LEAST MEAN SQUARE ERROR BASED
BLOCK TRUNCATION CODING
FOR IMAGE COMPRESSION
A THESIS
Submitted by
S.CHANDRAVADHANA
Under the guidance of
Dr. N. NITHIYANANDAM
in partial fulfillment for the award of the degree of
DOCTOR OF PHILOSOPHY
in
ELECTRONICS AND COMMUNICATION ENGINEERING
B.S.ABDUR RAHMAN UNIVERSITY
(B.S. ABDUR RAHMAN INSTITUTE OF SCIENCE & TECHNOLOGY)
(Estd. u/s 3 of the UGC Act. 1956)
www.bsauniv.ac.in
AUGUST 2014
B.S.ABDUR RAHMAN UNIVERSITY
(B.S. ABDUR RAHMAN INSTITUTE OF SCIENCE & TECHNOLOGY)
(Estd. u/s 3 of the UGC Act. 1956)
www.bsauniv.ac.in
BONAFIDE CERTIFICATE
Certified that this thesis LEAST MEAN SQUARE ERROR BASED BLOCK
TRUNCATION CODING FOR IMAGE COMPRESSION is the bonafide work of
CHANDRAVADHANA.S (RRN: 1084205) who carried out the thesis work under my
supervision. Certified further, that to the best of my knowledge the work reported herein
does not form part of any other thesis or dissertation on the basis of which a degree or
award was conferred on an earlier occasion on this or any other candidate.
SIGNATURE
Dr. N.NITHIYANANDAM
RESEARCH SUPERVISOR
Professor
Department of ECE
B.S. Abdur Rahman University
Vandalur, Chennai – 600 048.
SIGNATURE
Dr. P.K.JAWAHAR
HEAD OF THE DEPARTMENT
Professor & Head
Department of ECE
B.S. Abdur Rahman University
Vandalur, Chennai – 600 048.
ACKNOWLEDGEMENT
Foremost, I take this opportunity to thank the Chancellor, Dr.B.S.Abdur
Rahman, for his unending support to the student community. I take pride in
thanking Prof. J.A.K. Tareen, Ph.D., Vice Chancellor, for his immense support
and guidance.
I am sincerely grateful to the Dean (Academic Research), Dr.Raja
Prabhu, for sharing his truthful and illuminating views on a number of issues
related to the thesis. I express my warm thanks to Dr. S. Kaja Mohideen, Dean,
School of Electrical & Communication Sciences, for his inspiring support and
guidance. It gives me immense pleasure to thank Dr.P.K.Jawahar, HOD,
Electronics and Communication Engineering, for his valuable suggestions
during the course of writing this thesis.
I would like to express my sincere gratitude to my supervisor,
Dr.N.Nithiyanandam,
Professor,
Department
of
Electronics
and
Communication, for the continuous support of my Ph.D study and research, for
his patience, motivation, enthusiasm, and immense knowledge. His guidance
helped me in all the time of research and writing of this thesis.
I would like to express my sincere thanks to my doctoral committee
members Dr K.Boopathy Bagan, Professor, Department of Electronics
Engineering, MIT, and Dr.V.Sankaranarayanan, Professor, Department of
Information Technology, B.S.A.University, for their valuable suggestions and
whole hearted support in completing this work.
Last but not the least, I would like to thank all my friends and family
members for supporting me throughout my career.
S.CHANDRAVADHANA
ABSTRACT
Among the various spatial domain image compression techniques, Block
Truncation Coding (BTC) is one of the methods which has the least
computational complexity. But unfortunately, the bit rate obtained for a block
size of 4x4 is 2 bits per pixel. When the block size is increased for obtaining
higher compression ratio, and thereby lower bit rates for a band limited channel,
the annoying blocking artifacts and the blurred edges dominate the image. In
this research thesis, modification of the two - tone Block Truncation Coding is
done in order to improve the performance of the traditional BTC. The bit rate is
further reduced by increasing the block size to 8x8, 16x16, 32x32 and 64x64.
The parameters such as Peak Signal to Noise Ratio, Root Mean Square Error
and Contrast are measured and it is found that the proposed methods of BTC
are superior to the traditional BTC. The contrast of the image is enhanced and
the computational complexity of the modified methods is kept minimal. Another
method namely a “Least Mean Square Error Based Block Truncation Coding” is
formulated. This method of BTC reduces the mean square error of the whole
image to a minimum thereby improving the Peak Signal to Noise Ratio. This
paves the way for a nearly error free and compressed transmission of the
images through the communication channel.
A comparative study of the performance of the Traditional BTC, modified
methods of BTC and the Least Mean Square Error based BTC is done finally
and the results are tabulated. Four sample gray scale images have been taken
for analysis and it is found the modified methods and the Least Mean Square
Error based BTC are superior to the Traditional BTC. This work can be further
extended to colour images as well. The two tone BTC can be incorporated
separately to the Red, Green and Blue (R, G, B) components of a colour image
and further compression ratio can be achieved.
B.S.ABDUR RAHMAN UNIVERSITY
(B.S. ABDUR RAHMAN INSTITUTE OF SCIENCE & TECHNOLOGY)
(Estd. u/s 3 of the UGC Act. 1956)
www.bsauniv.ac.in
BONAFIDE CERTIFICATE
Certified that this thesis LEAST MEAN SQUARE ERROR BASED BLOCK
TRUNCATION CODING FOR IMAGE COMPRESSION is the bonafide work of
CHANDRAVADHANA.S (RRN: 1084205) who carried out the thesis work under my
supervision. Certified further, that to the best of my knowledge the work reported
herein does not form part of any other thesis or dissertation on the basis of which a
degree or award was conferred on an earlier occasion on this or any other candidate.
SIGNATURE
SIGNATURE
Dr. N.NITHIYANANDAM
RESEARCH SUPERVISOR
Professor
Department of ECE
B.S. Abdur Rahman University
Vandalur, Chennai – 600 048.
Dr. P.K.JAWAHAR
HEAD OF THE DEPARTMENT
Professor & Head
Department of ECE
B.S. Abdur Rahman University
Vandalur, Chennai – 600 048.
i
ACKNOWLEDGEMENT
Foremost, I take this opportunity to thank the Chancellor, Dr.B.S.Abdur
Rahman, for his unending support to the student community. I take pride in
thanking Prof. J.A.K. Tareen, Ph.D., Vice Chancellor, for his immense
support and guidance.
I am sincerely grateful to the Dean (Academic Research), Dr.Raja
Prabhu, for sharing his truthful and illuminating views on a number of issues
related to the thesis. I express my warm thanks to Dr. S. Kaja Mohideen,
Dean, School of Electrical & Communication Sciences, for his inspiring
support
and
guidance.
It
gives
me
immense
pleasure
to
thank
Dr.P.K.Jawahar, HOD, Electronics and Communication Engineering, for
his valuable suggestions during the course of writing this thesis.
I would like to express my sincere gratitude to my supervisor,
Dr.N.Nithiyanandam,
Professor,
Department
of
Electronics
and
Communication, for the continuous support of my Ph.D study and research,
for his patience, motivation, enthusiasm, and immense knowledge. His
guidance helped me in all the time of research and writing of this thesis.
I would like to express my sincere thanks to my doctoral committee
members Dr K.Boopathy Bagan, Professor, Department of Electronics
Engineering, MIT, and Dr.V.Sankaranarayanan, Professor, Department of
Information Technology, B.S.A.University, for their valuable suggestions
and whole hearted support in completing this work.
Last but not the least, I would like to thank all my friends and family
members for supporting me throughout my career.
S.CHANDRAVADHANA
ii
ABSTRACT
Among the various spatial domain image compression techniques,
Block Truncation Coding (BTC) is one of the methods which has the least
computational complexity. But unfortunately, the bit rate obtained for a block
size of 4x4 is 2 bits per pixel. When the block size is increased for obtaining
higher compression ratio, and thereby lower bit rates for a band limited
channel, the annoying blocking artifacts and the blurred edges dominate the
image. In this research thesis, modification of the two - tone Block Truncation
Coding is done in order to improve the performance of the traditional BTC.
The bit rate is further reduced by increasing the block size to 8x8, 16x16,
32x32 and 64x64. The parameters such as Peak Signal to Noise Ratio, Root
Mean Square Error and Contrast are measured and it is found that the
proposed methods of BTC are superior to the traditional BTC. The contrast of
the image is enhanced and the computational complexity of the modified
methods is kept minimal. Another method namely a “Least Mean Square
Error Based Block Truncation Coding” is formulated. This method of BTC
reduces the mean square error of the whole image to a minimum thereby
improving the Peak Signal to Noise Ratio. This paves the way for a nearly
error free and compressed transmission of the images through the
communication channel.
A comparative study of the performance of the Traditional BTC,
modified methods of BTC and the Least Mean Square Error based BTC is
done finally and the results are tabulated. Four sample gray scale images
have been taken for analysis and it is found the modified methods and the
Least Mean Square Error based BTC are superior to the Traditional BTC.
This work can be further extended to colour images as well. The two tone
BTC can be incorporated separately to the Red, Green and Blue (R, G, B)
components of a colour image and further compression ratio can be
achieved.
iii
TABLE OF CONTENTS
CHAPTER NO
TITLE
PAGE NO
ACKNOWLEDGEMENT
ii
ABSTRACT
iii
LIST OF TABLES
vii
LIST OF FIGURES
x
LIST OF ABBREVIATIONS AND SYMBOLS
xvii
INTRODUCTION
1
1.1
Image compression
1
1.2
Literature survey on image compression
1
1.2.1
Spatial Domain based Image Compression
1
1.2.2
Image Compression based on Block Truncation
1.
1.2.3
2.
Coding
3
Spectral Domain based Image Compression
7
BLOCK TRUNCATION CODING
FOR IMAGE COMPRESSION
11
2.1
Digital image fundamentals
11
2.2
Need for image compression
11
2.3
Traditional block truncation coding
12
2.4
‘CR’, ‘BR’, ‘RMSE’, ‘PSNR’ & ‘C’
parameters of compression
13
2.5
Illustration of BTC applied to an arbitrary 4x4 block
16
2.6
BTC application on sample images
19
2.7
Computational time for image processing
24
2.8
Conclusion
29
iv
3.
MODIFIED BLOCK TRUNCATION CODING
30
3.1
Modified BTC methods for improved contrast
30
3.2
Low mean and high mean values for BTC1
30
3.3
Low mean and high mean values for BTC2
31
3.4
Simulation results for sample images
32
3.4.1
Simulation results for copya.jpg image
32
3.4.2
Simulation results for city.jpg image
37
3.4.3
Simulation results for hurricane.jpg Image
41
3.4.4
Simulation results for boat.jpg image
45
3.4.5
Comparison of computational time
for BTC, BTC1 and BTC2
4.
49
LEAST MEAN SQUARE ERROR
BASED BLOCK TRUNCATION CODING
FOR IMPROVED PSNR VALUE
57
4.1
Mean square analysis for block truncation coding
57
4.2
Identification of least mean square error set
58
4.3
Simulation results
60
5.
SUMMARY OF RESEARCH FINDINGS,
CONCLUSION AND FUTURE SCOPE
5.1
68
Comparison of RMSE, CONTRAST and PSNR
values for the images of various BTC methods
68
5.2
Tabulation of the results for various BTC methods
70
5.3
Graphical representation of the comparative
results for various BTC methods
v
72
5.4
Discussions on the various BTC methods developed
and comparison with interpolative BTC
78
5.5
Conclusion
79
5.6
Scope for future work
79
REFERENCES
80
LIST OF PUBLICATIONS
84
TECHNICAL BIOGRAPHY
85
vi
LIST OF TABLES
TABLE NO
2.1
TITLE
PAGE NO
CR and BR values for various
block sizes of a 512x512 image.
16
2.2
Contrast value for the original images
21
2.3
RMSE, PSNR and Contrast value for
Traditional BTC for various block sizes
2.4
CPU time and elapsed time for various
block sizes of Traditional BTC for copya.jpg
2.5
25
CPU time and elapsed time for various
block sizes of Traditional BTC for city.jpg
2.6
22
25
CPU time and elapsed time for various
block sizes of Traditional BTC
for hurricane.jpg
2.7
CPU time and elapsed time for various
block sizes of Traditional BTC for boat.jpg
3.1
26
26
Comparison of computational
complexities between the Traditional BTC,
BTC1 and BTC2
3.2
32
RMSE, PSNR and contrast values
of BTC, BTC1 and BTC2 for
original image ‘copya.jpg’
3.3
35
RMSE, PSNR and contrast values
of BTC, BTC1 and BTC2 techniques for
the image ‘city.jpg
3.4
39
RMSE, PSNR and contrast values of
BTC, BTC1 and BTC2 techniques for
the image ‘hurricane.jpg’
3.5
RMSE, PSNR and Contrast values of
BTC, BTC1 and BTC2 techniques for
vii
43
the image ‘boat.jpg’
3.6
47
Elapsed time and CPU time for
BTC, BTC1 and BTC2 techniques
for image ‘copya.jpg’
3.7
49
Elapsed time and CPU time for
BTC, BTC1 and BTC2 techniques
for image ‘city.jpg’
3.8
51
Elapsed time and CPU time for
BTC, BTC1 and BTC2 techniques
for image ‘hurricane.jpg’
3.9
53
Elapsed time and CPU time for
BTC, BTC1 and BTC2 techniques
for image ‘boat.jpg’
55
4.1
15 sets of groups for a block of 4x4
58
4.2
MSE and PSNR for 15 sets of
groups for LMSE based BTC
method for copya.jpg
4.3
PSNR values for various block sizes
based on LMSE-BTC
4.4
61
62
MSE and PSNR for 15 sets of
groups for the LMSE based BTC
method for city.jpg
4.5
PSNR values for various block sizes
based on LMSE-BTC
4.6
63
64
MSE and PSNR for 15 sets of
groups for the LMSE based BTC
method for hurricane.jpg
4.7
PSNR values for various block sizes
based on LMSE-BTC
4.8
64
65
MSE and PSNR for 15 sets of
groups for the LMSE based BTC
method for boat.jpg
viii
66
4.9
PSNR values for various block sizes
based on LMSE-BTC
5.1
67
RMSE, PSNR and Contrast values of
BTC, BTC1, BTC2 and LMSE – BTC
techniques for the images copya.jpg
5.2
71
Comparison of LMSE- BTC and
Interpolative BTC
ix
79
LIST OF FIGURES
FIGURE NO
2.1
TITLE
PAGE NO
Graph showing the variation
of Compression Ratio and Bit
Rate for various block sizes
2.2
16
(a) 4x4 Pixels Block,
(b) Corresponding Bit Plane
2.3
Reconstructed 4x4 Block with
2.4
(a) Original Image copya.jpg
17
3
17
(b) – (f) Traditional BTC for block
size 4x4, 8x8, 16x16, 32x32
and 64x64 for copya.jpg
2.5
19
(a) Original Image city.jpg,
(b) – (f) Traditional BTC for block
size 4x4, 8x8, 16x16, 32x32
and 64x64 for city.jpg
2.6
20
(a) Original Image hurricane.jpg
(b) – (f) Traditional BTC for block
size 4x4, 8x8, 16x16, 32x32
and 64x64 for hurricane.jpg
2.7
20
(a) Original Image boat.jpg
(b) – (f) Traditional BTC for block
size 4x4, 8x8, 16x16, 32x32
and 64x64 for boat.jpg
2.8
21
Graph showing RMSE values
for copya.jpg, city.jpg, hurricane.jpg
and boat.jpg
2.9
23
Graph showing PSNR values
for copya.jpg, city.jpg, hurricane.jpg
and boat.jpg
x
23
2.10
Graph showing Contrast values
for copya.jpg, city.jpg, hurricane.jpg
and boat.jpg
2.11
24
Graph showing the elapsed time
and CPU Time for processing
the image copya.jpg (Traditional BTC)
for various block sizes
2.12
27
Graph showing the elapsed time
and CPU Time for processing the image
city.jpg (Traditional BTC)
for various block sizes
2.13
27
Graph showing the elapsed time
and CPU Time for processing the
image hurricane.jpg (Traditional BTC) for
various block sizes
2.14
28
Graph showing the elapsed time
and CPU Time for processing the
image boat.jpg (Traditional BTC) for
various block sizes
3.1
28
(a) Original Image ‘copya.jpg’;
[(b), (e), (h), (k), (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1images and
[(d), (g), (j), (m), (p)] BTC2 images,
for block sizes of 4x4, 8x8, 16x16,
32x32 and 64x64 respectively
3.2
34
Graph showing the comparison of
RMSE values between BTC, BTC1
and BTC2 techniques for ‘copya.jpg’
3.3
36
Graph showing the comparison of
Contrast values between BTC, BTC1
and BTC2 techniques for ‘copya.jpg’
3.4
(a) Original Image ‘city.jpg’;
[(b), (e), (h), (k), (n)] BTC images;
xi
36
(c), (f), (i), (l), (o)] BTC1 images
and [(d), (g), (j), (m), (p)] BTC2 images,
for block sizes of 4x4, 8x8, 16x16,
32x32 and 64x64 respectively
3.5
38
Graph showing the comparison of
RMSE values of BTC, BTC1 and BTC2
techniques for the image ‘city.jpg’
3.6
40
Graph showing the comparison of
Contrast values of BTC, BTC1
and BTC2 techniques for the
image ‘city.jpg’
3.7
40
(a) Original Image hurricane.jpg,
[(b), (e), (h), (k), (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1 images and
[(d), (g), (j), (m), (p)] BTC2 images for
block sizes of 4x4, 8x8, 16x16, 32x32
and 64x64 respectively
3.8
42
Graph showing the comparison of
RMSE values for BTC, BTC1
and BTC2 techniques for the image
‘hurricane.jpg’
3.9
44
Graph showing the comparison of
Contrast values of BTC, BTC1
and BTC2 techniques for the image
‘hurricane.jpg’
3.10
44
(a) Original Image ‘boat.jpg’,
[ (b),(e), (h), (k) , (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1 images and
[(d), (g), (j), (m), (p)] BTC2 images for
block sizes of 4x4, 8x8, 16x16, 32x32
and 64x64 respectively.
xii
46
3.11
Graph showing the comparison of
RMSE values for of BTC, BTC1
and BTC2 techniques for the image
‘boat.jpg’
3.12
48
Graph showing the comparison of
Contrast values of BTC, BTC1 and
BTC2 techniques for the image ‘boat.jpg’
3.13
48
Graph showing Elapsed time for BTC,
BTC1 and BTC2 techniques and
block sizes for image ‘copya.jpg’
3.14
50
Graph showing CPU time for BTC,
BTC1 and BTC2 techniques and
block sizes for image ‘copya.jpg’
3.15
50
Graph showing Elapsed time for BTC,
BTC1 and BTC2 techniques and
block sizes for image ‘city.jpg’
3.16
52
Graph showing CPU time for BTC,
BTC1 and BTC2 techniques and
block sizes for image ‘city.jpg’
3.17
52
Graph showing Elapsed time for BTC,
BTC1 and BTC2 techniques and
block sizes for image ‘hurricane.jpg’
3.18
54
Graph showing CPU time for BTC,
BTC1 and BTC2 techniques and
block sizes for image ‘hurricane.jpg’
3.19
54
Graph showing Elapsed time of BTC,
BTC1 and BTC2 techniques for
image ‘boat.jpg’
3.20
56
Graph showing CPU time of BTC, BTC1
and BTC2 techniques for image
‘boat.jpg’
4.1
(a) Original Image copya.jpg
(b) LMSE –BTC image copya.jpg,
xiii
56
(c) Original Image city.jpg (d) LMSE-BTC
image city.jpg, (e) Original Image
Hurricane.jpg, (f) LMSE –BTC
image hurricane.jpg, (g) Original
Image boat.jpg, (h) LMSE – BTC
image boat.jpg
4.2
61
Graph showing the MSE values of the
15 sets of the LMSE based BTC
for Copya.jpg.
4.3
62
Graph showing the MSE values of
the 15 sets of the LMSE based BTC
for city.jpg
4.4
63
Graph showing the MSE values of
the 15 sets of the LMSE based
BTC for hurricane.jpg
4.5
65
Graph showing the MSE values of the
15 sets of the LMSE based BTC
for boat.jpg
5.1
66
(a) Original Image copya.jpg
(b) Traditional BTC (c) BTC 1 (d) BTC 2
(e) LMSE based BTC for block size
of 4x4
5.2
68
(a) Original Image city.jpg
(b) Traditional BTC (c) BTC 1
(d) BTC 2 (e) LMSE based BTC for
block size of 4x4.
5.3
69
:(a) Original Image hurricane.jpg
(b) Traditional BTC (c) BTC1
(d) BTC2 (e) LMSE based BTC
for block size of 4x4
5.4
69
:(a) Original Image boat.jpg (b) Traditional
BTC (c) BTC1 (d) BTC2
(e) LMSE based BTC for block
size of 4x4
xiv
70
5.5
Graph showing the RMSE values
for various BTC methods for the
image copya.jpg
5.6
72
Graph showing the PSNR values
for various BTC methods for the
image copya.jpg
5.7
72
Graph showing the Contrast values
for various BTC methods for the
image copya.jpg
5.8
73
Graph showing the RMSE values
for various BTC methods for the
image city.jpg
5.9
73
Graph showing the PSNR values
for various BTC methods for the
image city.jpg
5.10
74
Graph showing the Contrast values
for various BTC methods for the
image city.jpg
5.11
74
Graph showing the RMSE values for
various BTC methods for the image
hurricane.jpg
5.12
75
Graph showing the PSNR values for
various BTC methods for the image
hurricane.jpg
5.13
75
Graph showing the Contrast values
for various BTC methods for
the image hurricane.jpg
5.14
76
Graph showing the RMSE values for
various BTC methods for the image
boat.jpg.
xv
76
5.15
Graph showing the PSNR values for
various BTC methods for the
image boat.jpg
5.16
77
Graph showing the Contrast values
for various BTC methods for the
image boat.jpg
xvi
77
LIST OF SYMBOLS AND ABBREVIATIONS
-
Standard deviation
-
Mean
BTC
-
Block truncation coding
PSNR
-
Peak signal to noise ratio
RMSE
-
Root mean square error
MSE
-
Mean Square Error
C
-
Contrast
CR
-
Compression Ratio
VQ
-
Vector Quantization
DCT
-
Discrete Cosine Transform
DPCM
-
Differential pulse code modulation
VBTC
-
Variable block truncation coding
ESPO
-
Equal Sign Position Optimization
AMBTC
-
Absolute moment block truncation coding
DRT
-
Dynamic range tuning
MPBTC
-
Moment preserving block truncation coding
JPEG
-
Joint Photographic Experts Group
BR
-
Bit Rate
LZW
-
Lempel Ziv Welch
SPIHT
-
Set Partitioning in hierarchical trees
xvii
1. INTRODUCTION
1.1
IMAGE COMPRESSION
In today's electronic world, digital still pictures and video images play a
significant role in multimedia based knowledge exchange applications. Such high
resolution digital pictures require a lot of memory space for image storage,
processing and retrieval by digital computers. Satellite and aerial images
generate big data files demanding large transmission time for image transfer. In
internet applications, such big data transmission slows down the net speed.
Image compression techniques [1] – [5] aim at reducing the transmission
file size, by using lesser bits for the images. This is realized by using fewer bits
per pixel of the image. Normally this bit reduction will affect the quality of the
image reproduced at the receiver. This process is known as ‘Lossy Image
Compression’ [10] - [15]. But images could also be compressed without reduction
in quality by employing suitable coding techniques. Inherently, such ‘Lossless
Image Compression’ methods [40] yield less compression, compared to ‘Lossy’
methods [16]. The ‘Compression ratio (CR)’, the ‘Peak Signal to Noise Ratio
(PSNR)’ and the ‘Contrast (C)’ are the parameters used to measure the quality of
image compression.
Both time-domain (spatial) [7], [18] and frequency - domain (spectral) [34]
– [35] image compression techniques are employed in image compression. Block
Truncation Coding (BTC) is an apparently elegant and efficient time-domain
compression technique, developed by Delp and Mitchell [10]. An extensive
literature survey on various image compression techniques has been carried out
and reported in section 1.2.
1.2
LITERATURE SURVEY ON IMAGE COMPRESSION
1.2.1
Spatial Domain based Image Compression.
Some of the spatial domain based image compression techniques
reported in the literature is briefly listed below.
In the year 1981, Healy D.J. and Mitchell O.R., [1] presented a technique
for bandwidth compression coding of sequential digitized video imagery. This
method uses a single bit quantization of the small blocks in a video frame. It can
be used for low altitude aircraft imagery with moderate video quality.
In the year 1983, Arce, G and Gallagher N.C., [2] proposed a BTC Image
Coding using “Median Filter Roots”. In this algorithm, the BTC bit plane is
represented with fewer coefficients than the conventional BTC bit plane. By this,
the bit rate is reduced and efficient transmission of the block truncated image is
done.
In the year 1990, Davignon A., [3] proposed a block classification scheme
using Binary Vector Quantization. In this method, the blocks of an image are
classified into shaded blocks and edge blocks. This classification of blocks
depends on the threshold value for each block. The code book for vector
quantization is then partitioned according to the visual perception of the blocks.
In 1991, Rabbani, M and Jones, P.W [4] published a tutorial on “Digital
Image Compression Techniques”, wherein various methods for compression of
digital images are discussed. This is a valuable tutorial providing the groundwork
for understanding many of the useful image compression techniques.
In the year 1991, Qiu G., Varley M.R. and Terrell T.J [5] presented a paper
on block truncation using Hopfield neural networks. Here the pixels are classified
using Hopfield neural networks thereby reducing the time consumption of the
process and improving the performance.
In 1993, Brower, B.V et al [6] proposed a spatial domain adaptive
differential pulse code modulation scheme using rate-controlled adaptive
differential pulse code modulation technique, for downlink applications.
In 1994 Chan, Y.K [7] presented a method for improved spatial domain
image compression by splitting the image into sub blocks of 2 * 2 and then each
block is compressed without much loss of detail by encoding it to 1, 2, or 3
intensity values.
In 2004 Tao, T and Mukherjee, A [8] used a spatial domain compression
based on the Lempel Ziv Welch algorithm to compress still images. The
improvements include multipattern matching and a faster implementation for
"simple patterns", with no symbol appearing more than once.
In 2011, Amin. A et al [9] proposed a lossless spatial compression
technique with improved compression ratio using Run Length Encoding
(RLE). Larger sequences are broken into small sequences using bit stuffing.
1.2.2 Image Compression based on Block Truncation Coding.
Some of the image compression techniques, based on Block Truncation
Coding and its variants, which have been reported in the literature, are listed
below.
In 1979 Edward J. Delp and Robert Mitchell, O [10] used a two-level
(one-bit) nonparametric quantizer in the Block Truncation Coding (BTC) algorithm
that preserves the mean and variance (first and second moments) of the blocks
in the image. This quantizer produces good quality images at data rates of 1.5
bits/pixel. No large data storage is required, and the computation is small.
In the year 1984, Lema M.D and Mitchell O.R., [11] presented an absolute
moment BTC for application to color images. This paper is based on preserving
the sample absolute moment of each block in the image and this can be
extended to color images as well.
In 1984, Halverson, D. et al [12] proposed
a generalized algorithm for
BTC that included a family of moment preserving quantizers with the potential for
improved performance.
In 1987 Udpikar V.R and Raina J.P [13] proposed a vector quantized
Block Truncation Coding, where the statistical overhead and the truncated block
exhibit properties that can be effectively used for their quantization as vectors.
The process of vector quantization results in reduced bit rates for the encoder.
In 1991, Wu, Y and Coll, D. C [14] proposed BTC-Vector QuantizedDiscrete Cosine Transform, an algorithm combining the simple computational and
edge preserving properties of BTC, and the high fidelity and high-compression
ratio of adaptive DCT, along with the high-compression ratio and good subjective
performance of VQ. This algorithm is claimed to have significantly reduced
coding delays than either VQ or DCT alone.
In 1991, Kamel, M et al [15] presented a variable BTC algorithm for image
compression. It is shown that there exists an optimal threshold for the
quantization in BTC algorithms (fixed and variable) that minimizes the errors.
Compared to the fixed BTC (fBTC), the variable BTC (vBTC) gives better
performance on all the tested images. The use of vBTC with optimal threshold
leads to a reduction of the error in the reconstructed images by almost 40% of the
error in the reconstructed images obtained by fBTC. This enhanced performance
suggests that the vBTC with optimal threshold is a better alternative to the fixed
block truncation coding.
In 1993,
Oshri, E, Shelly, N and
Mitchell, H.B. [16] proposed an
interpolative block truncation coding with three levels for compression of images.
This method of interpolation improves the quality of images for a specified bit
rate.
In the year 1993, Kurita, T and Otsu, N., [17] proposed a color image block
truncation coding for compression wherein the truncated errors are reduced to
achieve better quality for the color images.
In the year 1995, Ramana Rao, Y.V and Eswaran, C [18] proposed a new
BTC algorithm using look up tables. This algorithm produced images with better
subjective quality.
In 1997, Huang, C. S and Lin, Y [19] proposed
a Hybrid BTC in which a
universal codebook using Hamming codes and a differential pulse code
modulation (DPCM).
In 1998, Wu, Y.G and Tai, S.C [20] proposed an efficient BTC
compression method using a moment preserving technique to achieve the low-bit
rate block truncation coding (BTC). Compared with transform coding and vector
quantization, conventional BTC compression has the advantage of simple and
fast computation. The proposed technique is based on variable bit rate selection
for the blocks in the image. This method reproduces the images with moderate
image quality and bit rate of 0.5-1.0 bit/pixel.
In 1999, Kuo, C.H., et al [21] presented a compression algorithm based on
Classified
Interpolative
Block
Truncation
Coding
improved
with
Vector
Quantization. The bit rate and PSNR of this classified interpolative BTC algorithm
with VQ are better than those of the interpolative BTC algorithm with Vector
Quantization.
In 1999, Chang, L.W., et al [22] proposed a variable block truncation
coding with optimal quadtree segmentation (VBTC) to compress still images. The
distortion of the reconstructed image is minimal. A bit plane reduction scheme is
applied to achieve lower bit rates.
In 2000, Ma, K.K et al [23] developed an adaptive BTC algorithm ESPO,
(Equal Sign Position Optimization) for optimum pixel classification. Incorporation
of the ESPO algorithm into conventional Absolute Moment Block Truncation
Coding or AMBTC achieves minimum Mean Square Error.
In 2000, Beghdadi, A and Iordache, R [24] proposed a BTC method which
uses a contrast enhancement technique.
In 2001, Chang, K.W et al, [25] presented a Block Truncation Coding
(BTC) for real-time image coding at moderate bit-rate, with low computation and
storage demands..
In the year 2001, Kuo, C.H and Chen, C.F [26] proposed a multilevel
block truncation coding method to search for an optimal threshold value to
quantize the pixels in each block.
In 2003, Hu, Y.C et al [27] described an image compression scheme
based on moment preserving block truncation coding (MPBTC). To reduce the bit
rate of the traditional MPBTC scheme, the block search order coding technique is
employed to exploit the similarity among neighbouring image blocks. In addition,
smooth blocks (blocks having same intensity values) and complex blocks (blocks
having varied intensity values) are processed using different methods.
In the year 2006, Dhara, B.C and Chanda, B [28] proposed a colour image
compression based on block truncation coding using pattern fitting principle. In
this method the authors have exploited the high correlation present in the RGB
plane of the colour images. This correlation is reduced and new set of planes are
obtained for the BTC images. This method consumes less time than other
methods such as JPEG.
In 2010, Rhoma, E.M [29] proposed a least mean square error method for
Block Truncation Coding. The compression ratio is improved by coding only half
of the bits in the BTC bit plane of each block; the other half will be interpolated at
the receiver. The proposed interpolative algorithms minimize the errors caused
by the two level quantizer.
In 2011, Yang, Y et al [30] presented a fast BTC method based on a
truncated K-means algorithm. This utilizes the image inter-block correlation and
the convergence property of the k – means clustering algorithm. This algorithm
produces an optimum solution with good processing speed.
In the year 2011, Liu Y.F, Guo, J.M and Lee, J.D [31] presented a halftone
image classification using Least Mean Square algorithm and naive Bayes
classifier. The authors have developed a least mean-square filter for improving
the robustness of the extracted features, and employed the naive Bayes classifier
to verify all the extracted features for classification.
In 2013 Kekre, H.B et al [32] proposed an image compression method
using Multilevel Block Truncation Coding for image classification. Feature vectors
are extracted with four levels of Block Truncation Coding to classify the several
categories of images for performance comparison in six different color spaces.
1.2.3 Spectral Domain based Image Compression.
Some of the spectral domain based image compression techniques
reported in the literature are briefly described below.
In 1990, WaIlace, G.K [33] wrote “Digital compression and coding of
continuous tone still images” on the Joint Photographic Experts Group (JPEG)
standard. This standard describes the compression of still images by using
discrete cosine transform on the pixels and then a lossless coding technique is
applied to the DCT coefficients.
In 1993, Pennebacker, W. B and Mitchell, J. L [34] scripted the book titled
“JPEG Still Image Compression Standard”, detailing the Joint Photographic
Experts Group (JPEG) standard on color still image data compression. This new
guide to JPEG and its technologies offers detailed information on the new JPEG
signaling conventions and the structure of JPEG compressed data.
In 1993 Shapiro J.M [35] presented “Embedded image coding using zero
trees of wavelet coefficients”, where the bits in the encoded bit stream are
generated in order of importance yielding an embedded code.
In 1996, Said, A and Pearlman, W.A [36] proposed an image codec based
on set partitioning in hierarchical trees. The principle is based on partial ordering
by magnitude with a set partitioning sorting algorithm.
In 2000, Weinberger, M.J, Seroussi, G and Sapiro, G [37] proposed a
method for the lossless JPEG and near lossless compression of continuous tone
images.
In the year 2000, Marcellin, M.W et al [38] proposed the JPEG 2000
standards for still image compression. The encoder of the transmission system
was designed based on the JPEG 2000 format.
In the year 2002, Wu, Y.G [39] presented a work based on Image
Compression by sampling DCT Coefficients. In this paper an adaptive sampling
algorithm is used by calculating the difference area between correct points and
predicted points to decide the significant coefficients.
In the year 2010, Pan, Z et al [40] presented a technique where the image
is divided into independent bit planes, and then, the probability of bit “0” is
computed. This is compared with a predefined threshold for each bit plane, in
order to select the optimal block size. After this step, a modified quadtree coding
method is done to encode the block data.
In 2010, a 3D mesh geometrical image compression schemes for
hyperspectral images was proposed by Bayazit, U et al [41]. The proposed coder
is based on the region adaptive transform in the spectral mesh compression
method.
In the year 2011, Douak, F et al [42] proposed a lossy image compression
algorithm based on Discrete Cosine Transform. Here, after performing DCT in
each block, the block is adaptively scanned in order to obtain maximum runs of
zeros. This improves the compression ratio of the image.
The objectives of this research are:
i)
To improve the contrast of BTC images by suitable modification of
traditional BTC algorithm and compare the performance of
traditional and modified BTC algorithms.
ii)
To develop an algorithm for least mean square error based BTC
and to evaluate its comparative performance with traditional and
modified BTC.
This thesis of the research is organized as under.
.
This introductory Chapter 1 mainly deals with the literature survey on
Image Compression and the objectives of the research.
Chapter 2, explains the traditional BTC algorithm and its performance
appraisal for various parameters such as Compression Ratio, PSNR and
Contrast, for various block sizes.
In Chapter 3, the proposed modifications, to improve the contrast of the
reproduced image, are described. The performance parameters CR, PSNR and
Contrast of the modified BTC methods are compared with the traditional BTC.
In Chapter 4, a Least Mean Square Error (LMSE) based algorithm is
developed for improving the PSNR of the BTC image. The results of this LMSE
based BTC (LMSE-BTC) method is compared with traditional BTC and modified
BTC.
The concluding Chapter 5 summarizes the contributions made in this
thesis and indicates the scope for further research in this area.
1. BLOCK TRUNCATION CODING FOR IMAGE COMPRESSION
1.1
DIGITAL IMAGE FUNDAMENTALS
This chapter deals with the fundamentals of digital image signal representation
and the basic Block Truncation Coding (BTC) for image compression. A frame of a
digital image can be visualized as an orderly arrangement of ‘picture elements’ (pixels)
arranged in horizontal lines and many such lines are stacked one below the other. It
may also be visualized as a matrix of pixels arranged in rows and columns. For example
a ‘512 x 512’ image has 512 horizontal lines in a frame, each with 512 pixels. A pixel is
the tiniest, visible part of an image having its own color (hue) and brightness (intensity
of light). The brightness is referred as ‘luminance ‘(luma) and the color is referred as
‘chrominance’ (chroma). Any colour can be represented as a mixture of three primary
colors namely red, green and blue. When an image is scanned electronically, each pixel
of the image produces its own R, G, B (red, green, blue) signals corresponding to the
intensity of the primary colors in that pixel
[17], [28]. In digital processors, each of the
R, G, B signals are represented by 8 bits, corresponding to 256 quantization levels,
starting from zero intensity to full intensity. It is customary to explain any image
processing using monochrome (black and white) image, which can be extended to each
of the R, G, B components of the color image, separately [32].
1.2
NEED FOR IMAGE COMPRESSION
Digital images are in general stored in memories, preprocessed, transmitted and
reprocessed for final applications. The quantum of binary data
to be handled by an image processor is enormous. For example, a ‘256 x 256’ frame of
a monochrome image will have 524288 (256 x 256 x8) bits at the rate of 8 bits per pixel.
A 5 minutes video at the rate of 25 such frames per second will have 3932160000
(nearly 40 million) bits! Obviously, it will be advantageous to reduce the number of bits
before transmission with the capability of reproducing an acceptable image quality at
the receiver. This process is known as ‘Lossy Image Compression’. This will primarily
reduce the transmission time and also the storage memory required.
But images could also be compressed without reduction in quality by employing
suitable coding techniques. Inherently, such ‘Lossless Image Compression’ methods [9]
yield lesser compression, compared to ‘Lossy’ methods [30].
The ‘Compression ratio’ (CR) and ‘Bit Rate’ (BR)
are used to measure the
amount of image compression, while the ‘Peak Signal to Noise Ratio (PSNR)’ and
‘Root Mean Square Error’ (RMSE) are used to measure the resulting error of image
compression. Contrast (C) is is a measure of image visual quality.
Both time-domain [20] and transform based frequency-domain [37], [38], [39]
image compression techniques are employed in image compression. Block Truncation
Coding (BTC) is an apparently elegant and efficient time-domain compression
technique.
2.3
TRADITIONAL BLOCK TRUNCATION CODING
The Block Truncation Coding (BTC) was introduced by Delp and Mitchell [10], in
1979. This coding is based on dividing the image into non overlapping blocks of equal
size. In digital signal processors, an image is divided into smaller blocks of ‘k x k’ pixels
for processing. For example a ‘512 x 512’ frame may be divided into blocks of ‘8 x 8’
pixels. Sometimes microblocks of ‘2 x 2’ pixels, miniblocks of ‘4 x 4’ pixels, maxiblocks
of ’16 x 16’ pixels and macroblocks of
‘32 x 32’ pixels are also used.
BTC involves replacing the original intensity value of each pixel in a block either
by a ‘low mean’ intensity value ‘a’ or a ‘high mean’ intensity value ‘b’ based on a
threshold intensity value. This threshold is the mean intensity of the pixels in the block.
A ‘bit plane’ is created by representing the ‘a’ value pixels by ‘0’s and ‘b’ value pixels by
‘1’s.
a  x 
q
mq
b  x 
mq
q
(2.3.1)
(2.3.2)
Here, ‘m’ is the total number of pixels equal to 𝑘 2 (16 for a 4x4 block)
‘q’ is the number of ‘0’s in the bit plane
𝑥̅ is the mean intensity of ‘m’ pixels
‘σ’ is the standard deviation of intensities of ‘m’ pixels.
x
1 m
 xi, j
m i, j 1
̅̅̅2 − (𝑥̅ )2 ]0.5
𝜎 = [𝑥
x2 
1 m
2
 xi , j
m i, j 1
(2.3.3)
(2.3.4)
(2.3.5)
where 𝑚 = 𝑘 2 and 𝑥𝑖,𝑗 is the intensity value of the pixel (i,j) of the image,𝑥̅ is the mean
intensity, ̅̅̅
𝑥 2 is the mean of squared intensities and σ is the standard deviation (SD).
The encoder transmits the ‘bit plane’ of total ‘m’ bits, along with 𝑥̅ and ‘σ’ of each
8 bits. In the decoder, the ‘0’s and ‘1’s of the bit plane are replaced by 8-bit ‘a’s and ‘b’s
calculated from Eqns. 2.3.1 and 2.3.2 to reproduce the BTC image, which is a close
approximation of the original image.
2.4. ‘CR’, ‘BR’, ‘RMSE’, ‘PSNR’ & ‘C’ PARAMETERS OF COMPRESSION
As indicated in Section 2.3, the ‘compression ratio’ (CR) and ‘bit rate’ (BR) are
used to measure the amount of image compression, while the ‘Root Mean Square
Error’ (RMSE) and the ‘Peak Signal to Noise Ratio (PSNR)’ are used to measure the
resulting error of image compression. Contrast (C) is a measure of image visual quality.
The ‘compression ratio’ (CR) is defined as the ratio of the number bits of the
original image to the number bits after compression
Hence ‘compression ratio’
(CR) = ( 8 m ) / ( m + 16 )
(2.4.1)
The ‘Bit Rate’ (BR) is a parameter defined as the ratio of the number
generated
bits
after BTC, including the bits for 𝑥̅ and σ, to the number of pixels in the
image.
Hence
‘Bit Rate’ (BR)
=
(m +16) / m.
 (BR) x (CR)
=
8 Bits / pixel in original image.
The ‘ Root Mean Square Error’ (RMSE) is defined as,
1 262144 2 
RMSE 
  d i  
512  i  1

0.5
(2.4.2)
where ‘𝑑𝑖 ’ is the difference between the intensity of the 𝑖 𝑡ℎ pixel in the original image
and the reconstructed image, and 262144 is equal to 512 x 512.
The Peak Signal to Noise Ratio (PSNR) is defined as
PSNR  20 log10
 
X max
dB
RMSE
(2.4.3)
wherein ‘𝑋𝑚𝑎𝑥 ’ is the maximum pixel intensity in the 512x512 image.
The contrast (C) of an image is equal to the standard deviation of the intensity
values of the all the pixels of the image. Based on block by block approach, for a
‘512x512’ image of 4096 blocks of ‘8x8’ pixels, the Contrast ‘C’ of the image is
1
2
𝐶 = ( ) √[∑4096
𝑛=1 𝜎 𝑛 ]
64
(2.4.4)
where ‘σn’ is the Standard Deviation of the nth ‘8x8’ block, given by
1
2
𝜎𝑛 = ( ) √[∑64
𝑖=1(𝑥𝑖 − 𝑥̅ ) ]
8
(2.4.5)
where 𝑥𝑖 = intensity of the 𝑖 𝑡ℎ pixel of the nth ‘8x8’ block
𝑥̅ =
mean intensity of the ‘n’th ‘8x8’ block
The above equation for ‘C’ and ‘𝜎𝑛 ’ are applicable both for the original and the
reconstructed images.
After the application of BTC, ‘𝑝’ numbers of the pixels, represented by 0s in the
bit plane, are assigned with low-mean intensity ‘a’, and ‘𝑞’ (= 𝑘 2 − 𝑝) pixels,
represented by 1s in the bit plane, are assigned with high-mean intensity ‘b’. The
contrast ‘C’ of this BTC block is equal to the standard deviation of the ‘𝑝’ number of ‘a’s
and ‘𝑞’ (= 𝑘 2 − 𝑝) number of ‘𝑏’s. Using Eqn. (2.4.5), we get
𝜎𝑛 = [
(𝑏−𝑎)
𝑝+𝑞
1
] [𝑝𝑞]2
(2.4.6)
where,
𝑎 = low-mean intensity corresponding to 0s in the BTC bit plane
𝑏 = high-mean intensity corresponding to 1s in the BTC bit plane.
𝑝 = the number of 0s in the bit plane corresponding to low-mean ‘a’,
and
q = the
number of 1s in the bit plane corresponding to high-mean ‘b’.
While CR and BR are dependent only on the image block size, PSNR, RMSE and C are
dependent on the intensities of pixels. The CR and BR values are listed in Table 2.1 for
various block sizes of the image.
Table 2.1: CR and BR values for various block sizes of a 512x512 image.
64 x 64
pixels
Block
2 x2
4 x4
8 x8
16 x16
32 x32
size
pixels
pixels
pixels
pixels
pixels
m=k2
4
16
64
256
1024
CR
1.6
4
6.4
7.5294118
7.8769231 7.9688716
4096
BR
5
2
1.25
1.0625
1.015625
1.0039063
This Table 2.1 is graphically shown in Fig.2.1
9
8
7
CR and BR
6
5
4
CR
3
Bit Rate
2
1
0
2x2
4x4
8x8
16x16
32x32
64x64
Block size
Figure 2.1: Graph showing the variation of Compression Ratio and Bit Rate for various
block sizes.
As the block size increases, the bit rate decreases and the CR increases as
shown in figure 2.1.
2.5
ILLUSTRATION OF BTC APPLIED TO AN ARBITRARY 4X4 BLOCK
For illustration, a 4x4 block of pixels having arbitrary gray level intensities, in
shown in Figure 2.2, along with its corresponding bit plane.
(a)
(b)
Figure 2.2: (a) 4x4 Pixels Block, (b) Corresponding Bit Plane
Using equations (2.3.3) and (2.3.4) the mean (̅̅̅)
𝑥 of the 4x4 pixels block is 3
and the standard deviation (𝜎) is 2.64 . The encoder develops a single bit plane of 4x4
size by representing all 𝑥𝑖,𝑗 < 3̅ by 0s ,and all 𝑥𝑖,𝑗 ≥ 3 by 1s.This bit plane along with 𝑥̅
and σ are transmitted to the receiver.
Using the equations (2.3.1) and (2.3.2), the decoder in the receiver estimates a
low-mean value ‘a’ (0.007), to replace the 0s, and a high- mean value ’b’ (5.328),to
replace the 1s, in the received bit plane. Thus the 0s in the bit plane are replaced by
0.007 and the 1s in the bit plane are replaced by 5.328. The 4 x4 block of the image
reconstructed by the decoder is shown in Figure 2.3.
Figure 2.3: Reconstructed 4x4 Block with ̅̅̅
𝑥 ≈ 3.
Thus a 2-gray level truncation of the original block is created. This Block
Truncation Coding procedure is applied to all the blocks of the image. The decoder
recreates the truncated version of every block of the original image by estimating the
block’s ‘a’ and ‘b’ values, from the block’s 𝑥̅ and σ values using Eqns.2.3.1 and 2.3.2. In
any 4x4 block, the 8 bits of any pixel intensity are coded by a single bit. Additionally, 8
bits each are needed to code 𝑥̅ and σ values of the block.
Thus 128 bits of the block are compressed to 32 bits
Compression Ratio (CR) = 4.
A total of 32 bits are transmitted by the encoder for a 4x4 block of 16 pixels
Bit Rate (BR) is 32 / 16 = 2.
The RMSE for this 4x4 block is:
RMSE4x4
= [0.25] [ (1-0.007)2 + (3-5.328)2 + (5-5.328)2 + (1-0.007)2 +
(6-5.328)2 + (2-0.007)2 + (3-5.328)2 + (4-5.328)2 +
(5-5.328)2 + (1-0.007)2 + (2-0.007)2 + (3-5.328)2 +
(6-5.328)2 + (1-0.007)2 + (2-0.007)2
+ (3-5.328)2 ] 0.5
RMSE4x4 ≈ 1.5992
The PSNR for this 4x4 block is:
PSNR4x4 = 20log10 ( 6 / 1.5922 ) ≈ 9.5764 dB
Contrast of the original 4x4 block is:
C4x4= [0.25] [ (1-3)2 + (3-3)2 + (5-3)2 +(1-3)2 +
(6-3)2 + (2-3)2 + (3-3)2 + (4-3)2 +
(5-3)2 + (1-3)2 + (2-3)2 + (3-3)2 +
(6-3)2 + (1-3)2 + (2-3)2 + (3-3)2 ]
0.5
 C4x4 ≈ 1.6956
Contrast of the BTC reconstructed block is calculated as shown below:
C4x4 BTC = [0.25] [ (0.007-3)2 + (5.328-3)2 + (5.328-3)2 + (0.007-3)2 +
(5.328-3)2 + (0.007-3)2 + (5.328-3)2 + (5.328-3)2 +
(5.328-3)2 + (0.007-3)2 + (0.007-3)2 + (5.328-3)2 +
(5.328-3)2 + (0.007-3)2 + (0.007-3)2 + (5.328-3)2 ] 0.5
 C4x4BTC≈ 2.6396
2.6
BTC APPLICATION ON SAMPLE IMAGES
The BTC is applied to all the blocks of an image and the images are
reconstructed and compared with the original image.
Four sample images, copya.jpg, city.jpg, hurricane.jpg and boat.jpg are subjected
to the traditional BTC for various block sizes and the results are displayed in Figures 2.4
and 2.5, 2.6 and 2.7 respectively. The parameters such as RMSE, PSNR and Contrast
are measured for various block sizes and tabulated in Table 2.2. Figures 2.8, 2.9 and
2.10 show the graphical representation of the Table 2.2.
(a)
(d)
(b)
(c)
(e)
(f)
Figure 2.4: (a) Original Image copya.jpg (b) – (f) Traditional BTC for block size 4x4, 8x8,
16x16, 32x32 and 64x64 for copya.jpg.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2.5: (a) Original Image city.jpg, (b) – (f) Traditional BTC for block size 4x4, 8x8,
16x16, 32x32 and 64x64 for city.jpg.
(a)
(b)
(d)
(e)
(c)
(f)
Figure 2.6: (a) Original Image hurricane.jpg, (b) – (f) Traditional BTC for block size 4x4,
8x8, 16x16, 32x32 and 64x64 for hurricane.jpg.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2.7: (a) Original Image boat.jpg, (b) – (f) Traditional BTC for block size 4x4, 8x8,
16x16, 32x32 and 64x64 for boat.jpg.
The contrast of the original images are measured and tabulated. These values are
compared with the contrast of the Traditional BTC in this chapter. Table 2.2 shows the
contrast values of the four sample images.
Table 2.2 : Contrast value for the original images.
S.No.
Images
Contrast
1
Copya.jpg
55.7629
2
City.jpg
55.9065
3
Hurricane.jpg
51.4933
4
Boat.jpg
46.6772
Table 2.3 :RMSE, PSNR and Contrast value for Traditional BTC for various block sizes.
Image
copya.jpg
city.jpg
Block Size
RMSE
PSNR
Contrast
4x4
1.4936
45.24
78.8770
8x8
1.4114
45.85
79.5406
16x16
1.2784
46.21
79.6656
32x32
1.1014
46.44
80.7490
64x64
1.0007
46.98
80.9710
4x4
1.4884
45.25
69.0979
8x8
1.4107
45.90
70.4971
16x16
1.2056
46.68
72.3398
32x32
1.0640
46.87
72.5891
hurricane.jpg
boat.jpg
64x64
1.0006
46.99
73.0150
4x4
1.4954
45.27
88.7278
8x8
1.4106
45.86
88.8158
16x16
1.2526
46.65
88.8159
32x32
1.1152
46.83
88.9196
64x64
1.0061
46.97
89.2277
4x4
1.4887
45.29
66.5552
8x8
1.4130
45.83
67.6581
16x16
1.2423
46.64
69.5588
32x32
1.1064
46.88
69.5962
64x64
1.0078
47.01
69.6929
The graphical representations of the parameters which are tabulated in Table 2.3 are
shown in the Figure 2.8, 2.9 and 2.10 respectively. The sample images which are taken
for processing are of 300 dpi (dots per inch).
1.6
1.4
1.2
RMSE
1
RMSE(copya.jpg)
0.8
RMSE (city.jpg)
0.6
RMSE (hurricane.jpg)
0.4
RMSE (boat.jpg)
0.2
0
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 2.8: Graph showing RMSE values for copya.jpg, city.jpg, hurricane.jpg and
boat.jpg.
In figure 2.8, the RMSE decreases as the block size increases.
47.5
Peak Signal To Noise Ratio
47
46.5
46
PSNR (copya.jpg)
PSNR (city.jpg)
45.5
PSNR (hurricane.jpg)
45
PSNR (boat.jpg)
44.5
44
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 2.9: Graph showing PSNR values for copya.jpg, city.jpg, hurricane.jpg and
boat.jpg.
In figure 2.9, the PSNR increases as the block size increases.
100
95
90
Contrast
85
Contrast(copya.jpg)
80
Contrast(city.jpg)
75
Contrast(hurricane.jpg)
70
Contrast(boat.jpg)
65
60
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 2.10: Graph showing Contrast values for copya.jpg, city.jpg, hurricane.jpg and
boat.jpg.
The BTC image, thus reconstructed block by block, is not the exact original
image, but a good approximation, with only low mean and high mean intensities in any
block. Although the compression increases with block size, as already shown in Table
2.1, the quality of the reconstructed BTC image degrades rapidly, as shown in Table
2.3, and as seen in Figures 2.2, 2.3, 2.4 and 2.5. Annoying blocking artifacts and false
contours are visible in larger block sizes BTC images in Figures 2.4, 2.5, 2.6 and 2.7.
2.7
COMPUTATIONAL TIME FOR IMAGE PROCESSING
Another parameter of importance in image processing is the processing time.
Since BTC is a simple algorithm, the processing time is less. Further, the time to
process an entire image decreases with increase in block size.
CPU time (or process time) is the amount of time for which a central processing
unit (CPU) was used for processing instructions of a computer program or operating
system.
The elapsed time is the time taken for waiting for input/output (I/O) operations or
entering low-power (idle) mode.
The following Table 2.4, Table 2.5, Table 2.6 and Table 2.7 show the CPU
processing time and elapsed time for the Traditional BTC, for various block sizes.
Table 2.4: CPU time and elapsed time for various block sizes of Traditional BTC for
copya.jpg.
Block Size
Table 2.5:
Elapsed Time
CPU Time
(in Seconds)
(in Seconds)
4x4
7.4964
4.0716
8x8
3.9663
1.1076
16x16
2.9917
0.7020
32x32
2.8148
0.6396
64x64
2.6026
0.5421
CPU
time
and elapsed time for various block sizes of Traditional BTC for city.jpg
Block Size
Elapsed Time
CPU Time
(in Seconds)
(in Seconds)
4x4
7.1648
3.4593
8x8
5.0324
1.1604
16x16
4.0001
0.5072
32x32
3.5744
0.4656
64x64
3.1979
0.4385
Block Size
Elapsed Time
CPU Time
(in Seconds)
(in Seconds)
4x4
7.7197
3.0888
8x8
5.0510
1.1544
16x16
4.5638
0.6708
32x32
4.0711
0.6084
64x64
3.8789
0.4056
Table 2.6: CPU time and elapsed time for various block sizes of Traditional BTC for
hurricane.jpg
Table 2.7: CPU time and elapsed time for various block sizes of Traditional BTC for
boat.jpg
Time in Seconds
Block Size
Elapsed Time
CPU Time
(in Seconds)
(in Seconds)
4x4
6.1134
3.2760
8x8
4.1570
1.2792
16x16
3.5266
0.6864
32x32
3.1266
0.4836
64x64
3.0701
0.4801
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Elapsed Time
CPU Time
4x4
8x8
16x16
Block Size
32x32
64x64
Figure 2.11: Graph showing the elapsed time and CPU Time for processing the image
copya.jpg (Traditional BTC) for various block sizes.
In figure 2.11, the elapsed time and the CPU time decreases as the block size
Time in Seconds
increases.
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Elapsed Time
CPU Time
4x4
8x8
16x16
Block Size
32x32
64x64
Figure 2.12: Graph showing the elapsed time and CPU Time for processing the image
city.jpg (Traditional BTC) for various block sizes.
In figure 2.12, the elapsed time and the CPU time decreases as the block size
Time in Seconds
increases.
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
Elapsed Time
CPU Time
Figure 2.13: Graph showing the elapsed time and CPU Time for processing the
hurricane.jpg (Traditional BTC) using various block sizes.
Time in Seconds
In figure 2.13, the elapsed time and the CPU time decreases as the block size
increases.
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Elapsed Time
CPU Time
4x4
8x8
16x16
Block Size
32x32
64x64
Figure 2.14: Graph showing the elapsed time and CPU Time for processing the boat.jpg
(Traditional BTC) using various block sizes.
In figure 2.14, the elapsed time and the CPU time decreases as the block size
increases.
2.8
CONCLUSION
In this chapter, the traditional BTC method has been applied to four sample
images and the performance parameters such as PSNR, RMSE, Contrast, Elapsed
Time and CPU Time have been estimated and compared. It is seen that as the block
size is increased for processing, the visual quality of the image degrades rapidly with
severe blocking artifacts and blurred edges.
3. MODIFIED BLOCK TRUNCATION CODING
3.1
MODIFIED BTC METHODS FOR IMPROVED CONTRAST
To improve the quality of the BTC images, several methods have
been proposed, such as vector quantization (VQ) which improves the
compression ratio [3], [13]. Vector quantization is the process of quantizing
the values of the pixels of the blocks of images. This is also called as block
quantization. The pixel values are encoded from a multidimensional vector
space (image pixels) into a finite set of values from a discrete subspace of
lower dimension (block pixels).
Using moment preservation and visual information to further
compress the image and to retain the image quality for real time processing
has been proposed [11]. A hybrid coding method by using look up tables
(LUT) and VQ to encode the bit map and low mean of the blocks is used for
compressing the images [14]; However these methods are usually
associated with high computational complexity.
Since the main aim of compression is to reduce the bit rate, the block
size is increased for higher compression ratio and lower bit rates. But the
annoying blocking artifacts and the blurred edges are prominently visible
when the Traditional BTC is applied for higher block sizes. This is evident in
the images shown in Figure 2.4, 2.5, 2.6 and 2.7 respectively in chapter 2.
To overcome this problem, a heuristic method has been designed which
gives the modified ‘low mean’ intensity value ‘a’ and ‘high mean’ intensity
value ‘b’ for each block, resulting in image reconstruction with improved
contrast. Two such modified BTC methods are presented in this chapter.
Both the methods are based on using modified low mean ‘a’ and high
mean ‘b’ values. Four number of sample images are subjected to BTC,
BTC1 and BTC2. The resulting RMSE, PSNR and Contrast parameters are
estimated for various block sizes of the images, and compared. The results
are tabulated in various Tables and also graphically displayed in various
Figures.
3.2
LOW MEAN AND HIGH MEAN VALUES FOR BTC1.
The low mean ‘a’ and high mean ‘b’ of BTC, specified in Eqns. (2.3.1)
and (2.3.2) are reproduced below.
a = x −σ
q
m−q
b = x +σ
m−q
q
(3.2.1)
(3.2.2)
We heuristically modify them and label them as ‘a1’ and ‘b1’.
a1 = x − σ
q
k +m
b1 = x + σ
k +m
q
(3.2.3)
(3.2.4)
where ‘ ’ is the block size (
3.3
4/8/16/32).
LOW MEAN AND HIGH MEAN VALUES FOR BTC2.
The ‘a’ and ‘b’ values
are modified as ‘a2’ and ‘b2’ in BTC2, as
shown in (3.3.1) and (3.3.2).
a 2 = ( x + Minvalue) / 2
(3.3.1)
b2 = ( x + Maxvalue) / 2
(3.3.2)
where
denotes the minimum value of the pixel intensity in
denotes the maximum value of the pixel intensity
the block and
in the block. This second modification has lesser computational complexity
compared to the traditional method of BTC as shown in Table 3.1.
Table 3.1:Comparison of computational complexities between the
Traditional BTC, BTC1 and BTC2.
BTC
No. of additions/
No. of Divisions/
Square root
Techniques
subtractions
Multiplications
operations
Traditional BTC
[2(k x k] + 3
[k x k ] +9
2
BTC1
[2(k x k] + 3
[k x k ] +9
2
BTC2
[k x k] + 2
[k x k] + 2
0
Four sample images are taken and the modified methods of BTC are
processed on all the images for various block sizes and the results are
compared with the Traditional BTC method.
Also, the processing time of the CPU and elapsed time of the
algorithm is also measured and compared with the Traditional BTC method.
3.4
NUMERICAL ANALYSIS BASED ON SIMULATION RESULTS
FOR SAMPLE IMAGES
Four sample images, namely ,’copya.jpg’, ‘city.jpg’, ‘hurricane.jpg’,
‘boat.jpg’, are taken and processed with BTC ,BTC1 and BTC2 techniques
for various block sizes and the results are compared.
Also, the processing time of the CPU and elapsed time of the
algorithm are measured and compared.
3.4.1 SIMULATION RESULTS FOR ‘COPYA.JPG’ IMAGE.
The original ‘copya.jpg’ image and the 4x4, 8x8, 16x16, 32x32 and
64x64 block based processed images using the BTC, BTC1 and BTC2
techniques are shown in Figure 3.1.
(a) Original Image ‘copya.jpg’.
(b) 4x4 BTC
(c) 4x4 BTC1
(d) 4x4 BTC2
(e) 8x8 BTC
(f) 8x8 BTC1
(h) 16x16 BTC
(i) 16x16 BTC1
(j) 16x16 BTC2
(l) 32x32 BTC1
(m) 32x32 BTC2
(k) 32x32 BTC
(n) 64x64 BTC
(o) 64x64 BTC1
(g) 8x8 BTC2
(p) 64x64 BTC2
Figure 3.1: (a) Original Image ‘copya.jpg’; [(b), (e), (h), (k), (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1images and [(d), (g), (j), (m), (p)] BTC2 images, for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.2 shows the comparison of MSE, PSNR and contrast
values between BTC, BTC1 and BTC2 techniques for original image
‘copya.jpg’.
Table 3.2: RMSE, PSNR and contrast values of BTC, BTC1 and BTC2 for
original image ‘copya.jpg’.
Block Size
Technique
BTC
4x4
BTC 1
BTC 2
BTC
8x8
BTC 1
BTC 2
BTC
16x16
BTC 1
BTC 2
BTC
32x32
BTC 1
BTC 2
BTC
64x64
BTC1
BTC 2
RMSE
1.4936
1.4806
1.4164
1.4114
1.4071
1.4065
1.2784
1.2414
1.2248
1.1014
1.0588
1.0555
1.0007
1.0003
1.0000
PSNR
Contrast
45.24
78.8770
47.83
80.2447
47.99
82.2195
45.85
79.5046
48.56
80.4273
48.78
82.5615
46.21
79.6656
48.82
80.5774
48.96
82.9433
46.44
80.7490
48.99
80.9915
49.00
83.3243
46.98
80.9710
49.01
81.1503
49.03
83.7737
The contents of Table 3.2 are graphically shown in Figure 3.2 and 3.3. It is
clear that the RMSE decreases and contrast increases with the increase in
block size of the image ‘copya.jpg’, compared to the traditional BTC.
Figure 3.2: Graph showing the comparison of RMSE values between BTC,
BTC1 and BTC2 techniques for ‘copya.jpg’.
Figure 3.3: Graph showing the comparison of Contrast values between
BTC, BTC1 and BTC2 techniques for ‘copya.jpg’.
3.4.2 SIMULATION RESULTS FOR ‘CITY.JPG’ IMAGE.
The original ‘city.jpg’ image and the 4x4, 8x8, 16x16, 32x32 and
64x64 block based
images produced using BTC, BTC1 and BTC2
techniques are shown in Figure 3.4 .
(a) Original image ‘city.jpg’
(b) 4x4 BTC
(c) 4x4 BTC1
(d) 4x4 BTC2
(e) 8x8 BTC
(f) 8x8 BTC1
(h) 16x16 BTC
(i) 16x16 BTC1
(g) 8x8 BTC2
(j) 16x16 BTC2
(k) 32x32 BTC
(l) 32x32 BTC1
(m) 32x32 BTC2
n) 64x64 BTC
(o) 64x64 BTC1
(p) 64x64 BTC2
Figure 3.4: (a) Original Image ‘city.jpg’; [(b), (e), (h), (k), (n)] BTC images;
[(c), (f), (i), (l), (o)] BTC1 images and [(d), (g), (j), (m), (p)] BTC2 images, for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.3 shows the comparison of RMSE, PSNR and
contrast values of BTC, BTC1 and BTC2 techniques for the image ‘city.jpg’.
Table 3.3: RMSE, PSNR and contrast values of BTC, BTC1 and BTC2
techniques for the image ‘city.jpg.’
Block Size
4x4
8x8
16x16
32x32
64x64
Technique
RMSE
PSNR
Contrast
BTC
1.4884
45.25
69.0979
BTC 1
1.4609
45.56
74.4971
BTC 2
1.4557
45.67
75.3629
BTC
1.4107
45.90
70.4971
BTC 1
1.4095
45.98
74.9919
BTC 2
1.4016
45.99
75.7854
BTC
1.2056
46.68
72.3398
BTC 1
1.1639
46.75
75.1763
BTC 2
1.1145
46.80
77.3704
BTC
1.0640
46.87
72.5891
BTC 1
1.0578
46.93
75.2245
BTC 2
1.0456
46.97
84.4975
BTC
1.0006
46.99
73.0150
BTC1
1.0002
47.03
75.3372
BTC 2
1.0001
47.06
100.3550
The contents of Table 3.3 are graphically shown in Figure 3.5 and 3.6. It is
clear that the RMSE decreases and contrast increases with the increase in
block size of the image ‘city.jpg’, compared to the traditional BTC.
1.6
1.4
RMSE for
Traditional
BTC
1.2
RMSE for
BTC 1
RMSE
1
0.8
RMSE for
BTC2
0.6
0.4
0.2
0
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 3.5: Graph showing the comparison of RMSE values of BTC, BTC1
and BTC2 techniques for the image ‘city.jpg’.
100
95
Contrast for
Traditional
BTC
Contrast
90
85
Contrast for
BTC 1
80
75
Contrast for
BTC 2
70
65
60
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 3.6: Graph showing the comparison of Contrast values of BTC,
BTC1 and BTC2 techniques for the image ‘city.jpg’.
3.4.3 SIMULATION RESULTS FOR ‘HURRICANE.JPG’ IMAGE.
The Figure 3.7 shows the image ‘hurricane.jpg’ and its BTC, BTC1 and
BTC2 images for various block sizes.
(a) Original image ‘hurricane.jpg'.
(b) 4x4 BTC
(e) 8x8 BTC
(c) 4x4 BTC1
(f) 8x8 BTC1
(d) 4x4 BTC2
(g) 8x8 BTC2
(h) 16x16 BTC
(k) 32x32 BTC
(n) 64x64 BTC
(i) 16x16 BTC1
(l) 32x32 BTC1
(o) 64x64 BTC1
(j) 16x16 BTC2
(m) 32x32 BTC2
(p) 64x64 BTC2
Figure 3.7: (a) Original Image hurricane.jpg, [(b), (e), (h), (k), (n)] BTC
images;
[(c), (f), (i), (l), (o)] BTC1 images and [(d), (g), (j), (m), (p)] BTC2 images for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.4 shows the comparison of RMSE, PSNR
and contrast values of BTC, BTC1 and BTC2 techniques for the image
‘hurricane.jpg’.
Table 3.4: RMSE, PSNR and contrast values of BTC, BTC1 and BTC2
techniques for the image ‘hurricane.jpg’.
Block Size
4x4
8x8
16x16
32x32
64x64
Technique
RMSE
PSNR
Contrast
BTC
1.4954
45.27
88.7278
BTC 1
1.4685
45.54
90.3342
BTC 2
1.4462
45.78
91.5343
BTC
1.4106
45.86
88.8158
BTC 1
1.4101
45.92
91.2428
BTC 2
1.4040
45.97
91.7896
BTC
1.2526
46.65
88.7278
BTC 1
1.1628
46.72
91.3247
BTC 2
1.1402
46.81
94.9780
BTC
1.1152
46.83
88.9196
BTC 1
1.0604
46.92
91.5248
BTC 2
1.0567
46.99
101.5987
BTC
1.0061
46.97
89.2277
BTC1
1.0017
47.04
91.7761
BTC 2
1.0004
47.11
108.8039
The contents of Table 3.4 are graphically shown in Figure 3.8 and 3.9. It is
clear that the RMSE decreases and contrast increases with the increase in
block size of the image ‘hurricane.jpg’, compared to the traditional BTC.
1.6
1.4
RMSE for Traditional BTC
RMSE for BTC1
1.2
RMSE for BTC2
Figure 3.8: Graph showing the comparison of RMSE values for BTC, BTC1
and BTC2 techniques for the image
‘hurricane.jpg’.
Figure 3.9: Graph showing the comparison of Contrast values of BTC,
BTC1 and BTC2 techniques for the image ‘hurricane.jpg’.
3.4.4 SIMULATION RESULTS FOR ‘BOAT.JPG’ IMAGE.
The Figure 3.10 shows the image ‘boat.jpg’ and its BTC, BTC1 and BTC2
images for various block sizes.
(a) Original image ‘boat.jpg’
(b) 4x4 BTC
(c) 4x4 BTC1
(e) 8x8 BTC
(f) 8x8 BTC1
(d) 4x4 BTC2
(g) 8x8 BTC2
(h) 16x16 BTC
(i) 16x16 BTC1
(j) 16x16 BTC2
(k) 32x32 BTC
(l) 32x32 BTC1
(m) 32x32 BTC2
(n) 64x64 BTC
(o) 64x64 BTC1
(p) 64x64 BTC2
Figure 3.10: (a) Original Image ‘boat.jpg’,
[ (b),(e), (h), (k) , (n)]
BTC
images;
[(c), (f), (i), (l), (o)] BTC1 images and [(d), (g), (j), (m), (p)] BTC2 images for
block sizes of 4x4, 8x8, 16x16, 32x32 and 64x64 respectively.
The following Table 3.5 shows the comparison of RMSE, PSNR and
contrast values of BTC, BTC1 and BTC2 techniques for the image
‘boat.jpg.
Table 3.5: RMSE, PSNR and Contrast values of BTC, BTC1 and BTC2
techniques for the image ‘boat.jpg’.
Block Size
4x4
8x8
16x16
32x32
64x64
Technique
RMSE
PSNR
Contrast
BTC
1.4887
45.29
66.5552
BTC 1
1.4655
45.51
69.8724
BTC 2
1.4177
45.72
72.6433
BTC
1.4130
45.83
67.6581
BTC 1
1.4091
45.91
70.7878
BTC 2
1.4059
45.98
73.2778
BTC
1.2423
46.64
69.5588
BTC 1
1.1741
46.76
71.0560
BTC 2
1.1415
46.94
73.6965
BTC
1.1064
46.88
69.5962
BTC 1
1.0946
46.96
71.3211
BTC 2
1.0536
46.99
78.3487
BTC
1.0078
47.01
69.6929
BTC1
1.0014
47.06
72.0257
BTC 2
1.0007
48.21
87.2638
The contents of Table 3.5 are graphically shown in Figure 3.11 and 3.12. It
is observed that the RMSE decreases and contrast increases with the
increase in block size of the image ‘boat.jpg’, compared to the traditional
BTC.
1.6
1.2
RMSE for
Trditional BTC
RMSE for BTC 1
1
RMSE for BTC 2
RMSE
1.4
0.8
0.6
0.4
0.2
0
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 3.11: Graph showing the comparison of RMSE values for of BTC,
BTC1 and BTC2 techniques for the image ‘boat.jpg’.
90
85
Contrast
80
Contrast for
Trditional BTC
75
Contrast for
BTC 1
70
Contrast for
BTC 2
65
60
4x4
8x8
16x16
32x32
64x64
Block size
Figure 3.12: Graph showing the comparison of Contrast values of BTC,
BTC1 and BTC2 techniques for the image ‘boat.jpg’.
3.4.5 COMPARISION OF COMPUTATIONALTIME FOR BTC, BTC1 AND
BTC2.
In Section 2.7, the computational time for BTC images of various
block sizes are listed. In this Section, the computational time ( Elapsed Time
and CPU Time) for BTC1 and BTC 2 are compared with traditional BTC, in
respect of the images ‘copya.jpg’, ‘city.jpg’, ’hurricane.jpg’ and ‘boat.jpg’.
The results are listed in separate Tables and also illustrated graphically in
separate Figures.
Table 3.6: Elapsed time and CPU time for BTC, BTC1 and BTC2
techniques for image ‘copya.jpg’.
Block Size
4x4
8x8
16x16
32x32
64x64
Technique
Elapsed time
CPU time
In seconds
In seconds
BTC
7.4964
4.0716
BTC 1
4.5328
3.2349
BTC 2
3.6531
1.4820
BTC
3.9663
1.1076
BTC 1
3.7115
0.9861
BTC 2
3.4313
0.5748
BTC
2.9917
0.7020
BTC 1
2.9690
0.6724
BTC 2
2.9320
0.3276
BTC
2.8148
0.6396
BTC 1
2.7523
0.5814
BTC 2
2.7378
0.2496
BTC
2.6026
0.5421
BTC1
2.5663
0.4219
BTC 2
2.5446
0.1872
Elapsed Time in Seconds
8
7
6
5
Traditional BTC
4
BTC 1
BTC 2
3
2
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 3.13: Graph showing Elapsed time for BTC, BTC1 and BTC2
techniques and block sizes for image ‘copya.jpg’.
In figure 3.13, the elapsed time for BTC2 < BTC1 < BTC.
4.5
CPU Time (in Seconds)
4
3.5
3
2.5
Traditional BTC
2
1.5
BTC 1
1
BTC 2
0.5
0
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 3.14: Graph showing CPU time for BTC, BTC1 and BTC2 techniques
and block sizes for image ‘copya.jpg’.
In figure 3.14, the CPU time for BTC2 < BTC1 < BTC.
Table 3.7: Elapsed time and CPU time of BTC, BTC1 and BTC2 techniques
for image ‘city.jpg’.
Block Size
4x4
8x8
16x16
32x32
64x64
Technique
Elapsed time
CPU time
In seconds
In seconds
BTC
7.7197
3.4476
BTC 1
6.0120
3.0888
BTC 2
4.2625
1.5756
BTC
5.0510
1.1700
BTC 1
4.8926
1.1544
BTC 2
4.3002
0.6708
BTC
4.5638
0.5772
BTC 1
3.7930
0.6281
BTC 2
3. 5721
0.4912
BTC
4.0711
0.6084
BTC 1
3.4917
0.4524
BTC 2
3.2096
0.2964
BTC
3.8789
0.4197
BTC1
3.1327
0.4056
BTC 2
3.0026
0.1092
9
d time (in Seconds)
8
7
6
5
4
Traditional BTC
BTC 1
Figure 3.15: Graph showing Elapsed time for BTC, BTC1 and BTC2
techniques and block sizes for image ‘city.jpg’.
In figure 3.15, the elapsed time for BTC2 < BTC1 < BTC.
4
3.5
3
2.5
Traditional BTC
2
BTC 1
1.5
BTC 2
1
0.5
0
4x4
8x8
16x16
32x32
64x64
Figure 3.16: Graph showing CPU time for BTC, BTC1 and BTC2 techniques
and block sizes for image ‘city.jpg’.
In figure 3.16 , the CPU time for BTC2 < BTC1 < BTC.
Table 3.8: Elapsed time and CPU time of BTC, BTC1 and BTC2 techniques
for image ‘‘hurricane.jpg’.
Block Size
4x4
8x8
16x16
32x32
64x64
Technique
Elapsed time
CPU time
In seconds
In seconds
BTC
7.1648
3.4593
BTC 1
5.9649
3.1898
BTC 2
3.9714
1.5288
BTC
5.0324
1.1604
BTC 1
4.0308
1.1974
BTC 2
3.6239
0.5148
BTC
4.0001
0.5072
BTC 1
3.6242
0.5066
BTC 2
3.4812
0.3120
BTC
3.5744
0.4656
BTC 1
3.4013
0.4533
BTC 2
3.2911
0.2184
BTC
3.1979
0.4385
BTC1
3.1033
0.4122
BTC 2
3.0719
0.1872
8
Elapsed Time in Seconds
7
6
Traditional BTC
BTC 1
5
4
3
2
BTC 2
Figure 3.17: Graph showing Elapsed time of BTC, BTC1 and BTC2
techniques for image ‘hurricane.jpg’.
In figure 3.17 , the elapsed time for BTC2 < BTC1 < BTC.
4
3.5
3
2.5
Traditional BTC
2
BTC 1
1.5
BTC 2
1
0.5
0
4x4
8x8
16x16
32x32
64x64
Figure 3.18: Graph showing CPU time of BTC, BTC1 and BTC2 techniques
for image ‘hurricane.jpg’.
In figure 3.18 , the CPU time for BTC2 < BTC1 < BTC.
Table 3.9: Elapsed time and CPU time of BTC, BTC1 and BTC2 techniques
for image ‘boat.jpg’.
Block Size
Technique
Elapsed time
CPU time
4x4
8x8
16x16
32x32
64x64
In seconds
In seconds
BTC
6.1134
3.2760
BTC 1
5.6977
3.0108
BTC 2
4.1575
1.4820
BTC
4.1570
1.2792
BTC 1
3.5513
0.9828
BTC 2
2.5408
0.4212
BTC
3.5266
0.6864
BTC 1
3.4396
0.6084
BTC 2
2.7437
0.2964
BTC
3.1266
0.4836
BTC 1
2.7744
0.4680
BTC 2
2.5200
0.1872
BTC
3.0701
0.4801
BTC1
2.7690
0.4368
BTC 2
2.4988
0.1716
7
Elapsed Time in Seconds
6
5
4
Traditional BTC
3
BTC 1
2
1
BTC 2
Figure 3.19: Graph showing Elapsed time of BTC, BTC1 and BTC2
techniques for image ‘boat.jpg’.
In figure 3.19 , the elapsed time for BTC2 < BTC1 < BTC.
3.5
CPU Time in Seconds
3
2.5
2
Traditional BTC
1.5
BTC 1
1
BTC 2
0.5
0
4x4
8x8
16x16
32x32
64x64
Block Size
Figure 3.20: Graph showing CPU time of BTC, BTC1 and BTC2 techniques
for image ‘boat.jpg’.
In figure 3.20 , the CPU time for BTC2 < BTC1 < BTC.
4. LEAST MEAN SQUARE ERROR BASED BLOCK TRUNCATION
CODING FOR IMPROVED PSNR VALUE
4.1
MEAN SQUARE ANALYSIS FOR BLOCK TRUNCATION CODING
In order to improve the PSNR of BTC images, the best values for the
low-mean ‘a’ and high-mean ‘b’ for the BTC image blocks can be estimated
using Least Mean Square Error {LMSE} method. A suitable technique has
been developed in this research and the procedure is described next, using a
4x4 block example. The procedure can be used for larger size blocks also,
such as 8x8, 16x16, 32 x 32 etc.
Let us consider a 4x4 block of an image and arrange the intensity
values of the 16 pixels in ascending order from
to
.
Maintaining the
ascending order, the 16 values are divided into two groups by placing the
group divider, first between
between
and
and
, next between
and
,
then
and so on and so forth .This will yield the following 15
different sets of groups. The formation of these 15 sets of groups is shown in
the Table 4.1 shown below.
Table 4.1: 15 sets of groups for a block of 4x4
Set Number
Group 1
Group 2
1
to
2
to
3
to
to
4
to
to
5
to
to
6
to
to
7
to
to
8
to
to
9
to
to
10
to
to
11
to
to
12
to
to
13
to
to
14
to
,
15
to
In any set, the mean intensity of Group 1 is taken as ‘a’ and the mean
intensity of Group 2 is taken as ‘b’. The encoder estimates the variance σ12
of Group 1 pixels and σ22 of Group 2 pixels. The set with Least Mean Square
Error (LMSE) is identified as follows.
4.2
IDENTIFICATION OF LEAST MEAN SQUARE ERROR SET
Consider any of the 15 sets of a 4x4 block of an image. The nth set
has intensity values
to
in Group 1, with mean ‘a’, and
Group 2, with mean ‘b’.
After BTC, the sum of squared errors for Group 1 will be
to
in
(4.2.1)
which is equal to
(4.2.2)
Hence the Mean Square Error (MSE) will be
, where
is the Standard
Deviation of the Group 1.
Likewise the sum of squared errors for Group 2 will be
(4.2.3)
which is equal to
(4.2.4)
Hence the MSE will be
, where
is the Standard Deviation of the Group
2. For the nth set, the sum of squared errors is
(4.2.5)
(4.2.6)
Hence the MSE for the set is
(4.2.7)
This MSE is calculated for all the 15 sets of the block. The set with Least
Mean Square Error (LMSE) is chosen for BTC, and coded with 0s for Group
1 pixels, and 1s for Group 2 pixels. This bit plane of the block is transmitted
along with coded mean ‘a’ and mean ‘b’ values of the block. The decoder
recreates the image block by simply decoding the 0s as intensity ‘a’ and 1s
as intensity ‘b’. This decoded block, in comparison with the original block,
has the least error as it is chosen on LMSE criterion. This shows that the
block having the least mean square error will also have the maximum Peak
Signal to Noise Ratio (PSNR) value. This LMSE based BTC procedure is
repeated for all the blocks of the original image. A set of four images and
their LMSE based BTC (LMSE-BTC) images, using 4x4 block size, are
shown in the next section.
4.3
SIMULATION RESULTS
(a)
(c)
(e)
(b)
(d)
(f)
(g)
(h)
Figure 4.1: (a) Original Image copya.jpg (b) LMSE –BTC image copya.jpg,
(c) Original Image city.jpg (d) LMSE-BTC image city.jpg, (e) Original Image
Hurricane.jpg, (f) LMSE –BTC image hurricane.jpg, (g) Original Image
boat.jpg, (h) LMSE – BTC image boat.jpg.
The Mean Square Error values are calculated for each iteration of the
groups of blocks for the images and tabulated accordingly. Table 4.2, Table
4.3, Table 4.4 and Table 4.5 show the MSE values for fifteen different groups
of blocks for the first 4x4 block of each image.
Table 4.2: MSE and PSNR for 15 sets of groups for LMSE based BTC
method for Copya.jpg
Set
Mean
Number
Square
PSNR
Set
Mean
Number
Square
PSNR
Error
Error
1
0.64
48.77
9
0.62
49.54
2
0.62
49.54
10
0.64
48.77
3
0.61
50.79
11
0.63
49.12
4
0.62
49.54
12
0.60
50.56
5
0.63
49.12
13
0.66
46.45
6
0.62
49.54
14
0.64
48.77
7
0.64
48.77
15
0.63
49.12
8
0.61
50.79
-----
-----
-----
0.7
Mean Square Error
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Set Number for the groups
Figure 4.2: Graph showing the MSE values of the 15 sets of the LMSE based
BTC for Copya.jpg.
In the Figure 4.2, the 12th set has got the least mean square value.
Therefore the bit plane for this set is transmitted. Similarly the bit planes
having the least MSE value for all other 4x4 blocks of the entire image is
obtained and transmitted. The PSNR is calculated for all these LMSE – BTC
blocks and the average of the values are calculated. This average value
gives the PSNR of the reconstructed image. This average value of PSNR is
tabulated for various block sizes as shown in Table 4.3.
Table 4.3: PSNR values for various block sizes based on LMSE-BTC
Image
Copya.jpg
Block Size
PSNR
4x4
50.98
8x8
51.32
16x16
51.44
32x32
51.86
64x64
51.97
The Table 4.4 shown below gives the MSE values of the first 4x4
block of the image city.jpg after performing the LMSE – BTC algorithm.
Table 4.4: MSE and PSNR for 15 sets of groups for the LMSE based BTC
method for city.jpg
Set
Mean
PSNR
Number
Square
Set
Mean
Number
Square
Mean Square Error
Error
PSNR
Error
1
0.40
51.89
9
0.42
51.42
2
0.41
51.78
10
0.43
50.99
3
0.44
50.32
11
0.42
51.42
4
0.42
51.42
12
0.41
51.78
5
0.43
50.99
13
0.42
51.42
6
0.42
51.42
14
0.43
50.99
7
0.44
50.32
15
0.44
50.32
8
0.41
51.78
-----
-----
-----
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Set Number for the groups
Figure 4.3: Graph showing the MSE values of the 15 sets of the LMSE based
BTC for city.jpg
From the above graph it is clear that the first set in the first 4x4 block
of image ‘city.jpg’ gives the least value of the MSE. Therefore this bit plane
along with the values of ‘a’ and ‘b’ is transmitted. Similarly the bit planes for
all the other blocks are also obtained and transmitted. Table 4.5 shows the
average PSNR values for various block sizes of the image city.jpg.
Table 4.5: PSNR values for various block sizes based on LMSE-BTC
Image
Block Size
PSNR
4x4
51.86
8x8
52.01
16x16
52.19
32x32
52.34
64x64
52.55
City.jpg
Table 4.6: MSE and PSNR for 15 sets of groups for the LMSE based BTC
method for hurricane.jpg.
Set
Mean
Number
Square
PSNR
Set
Mean
Number
Square
Error
PSNR
Error
1
0.46
49.76
9
0.43
50.32
2
0.47
50.54
10
0.45
49.99
3
0.46
49.76
11
0.46
49.76
4
0.42
51.88
12
0.45
49.99
5
0.43
50.32
13
0.47
48.58
6
0.46
49.76
14
0.43
50.32
7
0.47
50.54
15
0.45
49.99
8
0.43
50.32
-----
-----
-----
Mean Square Error
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Set Number for the Groups
Figure 4.4: Graph showing the MSE values of the 15 sets of the LMSE based
BTC for hurricane.jpg.
In the Figure 4.4, the 4th set has got the least mean square value.
Therefore the bit plane for this set is transmitted. Similarly the bit planes for
all the other blocks are also obtained and transmitted. Table 4.7 shows the
average PSNR values for various block sizes of the image hurricane.jpg.
Table 4.7: PSNR values for various block sizes based on LMSE-BTC
Image
Hurricane.jpg
Block Size
PSNR
4x4
51.90
8x8
51.94
16x16
52.11
32x32
52.23
64x64
52.54
Table 4.8: MSE and PSNR for 15 sets of groups for the LMSE based BTC
method for boat.jpg.
Set
Mean
Number
Square
PSNR
Set
Mean
Number
Square
Error
PSNR
Error
1
0.53
48.32
9
0.52
49.86
2
0.56
48.01
10
0.53
48.32
3
0.51
50.22
11
0.52
49.86
4
0.55
48.26
12
0.55
48.26
5
0.53
48.32
13
0.56
48.01
6
0.52
49.86
14
0.52
49.86
7
0.53
48.32
15
0.55
48.26
8
0.55
48.26
-----
-----
-----
0.6
Mean Square Error
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Set Number for the Groups
Figure 4.5: Graph showing the MSE values of the 15 sets of the LMSE based
BTC for boat.jpg.
In the Figure 4.5, the 3rd set has got the least mean square value.
Therefore the bit plane for this set is transmitted. Similarly the bit planes for
all the other blocks are also obtained and transmitted. Table 4.9 shows the
average PSNR values for various block sizes of the image boat.jpg.
Table 4.9: PSNR values for various block sizes based on LMSE-BTC
Image
Boat.jpg
Block Size
PSNR
4x4
50.45
8x8
50.67
16x16
50.99
32x32
51.11
64x64
51.23
Thus, the Least Mean Square Error based BTC has been performed on four
sample images of 300 dpi. In the next chapter the results obtained for all the
BTC methods are compared and tabulated.
5. SUMMARY OF RESEARCH FINDINGS , CONCLUSION AND
FUTURE SCOPE
In this final chapter, the results of the research findings reported in
the previous chapters are consolidated, analyzed and a methodology is
developed for an optimum Block Truncation Coding.
5.1
COMPARISON OF RMSE, CONTRAST AND PSNR VALUES FOR
THE IMAGES OF VARIOUS BTC METHODS
In the previous chapters, based on the concept of traditional BTC,
two different modified methods of BTC, namely BTC1 and BTC2 were
developed. Also, a Least Mean Square Error based BTC was proposed in
the 4th chapter. In this section we will compare the RMSE, Contrast and
PSNR values for the various BTC methods for block size of 4x4. The
following figures 5.1, 5.2, 5.3 and 5.4 shows the comparative performance
for the sample image copya.jpg, city.jpg, hurricane.jpg and boat.jpg.
(a)
(b)
(d)
(c)
(e)
Figure 5.1: (a) Original Image copya.jpg (b) Traditional BTC (c) BTC 1 (d)
BTC 2 (e) LMSE based BTC for block size of 4x4.
(b)
(a)
(d)
(c)
(e)
Figure 5.2: (a) Original Image city.jpg (b) Traditional BTC (c) BTC 1 (d) BTC
2 (e) LMSE based BTC for block size of 4x4.
(b)
(a)
(d)
(c)
(e)
Figure 5.3:(a) Original Image hurricane.jpg (b) Traditional BTC (c) BTC1 (d)
BTC2 (e) LMSE based BTC for block size of 4x4.
(b)
(a)
(d)
(c)
(e)
Figure 5.4:(a) Original Image boat.jpg (b) Traditional BTC (c) BTC1 (d)
BTC2 (e) LMSE based BTC for block size of 4x4.
5.2
TABULATION OF THE RESULTS FOR VARIOUS BTC METHODS
The RMSE, PSNR and Contrast values of the above images are
tabulated as shown in Table 5.1. The comparisons are made for all the
images shown above for a block size of 4x4. The images are of the same
size (1024x1024) and the bit depth for the images are 300 dpi (dots per
inch).
Table 5.1: RMSE, PSNR and Contrast values of BTC, BTC1, BTC2 and
LMSE – BTC techniques for the images copya.jpg, city.jpg, hurricane.jpg
and boat.jpg.
Images
Copya.jpg
Technique
RMSE
PSNR
Contrast
BTC
1.4936
45.24
78.8770
BTC 1
1.4806
47.83
80.2447
BTC 2
1.4164
47.99
82.2195
LMSE-BTC
0.6324
50.98
85.0011
BTC
1.4884
45.25
69.0979
BTC 1
1.4608
45.56
74.4971
BTC 2
1.4557
45.67
75.3629
LMSE-BTC
0.7745
51.86
77.3459
BTC
1.4953
45.27
88.7278
BTC 1
1.4684
45.54
90.3342
BTC 2
1.4461
45.78
91.5343
LMSE-BTC
0.6480
51.90
93.2200
BTC
1.4886
45.29
66.5552
BTC 1
1.4655
45.51
69.8724
BTC 2
1.4176
45.72
72.6433
LMSE-BTC
0.7141
50.45
75.3244
City.jpg
Hurricane.jpg
Boat.jpg
5.3
GRAPHICAL REPRESENTATION OF THE COMPARATIVE
RESULTS FOR VARIOUS BTC METHODS
Figure 5.5: Graph showing the RMSE values for various BTC methods for
the image copya.jpg.
52.5
50
PSNR
47.5
45
42.5
40
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.6: Graph showing the PSNR values for various BTC methods for
the image copya.jpg.
86
85
84
83
82
Figure 5.7: Graph showing the Contrast values for various BTC methods for
the image copya.jpg.
1.6
1.4
1.2
RMSE
1
0.8
0.6
0.4
0.2
0
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.8: Graph showing the RMSE values for various BTC methods for
the image city.jpg.
55
52.5
Figure 5.9: Graph showing the PSNR values for various BTC methods for
the image city.jpg.
78
76
Contrast
74
72
70
68
66
64
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.10: Graph showing the Contrast values for various BTC methods
for the image city.jpg.
1.6
1.4
1.2
RMSE
1
0.8
0.6
0.4
0.2
0
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.11: Graph showing the RMSE values for various BTC methods for
the image hurricane.jpg.
55
52.5
PSNR
50
47.5
45
42.5
40
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.12: Graph showing the PSNR values for various BTC methods for
the image hurricane.jpg.
94
93
Contrast
92
91
90
89
88
87
86
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.13: Graph showing the Contrast values for various BTC methods
for the image hurricane.jpg.
1.6
1.4
1.2
RMSE
1
0.8
0.6
0.4
0.2
0
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.14: Graph showing the RMSE values for various BTC methods for
the image boat.jpg.
55
52.5
PSNR
50
47.5
45
42.5
40
BTC
BTC1
BTC2
LMSE -BTC
Various BTC Methods
Figure 5.15: Graph showing the PSNR values for various BTC methods for
the image boat.jpg.
76
74
Contrast
72
70
68
66
64
62
BTC
BTC1
BTC2
Various BTC Methods
LMSE -BTC
Figure 5.16: Graph showing the Contrast values for various BTC methods
for the image boat.jpg.
5.4
DISCUSSIONS ON THE VARIOUS BTC METHODS DEVELOPED
AND COMPARISON WITH INTERPOLATIVE BTC.
In the traditional BTC, it is found that the Contrast, RMSE and PSNR
which are the performance measures of an image, are poor. The images
have blurred edges and low contrast, as the block size is increased to
obtain higher compression ratio. This problem is overcome in the BTC1
method, wherein the block size ‘k’ was introduced in the formulae of
equations 3.2.1 and 3.2.2 and replaced with formulae in equations 3.2.3 and
3.2.4 respectively. Here the contrast values and PSNR are improved
substantially for higher block sizes.
In order to further improve the contrast and PSNR of the images,
BTC2 has been developed. In this method, the computational complexity
present in the Traditional BTC and BTC1 is reduced by incorporating only
additions and subtractions in the formulae used for substituting the low
mean and high mean values of the block. Also, the computational time
required by the processors is the less compared to other methods. Further,
the contrast and the PSNR values of the images have also been improved
substantially.
The third method developed is based on ‘Least Mean Square Error
criterion’. This method yields better contrast and PSNR values. However the
computational complexity is high for higher block sizes, since more number
of iterations is required. This means that for an 8x8 block, there would be 63
groups of bit planes and the encoder should get the mean values for each
block to get the ‘Least Mean Square Error’.
For comparison, the city.jpg image has also been processed using
Minimum Mean Square Error BTC [29] based on interpolation and the
results are compared with LMSE – BTC.
Table 5.2: Comparison of LMSE - BTC and Interpolative BTC
Block Size
4x4
8x8
16x16
32x32
64x64
5.5
Techniques
RMSE
LMSE – BTC
0.7745
Interpolative BTC
1.3242
LMSE – BTC
0.7523
Interpolative BTC
1.3211
LMSE – BTC
0.7363
Interpolative BTC
1.3201
LMSE – BTC
0.7322
Interpolative BTC
1.3199
LMSE – BTC
0.7291
Interpolative BTC
1.3176
CONCLUSION
The BTC1, BTC2 and LMSE based BTC methods developed are compared
and a consolidated tabulation of all the methods such as traditional BTC,
BTC1, BTC2 and LMSE based BTC is done in order to evaluate their
performance. These methods which are developed satisfy the objectives of
this research, set forth in Chapter 1. Further, based on the performance
analysis, it is concluded that LMSE based BTC is the best among the three
methods developed.
5.6
SCOPE FOR FUTURE WORK
This research work can be combined with various digital halftoning
techniques to further reduce the blocking artifacts and false contours in
reconstructed images.
The BTC methods developed can be extended to color images, by
individually dealing with the RGB primary color components of the pixels. It
can also be extended for compressing 3-D images, by dividing images into
suitable basic cube blocks of pixels.
REFERENCES
[1]
Healy D.J and Mitchell O.R, “ Digital Video Bandwidth Compression
using BTC”, IEEE Transactions on Communication, Vol. COM-29,
pp. 1809-1817, 1981.
[2]
Arce G and Gallagher N.C, “ BTC Image Coding using Median Filter
Roots”, IEEE Transactions on Communications, Vol. 31, No. 6, pp.
784-793, 1983.
[3]
Davignon A, “Block Classification Scheme using Binary Vector
Quantization for Image Coding”, International Journal of
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LIST OF PUBLICATIONS
1. Chandravadhana S and Nithiyanandam N, “Compression of Satellite images
using Lossy and Lossless Coding Techniques”, International Journal of
Engineering and Technology”, ISSN-
09754024, Vol 6, Issue 1,pp-118-128
February 2014, (indexed in Annexure I of B.S.A.University).
2. Chandravadhana S and Nithiyanandam N, “Least Mean Square Error Based
Block Truncation Coding” – Accepted for publication(ID - IJICT-80860)
in
“International Journal of Information and Communication Technology”, ISSN
1741-8070
(Inderscience
publications)
(indexed
in
Annexure
I
of
B.S.A.University).
3. Chandravadhana S and Nithiyanandam N, “Improved block truncation coding
using lossy and lossless compression techniques”, Proceedings of IEEE
International Conference on Communication and Signal Processing (ICCSP’13),
ISBN
No.
979-1-4679-1620-0,
pp-1294-
1298,
held
on
5.4.2013,
in
Adhiparasakthi College of Engineering, Melmaruvathur.
4. Chandravadhana S and Nithiyanandam N, “Code Compression Techniques for
Image signals”, National Conference NCRVIC 2012, held in B.S.Abdur Rahman
University.
COMMUNICATIONS UNDER REVIEW
1.
Chandravadhana S and Nithiyanandam N, “Block processed error diffusion for
high speed compression of still images”, “WSEAS Transactions on Signal
Processing”, Print ISSN: 1790-5052 , E-ISSN: 2224-3488. (indexed in Annexure I
of B.S.A.University).
TECHNICAL BIOGRAPHY
S.CHANDRAVADHANA (RRN: 1084205) was born on 16th June 1969, in
Madurai, Tamilnadu, India. She did her high school in Kendriya Vidhyalaya,
Trichy and higher secondary in Savithri Vidhyasala, Trichy, scoring 90.5%. She
received her B.E (ECE) Degree with first class from Madurai Kamaraj University
in 1991. She received her M.E (Applied Electronics) Degree with first class and
distinction from Sathyabama University in 2007. She was teaching courses in
Electronics and Communication engineering in various institutions from 1997
and at S.M.K.Fomra Institute of Technology, from 2003 to 2011. Currently she is
teaching at Agni College of Technology, Anna University, Chennai. She is also
a research scholar at B.S.Abdur Rahman University. Her areas of research
interest are image processing, digital communication, and wireless sensor
networks. The e-mail ID is: [email protected]. Contact phone number
is: 091-9994186091.
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