99.
99,
99,
99.
.0,
99,
.0,
cqtable[8]
.0,
.0,
.0,
.0,
.0,
.0,
.0,
.0,
,0,
.0,
.0,
.0,
.0,
.0,
.0,
.0,
.0,
.0,
.0,
.0,
,0,
.0,
99.
,0,
99.
,0,
99,
99,
99,
.0,
99,
99,
.0,
.0,
99,
.0,
99.
.0,
99,
99,
99.
.0,
99.
.0,
99,
.0,
99. 0,
99. 0,
99.
99,
,0,
99,
.0,
.0,
.0,
99,
,0,
,0,
99.
.0,
space.*/
.0,
99,
.0,
color
.0,
99,
99. 0,
*/
=
Quantization
Luminace
quantization
,0
}; switch
case
(crs->hdr.comp_type) CP_SHORT
"cexec_jpeg (NOT_OK) ;
crs_warn( return
{
: :
char
computations
not
yet
implemented");
:
long
computations
not
yet
implemented");
break ; case
CP_LONG
crs_warn( return
:
"cexec_jpeg
(NOT_OK)
;
break; case
CP_FLOAT
case
CP_DOUBLE
: :
87
width
11
.
(crs->hdr
=
crs->hdr
=
/*
(crs->hdr
=
height
A brief
image_width .
* .image_width
set
of
3)
image_height
3
hdr
pre-calculations
3;
.color_planes;
of
the
q-table
values
multiplied
times
the
quantization
factor
(QFACT)
.
This
is done to
make
the algorithm
for
little bit
a
faster.
0; xp < 8; xp++) { (xp 0; yp < 8; yp++) (yp
*/
=
for
=
if
(xfcn_jpeg->val [1]
qtabl_fact[xp] [yp]
=
[yp] [yp]
=
qtab2_fact[xp] qtab3_fact[xp] /*
Set up
=
{
{ lqtable[xp] [yp] lqtable[xp] [yp] lqtable[xp] [yp] ==1.0)
quantization
for RGB.*/
tables
} if
else
(xfcn_jpeg->val [1]
[yp] qtab2_fact [xp] [yp] qtab3_fact[xp] [yp] qtabl_fact[xp]
/*
Set up
=
=
=
{ [yp] lqtable [xp] [yp] cqtable[xp] [yp] ==2.0)
cqtable[xp]
quantization
for XYZ.*/
tables
} {
else
qtabl_fact qtab2_fact qtab3_fact /*
[xp] [yp] [xp] [yp] [xp] [yp] Q-
Set up
tables
=
lqtable [xp] [yp]
=
cqtable[xp]
=
cqtable[xp]
for
other
[yp] [yp]
color
spaces
.
}
[xp] [yp] *= xf cn_jpeg->val [0] ; [xp] [yp] *= xf cn_jpeg->val [0] ; *= xf cn_jpeg->val [0] ; qtab3_fact [xp] [yp] < for (xt xt 0; 8; xt++) { for (yt 0; yt < 8; yt++) { cos ( ( ( (2*xt)+l) *xp*PIE) /16. 0) dctbasis[xp*8+xt] [yp*8+yt] * cos( ( ( (2*yt)+l)*yp*PIE) /16.0) ; cos ( ( ( (2*xp) +1) *xt*PIE) /16 idctbasis[xp*8+xt] [yp*8+yt] * cos(( ( (2*yp)+l)*yt*PIE)/16.0) ; } qtabl_fact
qtab2_fact
=
=
=
=
}
if
if
(xfcn_jpeg->val[l] eob[0]
=
eob[l]
=
eob[2]
=
=
eob[l]
=
eob[2]
=
10; 11; 10;
==1.0)
{
==2.0)
{
==0.0)
{
}
(xfcn_jpeg->val[l] eob[0]
if
11; 11; 11;
}
(xfcn_jpeg->val[l]
11; 10;
eob[0]
=
eob[l]
=
eob[2]
=10;
}
88
.0)
for
(xc
if
0;
=
xc
val [1]
1.0)
==
[xc] [0] [xc] [1] [xc] [2]
{
=
DCLbitlut
=
DCLbitlut DCLbitlut
=
Set up Huffman
DC
codes
[xc] [xc] [xc]
for RGB space.*/
} if
(xfcn_jpeg->val [1] 2.0) { [xc] [0] DCCbitlut [xc] DCbitlut [xc] [1] DCLbitlut [xc] DCbitlut [xc] [2] DCCbitlut [xc]
else
==
DCbitlut
=
=
=
/*
Set up Huffman DC codes
; ; ;
for XYZ.
*/
}
{
else
DCbitlut DCbitlut DCbitlut /*
[xc] [0] [xc] [1] [xc] [2]
=
DCLbitlut
= =
DCCbitlut DCCbitlut
= =
Set up Huffman
DC
codes
[xc] [xc] [xc]
for L C C
spaces.*/
} for
(xc
=
for if
0;
16;++xc ) { 0; yc < 1 0;++yc) { (xfcn_jpeg->val [ 1] 1.0) xc
(yc
val[l]
==2.0)
[xc] [yc] [0] [xc] [yc] [1] [xc] [yc] [2]
Set up Huf fman AC
{
=
ACCbitlut
=
ACLbitlut
=
ACCbitlut
codes
[xc] [yc] [xc] [yc] [xc] [yc]
for XYZ
space
.
} else
{ ACbitlut ACbitlut ACbitlut /*
/*
the
actual
=
ACLbitlut
=
ACCbitlut
=
ACCbitlut
codes
(xb
[xc] [yc] [xc] [yc] [xc] [yc]
for L C C
*/
spaces.
compression/decompression.
0; xb < width; xb += 8) { ff lush(stdout) ; printf ("rows %4d\r", xb) ; for (yb 0; yb < height; yb += 8) { for (xp 0; xp < 8; xp++) { for (yp 0; yp < 8; yp++) { for
/*
Set up Huf fman AC
begins
And here
[xc] [yc] [0] [xc] [yc] [1] [xc] [yc] [2]
.
=
*/
=
=
=
xtmp
index
=
xb =
source source
source
+
xp;
ytmp
(yb+yp)*ll
[xp] [yp] [0] [xp] [yp] [1] [xp] [yp] [2]
+
=
yb
+
yp;
(xb+xp) *crs->hdr
.color_planes;
crs->cdata[index+0]
HALFSCL
crs->cdata[index+l]
HALFSCL
crs->cdata
}
89
[index+2
]
HALFSCL
*/
} /*
This
for
section
of
code
computes
0; xp < 8; xp++) { (xp for (yp 0; yp < 8; yp++) sum [ 0 ] 0.0; sum[l] 0.0; sum [ 2 ] 0.0;
the
FDCT coefficients.
=
{
=
=
=
=
if
( (yp
0) && (xp 0.5; if ( (yp 0) && 0.707107; if ( (yp != 0) && 0.707107;
CC
==
0) )
==
=
else
==
CC
(xp
!=
0))
(xp
==
0))
=
else
CC
=
else
CC
for
1.0;
=
(xt
0;
xt++) { 8; yt++) { basis = dctbasis [xp*8+xt] [yp*8+yt] ; * sum[0] += (source [xt] [yt] [0] basis) += sum[l] (source[xt] [yt] [1] * basis) * sum[2] += (source[xt] [yt] [2] basis) } } dctcof [xp] [yp] [0] (0.25*CC*sum[0] ) dctcof [xp] [yp] [1] (0.25*CC*sum[l] ) dctcof [xp] [yp] [2] (0.25*CC*sum[2] )
for
=
(yt
=
xt
0;
