An Efficient APOA Techniques For Generalized Residual Vector Quantization Based Image Compression

AN EFFICIENT APOA TECHNIQUES FOR GENERALIZED RESIDUAL
VECTOR QUANTIZATION BASED IMAGE COMPRESSION
Divya A1
and Dr.Sukumaran S2
1Ph.D Research Scholar, Department of Computer Science, Erode Arts and Science College, Erode, Tamil Nadu, India
2Associate Professor, Department of Computer Science, Erode Arts and Science College, Erode, Tamil Nadu, India
Email: 1divi.ard@gmail.com, 2prof_sukumar@yahoo.co.in
ABSTRACT
Vector quantization (VQ) is a powerful technique in the field of digital image compression. The generalized
residual codebook is used to remove the distortion in the reconstructed image for further enhancing the quality of the
image. Already, Generalized Residual Vector Quantization (GRVQ) was optimized by Particle Swarm Optimization (PSO)
and Honey Bee Mating Optimization (HBMO). The performance of GRVQ was degraded due to instability in convergence
of the PSO algorithm when particle velocity is high and the performance of HBMO algorithm is depended on many
parameters which are required to tune for reducing size of codebook. So, in this paper the Artificial Plant Optimization
Algorithm (APOA) is used to optimize the parameters used in GRVQ. The Extensive experiment demonstrates that
proposed APOA-GRVQ algorithm outperforms than existing algorithm in terms of quantization accuracy and computation
accuracy.
Keywords: Vector Quantization, Compression, APOA, GRVQ, PSO and HBMO.
INTRODUCTION
In Digital Image, the storing and transferring of
the large amount of data is the challenging issue in recent
days because the uncompressed data is occupied large
amount of data and transmission bandwidth. The image
compression is mapped the higher dimensional space into
a lower dimensional space. Image compression is
categorized as Lossy and Lossless (Chen, S. X., and Li, F.
W 2012). The original image is completely recovered by
lossless compression. In a medical field, the Lossless
compression is efficiently used whereas lossy compression
is used in natural images and other applications where the
minor degrade is accepted and get significant decreases in
bit rate. This paper is focused on Lossy Compression
technique using VQ for compressing images.
VQ is a lossy data compression based on
the principle of block coding (Horng, M. H 2012). It is a
fixed-to-fixed length encoding algorithm. Applying VQ on
multimedia is challenging problem due to the handle
multi-dimensional data. In 1980, Linde, Buzo, and Gray
(LBG) proposed a VQ algorithm based on training
sequences (Chen, Y., et.al.2010). The use of training
sequences bypasses the need for multi-dimensional
integration. In VQ distance is found among blocks with
extra fix (Babenko, A., and Lempitsky, V 2014). The
GRVQ is removed this extra fix by introducing
regularization on the codebook learning phase (Shicong
Liu., et.al.2017). The GRVQ reduces the complexity of the
VQ methods. The main goal of GRVQ is iteratively select
a codebook and optimize it with the current residual
vectors and then re-quantize the dataset to obtain the new
residual vectors for the next iteration.
The GRVQ was optimized by using PSO and
HBMO algorithm (Divya, A.., and Sukumaran, S 2017).
The performance of the PSO was reduced if the particle
velocity is high it undergoes instability in convergence and
the HBMO algorithm performance is depend on several
parameters and many independent parameters are required
to tune for designing efficient codebook these leads to
increase the complexity. In order to further improve
GRVQ in this paper, the APOA is presented to optimize
the quantization accuracy and computation efficiency.
In section II, various research methodologies are
that are to be evaluated are discussed in a detailed manner.
In section III, discussed and detailed about the proposed
methodologies, in section IV the results of the proposed
and existing methodologies are discussed. Finally in
section V, the conclusion of the research work is
presented.
LITERATURE SURVEY
Horng et al. [HOR11] the new novel method was
presented based on Honey Bee Mating Optimization
technique to enhance the performance of LBG
compression technique. The new method was found the
optimal result from the training data and constructs the
codebook based on vector quantization. The performance
of the proposed method was compared with LBG, PSO-
LBG and QPSO-LBG algorithms. The result shows, the
HBMO-LBG was more reliable and reconstructed images
get the higher quality than all other algorithms.
Yang et al. [YAN09] introduced to solve the
optimization problems. The proposed Cuckoo Search
Optimization Algorithm was compared with genetic
algorithm and particle swarm algorithm the result shows
that the CS was superior for multi model objective
functions. Moreover, the CS was more robust for many
optimization problems and can easily extent with multi
objective optimization applications with several
constraints even with NP-hard problems.
Omari et al. [OMA15] presented to improve the
quality of the reconstructed image after decompression.
The lossy compression was applied to gain the high
compression ratios. The proposed approach was used to
reduce the rational numbers in to the non dominator form
and enhance the efficiency of the genetic algorithm to find
the better rational numbers with shorter form.
Bai et al. [BAI 16] proposed to improve the
performance of the vector compression. The Multiple
Stage Residual Model (MSRM) utilized to residual vector
and improve the image classification. The MSRM with
VQ was used to adjust the vector compression and deliver
the higher performance compare with traditional
algorithms.
International Journal of Computer Science and Information Security (IJCSIS),
Vol. 16, No. 2, February 2018
136 https://sites.google.com/site/ijcsis/
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Tsolakis et al. [TSO12] presented the fuzzy
clustering based vector quantization to achieve the optimal
result of the vector quantization. The c means and fuzzy
means algorithm was utilized by Fuzzy Clustering Based
Vector Quantization to handle the limitation of vector
quantization such as dependence on initialization, high
computational cost and VQ was required to assign each
training sample to only one cluster. The result shows
statistically increase the performance than the classical
methods, its intensive based on the design parameters, the
reconstructed images were maintains the high quality in
terms of distortion measure.
Enireddy et al. [ENI15] was presented the
improved cuckoo search with particle swarm optimization
algorithm to overcome the limitation of medical image
retrieval problem for compressed images. In this approach,
the images were compressed using Haar wavelet. The
features were extracted using the Gabor filter and Sobel
edge detector. Then the exacted features were classified by
using the partial recurrent neural network (PRNN).
Finally, the novel particle swarm optimization (PSO)–CS
was used for the optimization of the learning rate of the
neural network.
Kumar et al. [KUM14] presented the hybrid
method to integrate Artificial bee colony (ABC) algorithm
and crossover operator from genetic algorithm with ABC
for continuous optimization. The proposed method was
called as CbABC. The result shows that the CbABC
algorithm was improved the Travelling Salesman Problem
(TSP) than the traditional ABC algorithm. Then the
proposed algorithm has the ability to get the local
minimum and this can be efficiently used for the
separable, multivariable, multi model function
optimization.
Chiranjeevi et al. [CHI16] proposed the modified
firefly algorithm based on vector quantization to improve
the reconstructed image quality and fitness function value
and reduce the convergence time than the traditional
firefly algorithm. The proposed Modified Firefly
Algorithm was increased the brightness of the fireflies
compare to traditional fireflies to improve the fitness
function and it’s used to generate the global codebook for
efficient vector quantization for improving the image
compression.
Liu et al. [LIU10] presented the efficient
compression method to compress the encrypted greyscale
images through Resolution Progressive Compression
(RPC) for improving the efficiency of compression
methods. The result shows the proposed approach has
better coding efficiency, less computational complexity
than traditional approaches. In this method, initially the
encoder sending the down sampled version of cipher text
after that in the decoder the low resolution image was
decoded and decrypted. Then, combined all the predicted
image with the secret encryption secret key which was
consider as the side information (SI) to decode the
resolution level. This process was iterated continuously till
the whole image was decoded. Moreover, the removal of
Markovian properly in slepian wolf decoding, the
complexity of decoding was reduced significantly.
Tsai et al. [TSA13] presented the fast ant colony
optimization to handle the issue of codebook generation.
This method analysed the following two observations, the
first observation was observed while the convergence
process of ACO for CGP, patterns or sub solutions were
achieve the required states at various times. The second
observation were performed in the most of the patterns
were allocated to the same code words after the certain
number of iterations. Based on these observations enhance
the pattern reduction and speed up the computation time
of Ant Colony System (ACS) and Code book Generation
Problem (CGP).The result shows the Fast Ant Colony
Optimization iteratively reduces the computation time of
ACS and CGP.
PROPOSED METHODOLOGY
In proposed methodology, the GRVQ is
optimized through APOA to achieve the better
quantization accuracy and computation efficiency.
Artificial Plant Optimization based Generalized
Residual Vector Quantization (APOA-GRVQ)
In the proposed methodology, the Artificial Plant
Optimization based Generalized Residual Vector
Quantization (APOA-GRVQ) is initially applied in the
codebook. The APOA is optimized the codebook based on
optimal fitness value of the APOA. In APOA, the fitness
value is calculated based on the function of Photosynthesis
and Phototropism.
The APOA is inspired by natural growth plant
process. In the APOA, the individual represents one
potential branch and several operators are adopted during
the growth period. The photosynthesis operator produces
the energy created by sunlight and other materials while
phototropism operator guides the growing direction
according to various conditions. Additionally, the apical
dominance operator is essential to make minor adjustment
for the growth direction.
In order to simulate the plant growing
phenomenon it’s important to provide the connection
between growing process and optimization problem. The
principle of APOA, the search space should be mapping
into the whole plant growing environment and the each
individual mark it as the virtual branch. Moreover, the
provisions are supplied. For example, water, carbon
dioxide and other materials are supposed to be
inexhaustible except the sunlight. Since, the light intensity
is varying for several branches, it could be consider as the
fitness value for each branch.
Photosynthesis produces the energy for the
branch growing. The rate of the photosynthetic is plays the
important role to measure how much energy produced. In
botany, the light response curve is measured the
photosynthetic rate and many models have been proposed
in the past research, like rectangular hyperbolic model,
non rectangular hyperbolic model, updated rectangular
hyperbolic model, parabola model, straight line model and
exponential curve models. In this research, the rectangular
hyperbolic model is utilized to measure the quality of
obtained energy:
( ) =
( )
( )
− (1)
( ) -photosynthetic rate of branch I at time t,
- Initial quantum efficiency
-Maximum photosynthetic rate
– Dark respiratory rate
The following three parameters , are
controlled the size of the photosynthetic rate. The ( )
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denote as the light intensity and it’s defined as follows the
equation (2).
( ) =
( ) ( )
( ) ( )
(2)
The ( ) and ( ) are the worst and best light
intensities at time t respectively, ( ) denoted as the light
intensity of branch i.
Phototropism is directional growth in which the
direction of growth is determined by the direction of the
light source. In APOA branches favor those positions with
high light intensities so that they can produce more
energy. Then, each branch will be attracted by these
positions. Therefore, branch i takes the following growing:
( + 1) = ( ) + ( ) () (3)
The GP is a parameter reflecting the energy
conversion rate and used to control the growing size per
unit time. The Fi (t) denotes the growing force guided by
photo synthetic rate, rand () represents a random number
sampled with uniformly distribution.
For each branch I, Fi(t) is computed by the
( ) = ( ) ( )
( ) − ( ) (4)
Where the ‖. ‖ describes the Euclidean distance, can
be computed as the following way
( ) = ∑ . ( )
− ( )
(5)
The dim represent the problem dimensionality,
coe is the parameter used to control the direction:
Coe=
1 ( ) > ( )
−1 ( ) < ( )
0 ℎ
(6)
Moreover the small probability Pb is introduced
to reflect some random events influences.
( + 1) = + ( − ).rand1 (), if (rand2()
<Pb) (7)
The rand1 () and rand2 () are two random numbers with
uniformly distribution, respectively.
In this work, the each branch is considered as the
individual codebook. Light intensity is considered as the
fitness value. Each codebook is optimized based on the
fitness value. The following algorithm 3.2 describes the
step by step process how to achieve the optimized APOA-
GRVQ.
Algorithmic Steps for APOA-GRVQ
Initialized APOA parameters m-number of branches
randomly from the problem search space, which is an n-
dimensional hypercube. The each branch is considered as
the individual codebook.
Input: Initial code book C, number of branches B, number
of elements K per branch during growing period;
Initial codebook is represented as =
{ (1), … … … … … ( )}, b∈ [B].
Output: Optimized codebooks { : [ ]}
Step 1: Encoding of → ( ( ), ( ), … … ( ))
Step 2: For each branch i
Calculate current residual of xi for each codebook:
e = X − c (i (x))
Represents the ith input image.
Step 3: Calculate the fitness value (light intensity) for
each codebook
calc(C) =
1
D(C)
=
N
∑ ∑ u X X − C
is jth codeword of size in a codebook of size
and is 1 if is in
the jth cluster otherwise zero.
Step 4: Initially select a codebook randomly and find its
fitness value. If there is a brighter
Codebook, then it moves toward the high light
intensity (highest fitness value)
based on step 6 to step 8.
Step 5: Calculate Photosynthesis is as follows
for i=1 to b do
Computing the light intensity Uf (xi) by using
Equation (2)
Computing the photosynthetic rate pi by using
Equation (1)
End do
Step 6: Calculate Phototropism
for i=1 to n do
if rand2() < pb
( + 1) ← ( ) By using Equation (7)
Else
( + 1) ← ( ) With Equation (3)
end if
end do
Step 7: If the number of iteration reaches the maximum
number of iteration, then stop and display the results.
Fig. 1. Flow Chart of the Proposed Methodology
RESULT AND DISCUSSION
Experiments are conducted in MATLAB
simulation and they are performed on three images such as
Peacock, Panda and Church. The comparison is performed
among LBG, Cuckoo-LBG, PSO-GRVQ, HBMO-GRVQ
and APOA-GRVQ methods.
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Methods/
Images
Peacock Panda Church
Original
Image
LBG
Cuckoo-
LBG
PSO-
GRVQ
HBMO-
GRVQ
APOA-
GRVQ
Fig .2 Comparison results of reconstructed image
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Compression Ratio ( )
Compression Ratio is determined the data
compression ability by finding the ratio between original
image (C ) and compressed image (C ). It is defined by,
C (%) = (8)
Table 1 Comparison of Compression Ratio for
Peacock, Panda and Church image
Images
/
Method
Existing Proposed
LBG CUCKOO-
LBG
PSO-
GRVQ
HBMO-
GRVQ
APOA-
GRVQ
Peacock 27.9561 28.8594 29.8261 33.8256 41.8846
Panda 26.7577 28.1826 36.4846 38.5059 45.4231
Church 28.2912 29.1586 39.7180 40.1846 44.2142
Fig 3 Comparison Result of Compression
Ratio
Figure 3 shows the comparison results of
proposed APOA-GRVQ technique with existing LBG,
Cuckoo-LBG, PSO-GRVQ and HBMO-GRVQ in terms of
compression ratio. X axis is taken as various compression
methods and Y axis is taken as compression ratio in
percentage. From the bar chart the proposed The APOA-
GRVQ techniques give better high compression ratio for
Peacock, Panda and church image.
Structure Similarity
Structural similarity measure depends on the
human visual system, that combines the structure,
luminance and contrast information for assessing the
visual quality of decompressed image.
Table 2 Comparison of structure similarity for
Images /
Method
Existing Proposed
LBG
CUCKO
O-LBG
PSO-
GRVQ
HBMO-
GRVQ
APOA-
GRVQ
Peacock 0.9036 0.9114 0.9191 0.9212 0.9164
Panda 0.8618 0.9084
0.9368
0.9593 1.0414
Church 0.9057 0.9138 0.9213 0.9183 0.9241
Fig 4 Comparison Result of Structure
Similarity
structure similarity. X axis is taken as various compression
methods and Y axis is taken as structure similarity. From
the bar chart the proposed The APOA-GRVQ techniques
give better high structure similarity for Peacock, Panda
and church image.
Peak Signal Noise Ratio (PSNR)
The PSNR is quality measurement between the
original and a compressed image. The higher PSNR, value
represents the best quality of the decompressed image.
PSNR (dB) = 10 log ( ) (9)
R is the maximum peak pixel values of input
image.MSE is mean square error between input and
decompressed image.
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Table 3 Comparison of Peak Signal Noise Ratio for
Images /
Method
Existing Proposed
LBG CUCKOO-
LBG
PSO-
GRVQ
HBMO-
GRVQ
APOA-
GRVQ
Peacock 31.0356 31.8116 32.1223 32.2836 34.7935
Panda 29.1514 30.6551 33.2738 35.8325 37.4321
Church 31.3487 32.1164 32.3647 32.6504 35.1425
Fig 5 Comparison Result of Peak Signal Noise
Ratio
peak signal noise ratio. X axis is taken as various
compression methods and Y axis is taken as peak signal
noise ratio values. From the bar chart, the proposed
APOA-GRVQ techniques gives better high peak signal
noise ratio for Peacock, Panda and church image.
Bit Rate (kb/s)
Amount of data processed in a given time is
termed as Bit rate. The measurement of bit rate is bits per
second, kilobits per second, or megabits per second.
Table 4 Comparison of Bit Rate for Peacock, Panda
and Church image
Images /
Method
Existing Proposed
LBG CUCKOO-
LBG
PSO-
GRVQ
HBMO-
GRVQ
APOA-
GRVQ
Peacock 2.5105 5.2211 5.7399 7.7182 8.7124
Panda 5.2211 4.3229 5.1602 7.8156 8.4314
Church 2.4857 4.0764 5.0628 7.0609 8.0864
Fig 6 Comparison Result of Bit Rate
Bit Rate. X axis is taken as various compression methods
and Y axis is taken as Bit rate values. From the bar chart
the proposed The APOA-GRVQ techniques give better
high bit rate for Peacock, Panda and church image.
CONCLUSION
The proposed APOA is efficiently optimized the
GRVQ. The proposed APOA algorithm is very easy to
implement and efficiently solved the issue whose optimal
solutions are in the feasible region. In APOA, each branch
represents an individual codebook which provides the
potential solution. Furthermore, the photosynthesis
operator is efficiently found the energy while
phototropism operator guides the growing directions. The
experimental results showed the proposed algorithms can
increases the quality of images with respect to existing
algorithms such as HBMO–GRVQ, PSO–GRVQ, Cuckoo-
LBG and LBG. The proposed APOA-GRVQ algorithm
can provide better quantization accuracy and computation
accuracy in term of following performance parameters
such as Compression Ratio, Peak-Signal Noise Ratio
(PSNR), Structural Similarity, and Bit Rate.
REFERENCES
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Babenko. A, and Lempitsky. V, “ Additive quantization
for extreme vector compression”, In Proceedings of the
IEEE Conference on Computer Vision and Pattern
Recognition (pp. 931-938), 2014.
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Shicong Liu, Junru Shao, Hongtao Lu, “Generalized
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AUTHORS
A.Divya received the Bachelor of
Computer Science (B.Sc.) degree from
the Bharathiar University, in 2012. She
done her Master of Computer Science
(M.Sc) degree in Bharathidasan
University in 2014 and she awarded
M.Phil Computer Science from the Bharathiar
University, Coimbatore, in 2015. Currently she is
doing her Ph.D Computer Science in Erode Arts
and Science College. Her Research area includes
Digital Image Processing.
Dr. S. Sukumaran graduated in 1985
with a degree in Science. He obtained
his Master Degree in Science and M.Phil
in Computer Science from the
Bharathiar University. He received the
Ph.D degree in Computer Science from
the Bharathiar University. He has 28
years of teaching experience starting from
Lecturer to Associate Professor. At present he is
working as Associate Professor of Computer
Science in Erode Arts and Science College,
Erode, Tamilnadu. He has guided 6 Ph.D
Scholars and more than 55 M.Phil research
Scholars in various fields. Currently he is
Guiding 5 M.Phil Scholars and 8 Ph.D Scholars.
He is member of Board studies of various
Autonomous Colleges and Universities. He
published around 68 research papers in national
and international journals and conferences. His
current research interests include Image
processing and Data Mining, Networking.
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