ADAPTIVE LIFTING BASED IMAGE COMPRESSION SCHEME USING INTERACTIVE ARTIFICIAL BEE COLONY ALGORITHM

ADAPTIVE LIFTING BASED IMAGE
COMPRESSION SCHEME USING
INTERACTIVE ARTIFICIAL BEE COLONY
ALGORITHM
Vrinda Shivashetty1 and G.G Rajput2
1

Department of Computer Science, Gulbarga University Gulbarga, India
[email protected]
2

Department of Computer Science,
Rani Channamma University, Belagavi, India
[email protected]

ABSTRACT
This paper presents image compression method using Interactive Artificial Bee Colony (IABC)
optimization algorithm. The proposed method reduces storage and facilitates data transmission
by reducing transmission costs. To get the finest quality of compressed image, utilizing local
search, IABC determines different update coefficient, and the best update coefficient is chosen
optimally. By using local search in the update step, we alter the center pixels with the coefficient in 8-different directions with a considerable window size, to produce the compressed
image, expressed in terms of both PSNR and compression ratio. The IABC brings in the idea of
universal gravitation into the consideration of the affection between onlooker bees and the
employed bees. By passing on different values of the control parameter, the universal
gravitation involved in the IABC has various quantities of the single onlooker bee and employed
bees. As a result when compared to existing methods, the proposed work gives better PSNR.

KEYWORDS
IABC, Image Compression, Wavelet Transform, Adaptive Lifting Scheme, PSNR.

1. INTRODUCTION
The wavelet coding method has been recognized as an efficient coding technique for lossy image
compression. The wavelet transform decomposes a typical image data to a few coefficients with
large magnitude and many coefficients with small magnitude. As most of the energy of the image
concentrates on these coefficients with large magnitude, lossy compression systems just by using
coefficients with large magnitude can realize the reconstructed image with good quality and high
compression ratio. For wavelet transforms, Lifting scheme(LS) allows efficient construction of
the filter banks. The restriction of this structure is that the filter structure is fixed over the entire
signal. In many applications to shape itself to the signal it is very much desirable to design the
filter banks. A number of such adaptive Lifting Schemes are proposed in the literature[12,14]
which consider local characteristics of the signal for adapting. In this paper, image compression
using IABC is proposed based on intelligent behavior of Honey bee swarms [8]. The paper is
described as follows. In section II Compression techniques discussed, In section III a general
lifting scheme is discussed and compared with the adaptive lifting scheme where the update step
David C. Wyld et al. (Eds) : CSITY, SIGPRO, DTMN - 2015
pp. 09–21, 2015. © CS & IT-CSCP 2015

DOI : 10.5121/csit.2015.50302

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is modified with the IABC algorithm. Section IV discusses about the proposed work. Section V
explains the IABC algorithm and section VI describes the proposed algorithm.

2. COMPRESSION TECHNIQUES
The image compression techniques are generally classified into two categories depending whether
or not an exact replica of the original image could be reconstructed using the compressed image.
These are:
1. Lossy technique
2. Lossless technique

1. Lossy Compression Techniques
Lossy schemes provide much higher compression ratios than lossless schemes. Lossy schemes are
widely used since the quality of the reconstructed images is adequate for most applications. By
this scheme, the decompressed image is not identical to the original image, but reasonably close
to it. The most popular current lossy image compression methods use a transform-based scheme.

2. Lossless Compression Techniques
In lossless compression techniques, the original image can be perfectly recovered from the
compressed image. These are also called noiseless since they do not add noise to the signal. It is
also known as entropy coding since it use decomposition techniques to minimize redundancy.

3. LIFTING SCHEME
Lifting scheme is used to implement critically sampled filter banks which have integer output.
The lifting scheme can custom design the filters, essential in the transform algorithms.
Independent of translating and dilating, needless of frequency analysis lifting scheme is processed
into space domain. An answer to the algebraic stage of wavelet construction is provided by lifting
scheme, which leads to a fast in-place calculation of the wavelet transform, i.e. it does not require
auxiliary memory. Different wavelets show different image compression effect; the compressed
image quality and the compression rate is not only relational to the filter length, but also concerns
with regularity and local frequency, vanishing moment, orthogonality, biorthogonality. In this
paper, we implement adaptive lifting scheme based upon wavelet decomposition. Then, with the
help of IABC algorithm, we find the best directional window size to get better compression ratio
with considerable quality.
A. The Lifting Concept
Lifting is a spatial (or time) domain construction of bi-orthogonal wavelets. The lifting scheme
procedure consists of three steps: Split, Predict and Update (Fig. 1) and inverse Lifting scheme is
shown in Fig. 2.
Split:
Split the original data into two disjoint subsets. Though any disjoint split is possible, in the
standard lifting scheme we split the original data set x[n] into the even indexed points, xe[n]x[2n], and the odd indexed points xo[n]=x[2n+1]

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Predict:
Generate the detail signals d[n] as the predicting error using prediction operator P
d[n] =xo[n]-P(xe[n])

(1)

Update:
To obtain scaling coefficients c[n] that represent a coarse approximation to the original signal
x[n] merge xe[n] and d[n]. This is accomplished by applying an U update operator to the wavelet
coefficients and adding to xe[n].
c[n]=xe[n]+U(d[n])

(2)

The above three steps is described as lifting stage. Iteration of the lifting stage on the output c[n]
creates the complete set of DWT scaling and wavelet coefficients Cj[n] and dj[n]. At each step,
we weight the Cj[n] with ke and dj[n] with ko respectively. The energy of the underlying scaling
and wavelet functions is normalized.
The lifting stesp are inverted, even if P and U are nonlinear, non-invertible, or space-varyi.ng
Rearranging (1) and (2), we have
xe[n]=c[n]-U(d[n]),
xo[n]=d[n]+P(xe[n]).

Fig.1. Lifting stage: Split, Predict, Update

As long as for the inverse and forward transforms U and P are chosen, the original signal will be
perfectly reconstructed. The inverse lifting stage is shown in Fig.2.

Fig.2. Inverse lifting steps: undo the Update, undo the Predict, and Merge the even and odd samples

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B. Adaptive lifting scheme
The adaptive lifting scheme is classical lifting modification . The Fig.3 shows the adaptive update
lifting scheme followed by a fixed prediction. At each sample n According to a decision function
D(x[n],y) an update operator is chosen. As in the classical and space-varying lifting, the critical
point is that D(x[n],y) depends on y, and it also depends on the sample being updated. The update
operator and addition are fixed, in the standard lifting scheme. The choice of addition and the
update operator depends on the information locally available within both the approximation
signal and the detail signal in the adaptive lifting scheme.

Fig.3. Adaptive update lifting scheme

According to the structure of lifting, Adaptive Lifting Scheme performs update first , and then
performs prediction. Assume x=xo (2m,2n), where xo is the input image, which is split into two
signal one is x average signal and y detail signal . The y detail signal includes yh horizontal signal
, yv vertical signal, and yd diagonal signal.
The 2-D adaptive lifting formation is as follows:
Update: Coefficient yh,yv,yd are used to update x:
x'= U(x,yh,yv,yd)

(3)

Here, U is update operator, in which coefficients are chosen by D decidable factor.
Prediction: Updated low-frequency Coefficient x' is used to predict yh,yv,yd :
yh'= yh - ph(x, yv,yd)

(4)

yv= yv-pv(x- yd)

(5)

yd= yd-pd(x')

(6)

The ph,pv,pd, are prediction schemes for different frequency bands. According to the local feature
adjacent to x, yh,yv, and yd the scheme adaptively chooses U update operator and P prediction
operator. Without recording any overhead information. the perfect reconstruction is ensured by
the update and prediction scheme The choice of U update operator and the addition operator⊕ in
adaptive lifting scheme depends on the information locally available in the x approximation
signal and the y detail signal. In reality, this choice will be triggered by the so called decision map
D:X×Y → DZ where D is the decision set. We have a different Ud update operator and addition
⊕d for every possible decision dЄD of the decision map,. Thus the analysis step is given as

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follows,
(7)
At location n dn=D(x,y)(n) is the decision. Assuming that the reversibility condition ⊕d holds for
every possible decision dЄD and it is given by
(8)
where ⊝dn denotes the subtraction that inverts ⊕d.
The decision dn = D(x,y)(n) depends on the x original signal. On the other hand, during synthesis,
we do not know but “only” its update x'. In general, this prohibits the dn computation and in such
cases, perfect reconstruction is out of reach. However, it is still possible to recover dn as there
exist a number of situations from an posterior decision map.

4. PROPOSED BLOCK DIAGRAM

Fig. 4. Proposed Block diagram

In this method it is observed that, wavelet transform did not yield better quality for more detail
texture image, so it gives a way for adaptive lifting scheme based decomposition. To determine
the best directional window size and to produce the better quality for more detail texture image
by local search process an Interactive Artificial Bee Colony algorithm, recent and successful
optimization tool, is used. The lossless encoding technique is used to get a perfect compressed
image. After the encoding process, data will be in digital form so that one can store or transmit
the data to the long distance. For compressed data the image is reconstructed by applying
decoding process followed by Inverse adaptive lifting scheme.

A. Need for Interactive Artificial Bee Colony algorithm
Choosing a global update coefficient does not give better compression ratio and quality.
Interactive Artificial Bee Colony Algorithm by local search finds different update coefficient and
helps to determine the best update coefficient optimally to get best quality of compressed image.

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In update step, the center pixels are modified with the co-efficient in 8-different direction with a
considerable window size and by using local search algorithm. To determine best directional
window with an considerable size an IABC algorithm is used.

5. INTERACTIVE ARTIFICIAL BEE COLONY ALGORITHM
The most recently defined algorithm, motivated by the intelligent behavior of honey bees is
Interactive Artificial Bee Colony Algorithm. It is as simple as Artificial Bee Colony Algorithm
and differential Evolution(DE) algorithms Particle Swarm Optimization, and uses common
control parameters such as maximum cycle number and colony size. As an optimization tool,
IABC provides a population-based search procedure in which artificial bees with the time
modifies the individuals called food positions and the aim of bee’s is to discover the food sources
placed with high nectar amount and at last the one with highest nectar.
In IABC algorithm, the solution space randomly spray percentage of the populations , fitness
values called as nectar amounts is calculated, represents the ratio of employed bees to the total
population. When these populations are positioned into the solution space they are called
employee bees. The probability of selecting a food source is then calculated, select a food source
to move by roulette wheel selection for every onlooker bees and then nectar amounts of them is
determined. If the employed bees fitness values does not improve by predetermined number of
iterations continuously, called “LIMIT”, such food sources are abandoned, and these employed
bees become the scouts. The scouts are moved. The position and the best fitness value found by
the bees is memorized. We check whether the termination condition is satisfied by the total
number of iterations. If the condition for termination is satisfied, terminate the program and
output the results. The flow chart for IABC is shown in Fig. 5.
The process of the IABC can be described in 6 steps:
Step 1. Initialization phase:
In Initialization phase within the maximum boundaries of each pixels an window size is
chosen
area=1+floor(maxarea*rand(1));
row=5+floor(r*rand(1));
col=5+floor(c*rand(1));
Step 2. Employed bees phase
In Employed bees phase of the algorithm, a local search xi, is conducted in the neighbourhood of
each directional window, defined by using:
a1=img(row-area, col-area);
b1=img(row,col-area);
c1=img(row+area,col-area);
d1=img(row+area,col+area);

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Fig. 5. Flow chart for IABC Algorithm

If we get fitness better than before, then memorize the current one.
If(localPSNR>prevPSNR)
prevPSNR=localPSNR;
bestimg=recconstimg;
After generating a new neighbour solution by local search, the new solution fitness (quality) is
evaluated and better one is kept in the population. Now the counter is incremented for each local
search up to 8 level.
Step 3. Onlooker bees phase:
In Onlooker bees phase of the algorithm, the probability of selecting a food source is calculated
by using equation

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( ), is the employed bee fitness value that is picked by applying the roulette wheel selection.
Pi is the probability of selecting the th employed bee. ( ) randomly selected employed
bee fitness value
By roulette wheel selection, select a food source to move for every onlooker bees and then the
nectar amounts is determined. The onlookers movement follows the below equation

Step 4. Scout bees’ phase
In the Scout bees’ phase If the employed bees fitness values does not improve by predetermined
number of iterations continuously, called “LIMIT”, such food sources are abandoned, and these
employed bees become the scouts. The scouts are moved by the equation

Step 5. Update the Best Food Source found so far:
In this step the best fitness value and the position is memorized, which are found by the bees.
Step 6. Termination Checking:
In this step check whether the termination condition is satisfied by the total number of iterations.
If the condition for termination is satisfied, terminate the program and output the results.;
otherwise go back to the Step 3.

6. PROPOSED ALGORITHM
In the proposed method, the input image is decomposed using wavelet lifting scheme and then the
Interactive artificial bee colony algorithm is used in the update process to get considerable
quality.
A. Algorithm steps:
Step 1: Input the Gray scale Image.
Step 2: split the image into odd and even pixel regions.
Step 3: Decompose the image as (odd-even) for next prediction step.
Step 4: Fix the maximum coverage size as ‘M’ and initialized
‘K=0’ for prediction co-efficient. Where M is maximum window size, upto which it will do local
search for each center pixels maximum window size in our program is 5.

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Step 5: Each pixel in the decomposed image is Scanned and its present fitness value and
compression ratio is calculated.
Step 6: To predict ‘a’ and ‘b’ call direction finding algorithm co-efficient of all 8-direction
combination. The 8- direction combinations are a1,b1,c1,d1,a2,b2,c2,d2
DL

HL

VT

DR

DL

VT

HL

HL

X

HR

DD

DD

VD

DB

DD

VD

HR

DB

Fig.6. Directional coefficient for center pixel ‘x’

Where x is an center pixel to be update
HL is predicted coefficient in horizontal left direction
HR is predicted coefficient in horizontal right direction
VT is predicted coefficient in vertically top direction
VD is predicted coefficient in vertically down direction
DL is predicted coefficient in diagonally top left direction
DR is predicted coefficient in diagonally top right direction
DB is predicted coefficient in diagonally bottom left direction
DD is predicted coefficient in diagonally bottom right direction
Step 7: By using Update lifting formula for each direction prediction calculate update weight and
find compression ratio and PSNR.
The Peak Signal to Noise Ratio(PSNR) represents a measure of the peak error and is expressed
in decibels. PSNR is defined by

Step 8: The best individual is memorized , CR and its direction using IABC local search.
Step 9: To predict and update the best value for different range of window size iterate K from
(0 to M) .
Step 10: Using IABC local search, memorize the best window size in terms of its MSE and CR
for each reference pixel.

7. EXPERIMENTAL RESULTS
The proposed algorithm is tested on standard images with different image formats. The
Reconstructed images are shown in figure 7. The results are tabulated for various images in
Table(1).Lena image is a JPEG image and the results obtained is better than existing methods.

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Fig. 7. Reconstructed Images with lifting with IABC (a) Original Image (b) Output of lifting scheme with
IABC.

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Table 1: Comparison table for cameraman image

PSNR fro different images obtained using Lifting
Scheme using IABC

Compression
Ratio

Cameraman
Image

Lena
Image

Barbara
Image

Pepper
Image

Rice
Image

30

41.78

43.4

42.39

40.83

40.27

40

38.92

39.4

38.95

38.10

37.82

50

38.63

38.2

38.31

37.85

36.74

60

34.26

33.9

33.78

34.57

33.74

Fig. 8: Graph representing CR Vs PSNR for different images.

8. CONCLUSION AND FUTURE ENHANCEMENTS
In this paper, a method to optimize the prediction function used in lifting scheme using IABC
algorithm for image compression is proposed. IABC algorithm is implemented in update process
of lifting scheme to give better PSNR. From the experimental results, it is concluded that
proposed method yields improved quality compare to existing methods in the literature. The
proposed method gives the way to reduce the data to represent the image and thereby decreases
transmission bandwidth. Hence, the transmission cost and memory cost is reduced.
In future work, Interactive Artificial Bee Colony algorithm shall be implemented in the
thresholding process to reduce the number of coefficient representing the image by optimally
choosing the thresholding value to get more better compression and quality.

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REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]

[7]

[8]

[9]
[10]
[11]

[12]
[13]
[14]
[15]

[16]
[17]
[18]
[19]

[20]

[21]

Subramanya A. “Image Compression Technique, “ potentials IEEE, Vol. 20, issue 1,pp19-23, FebMarch 2001.
Rafael C. Gonzalez, Richard Eugene; “ Digital image processing”, Edition 3, 2008,page 466.
W. Sweldens, “The lifting scheme: A new philosophy in biorthogonal wavelet constructions”, in Proc.
SPIE, vol. 2569,1995,pp. 68-79.
W. Sweldens, “The lifting scheme: A construction of second-generation wavelets”, SIAM J. Math.
Anal., vol. 29, no. 2, pp. 511-546,1997.
A.R. Calderbank, I Daubechies, W. Sweldens, and B-L Yeo, “Wavelet transforms that map integers to
integers”, J. Appl. Comput. Harmon, Anal., vol.5, no. 3, 1998.
M. Adams and F. Kossentini, “Reversible Integer-to-Integer Wavelet Transforms for Image
Compression: Performance Evaluation and Analysis”, IEEE Trans.On Image Processing, vol.9,
no.6, pp. 1010-1024, Jun 2000.
N.V Boulgouris, D. Tzovaras, and M.G. Strintzis, “Lossless image compression based on optimal
prediction, adaptive lifting, and conditional arithmetic coding”, IEEE, Trans. Image Process., vol. 10,
no. 1,pp. 1-14, Jan. 2001.
Pei-Wei Tsai, Jeng-Shyang Pan, Bin-Yih Liao, and Shu- Chuan Chu,” Enhanced Artificial Bee
Colony Optimization”, International Journal of Innovative Computing, Information and control,
vol.5, no.12, pp.1-12, Dec. 2009.
J. Kennedy, R.C. Eberhart, and Y.Shi, “Swarm Intelligence”, Morgan Kaufmann Publishers, San
Francisco,2001.
B. Akay and D. Karaboga, “Parameter tuning for the artificial bee colony algorithm,” ICCCI 2009
(R.Kowalezyk, N.T. Nguyen and S.M.Chen,eds.), LNAI, vol. 5796, 2009, pp. 608-619.
V . U Kale and N.N. Khalsa, “Performance evaluation of various wavelets for image compression of
natural and artificial images”, International Journal of Computer Science and communication
1(2010), no.1, pp. 179-184.
D. Karaboga and B. Akay, A survey: “Algorithms simulating bee swarm intelligence”, Artificial
Intelligence Review 31(2009), no. 1, pp. 55-68.
G. Piella and H.J.A.M. Heijmans, “Adaptive lifting schemes with perfect reconstruction”, Research
Report PNARO104,CWI, Amsterdam, Feb. 2001.
F.W. Moore, “A genetic algorithm for optimized reconstruction of quantized signals”, Evolutionary
computation, 2005. The 2005 IEEE congress on, vol. 1,2005, pp. 105-111.
R. Ramanathan, K. Kalaiarasi, D. Prabha, “Improved wavelet based compression with adaptivelifting
scheme using Artificial Bee Colony algorithm”, International Journal of Advanced Research in
Computer Engineering & Technology, Vol 2 , Issue 4, April 2013.
W. Trappe and K.J.R.Liu, “Adaptivity in the lifting scheme,” in 33th Conference on Information
science and systems, Baltimore, March 1999, pp. 950-958.
D. Karaboga, “ An Idea Based On Honey Bee Swarm For Numerical Optimization”, Technical
Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.
E. Bonabeau, M. Dorigo, and G. Theraulaz, “Swarm Intelligence: From Natural to Artificial
Intelligence”, NY: Oxford University Press,1999.
P.-W. Tsai, J.-S. Pan, S.-M. Chen, B. –Y. Liao, and S.-P. Hao, “Parallel Cat Swarm Optimization”,
Proc. Of 7th International Conference on Machine Learning and Cybernetics, pp. 3328-3333,
Kunming, China, 2008.
Y. Guo, X.Gao, H. Yin, and Z. Tang, “Coevolutionary Optimization Algorithm with
Dynamic Sub-population Size”, International Journal of Innovative Computing, Information and
Control, vol.3, no.2, pp.435-448, 2007.
M. Dorigo and L.M. Gambardella, “Ant Colony Optimization for Data Clustering”, Proc. Of 8th
Pacific Rim International Conference on Artificial Intelligence, Auckland, New Zealand, LNAI 3157,
pp. 534-543,2004.

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AUTHOR PROFILE
Vrinda Shiva Shetty received B.E from Gurbarga University and M.Tech degree from VTU in Computer
Science and Engineering and presently pursuing Ph.D in Image Compression from the University of
Gulbarga University, Gulbarga, and Karnataka. Field of Interest includes Intelligent Image Processing,
Evolutionary Computation.
Dr. G. G. Rajput currently working as Associate Professor in the Department of Computer Science at Rani
Channamma University Belagavi, Karnataka State, India. The Area of interest includes Image processing,
Pattern recognition, Operations Research and Software Engineering.