CLUSTERING BASED ADAPTIVE
IMAGE COMPRESSION SCHEME USING
PARTICLE SWARM OPTIMIZATION
TECHNIQUE
1. M.Mohamed Ismail , Research scholar, Karpagam University, Coimbatore
2. Dr.K.Baskaran, Associate Professor,Dept of computer science, Government College of Technology, Coimbatore.
Abstract : This paper presents an image compression scheme with particle swarm optimization technique for clustering. The PSO technique is a powerful general purpose optimization technique that uses the concept of fitness.It provides a mechanism such that individuals in the swarm communicate and exchange information which is similar to the social behaviour of insects & human beings. Because of the mimicking the social sharing of information ,PSO directs particle to search the solution more efficiently.PSO is like a GA in that the population is initialized with random potential solutions.The adjustment towards the best individual experience (PBEST) and the best social experience (GBEST).Is conceptually similar to the cross over operaton of the GA.However it is unlike a GA in that each potential solution , called a particle is flying through the solution space with a velocity.Moreover the particles and the swarm have memory,which does not exist in the populatiom of GA.This optimization technique is used in Image compression and better results have obtained in terms of PSNR, CR and the visual quality of the image when compared to other existing methods.
Keywords: Discrete wavelet transform ,adaptive lifting , pso, clustering , image compression.
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. Since 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 both high compression ratio and the reconstructed image with good quality at the same time. Lifting Scheme (LS) [1,2,3,4] allows efficient construction of the filter banks for wavelet transforms. The limitation of this structure is that the filter structure is fixed over the entire signal. In many applications it is very much desirable to design the filter banks to shape itself to the signal. Several such adaptive Lifting schemes were proposed earlier which consider local characteristics of the signal for adapting. Claypole et al [5] introduced a technique of adaptive filtering which enables to choose the Prediction operators according to the local properties of the image. Boulgouris et al [6] proposed a method of defining lifting operators by constraining the sum of coefficients and by reducing the variance of the signal. A.Gouze et al [7] adapted the lifting method without any a priori model of the image autocovaiance. This method optimizes the update lifting step in order to minimize the distortion. In this paper we propose a new method to obtain wavelet transforms for application in image compression. We have considered a method of changing prediction functions of the LS for each image to improve the compression ratio, gaining a more accurate prediction of pixels in the image. The goal of this paper is to propose an adaptive LS using the Particle Swarm Optimization (PSO) algorithm. Specifically, PSO is used to improve the accuracy of the prediction functions in LS. The proposed method exhibits better accuracy in prediction and can reduce the entropy better than the conventional prediction function on the average.
2.2 PROCEDURE OF LIFTING
The procedure of LS consists of three steps: Split, Predict and Update (Fig. 1).
Split: Split the signal into two disjoint subsets of samples. We divide the original signal x[n] into even and odd components: xe[n] and xo[n], where xe[n] = x[2n] and xo[n]= x[2n+1].
Figure1:Liftingscheme and inverseLifting scheme
Update: Generate the coarser signals c[n] by applying an update operator U to d[n] and adding the result to xe[n]: c[n] xe[n] U(d[n]) (2)
This represents a coarse approximation to the original signal x[n]. These three operations can be applied to c[n] repeatedly. we can easily obtain the inverse lifting scheme of any combination of prediction P and update U. From the equation (1) and (2), xe[n] and xo[n] can be calculated from c[n] and d[n] as shown in the next equations: xo [n] d[n] P(xe [n]) (3)
xe [n] c[n] -U(d[n]) (4)
2.3 LIFTING SCHEME ON TWO DIMENSIONAL IMAGE DATA
When LS transforms the two dimensional data, the procedure explained in the previous subsection is applied two times. At the first step, each row of the image is transformed and divided into two sub images, the sets of {c[n]} and {d[n]}. Secondly, each sub image is scanned vertically, and their columns are transformed similarly. As a result, the original image data is divided into four sub images, cc, cd, dc and dd. The sub image cc can be repeatedly transformed by LS, and this repetition is called multi-resolution analysis.
In the next subsections, these features are explained. Particle Swarm Optimization
Particle swarm optimization (PSO) is a population based stochastic optimizationtechnique developed by Eberhart and Kennedy in 1995,inspired by social behavior of bird flocking or fish schooling. The PSO is a population-based optimization technique, where thepopulation is called swarm.
The basic PSO algorithm can be described as follows: Each particle in the swarm represents a possible solution to the optimization problem existing. During PSO iteration,every particle accelerates independently in the direction of its own personal best solutionfound so far, as well as the direction of the global best solution discovered so far by any other particle .Therefore, if a particle finds a promising new solution, all other particles willmove closer to it, exploring the solution space more thoroughly .
Let s denotes the swarm size. Each particle 1 ≤ i ≤ s is characterized by three attributes (1) The particle position vector Yi;
(2) The particle position change (velocity) vector Vi;
(3) The personal (local) best position achieved by the particle so far Ŷi. Moreover, let Gdenote the best particle in the swarm.
Particle Swarm Optimization Algorithm
This algorithm can be resumed as follows:
1. Initialize Yi and Vi, and set Ŷi = Yi for i = 1, 2… s. 2. Evaluate each particle Yi for i = 1, 2… s.
3. Let G to be the best particle in {Ŷ1, Ŷ 2... Ŷ s} 4. For i = 1, 2… s. do:
Update Vi according to:
V =wV +c r (Yˆ -Y )+ c r (G-Y ) - (1) Update Yi according to:
P
Yi = Yi + Vi - (2)
5. Go to Step 3, and repeat until convergence.wherew inertia weight factor; c 1,c 2 self-confidence factor and swarm-confidence factor, respectively; r 1, r 2 two random numbers uniformly distributed between 0 and 1. If Yi is better than Ŷi , then Ŷi =Yi
5. Go to Step 3, and repeat until convergence.
Particles' velocities on each dimension are clamped to a maximum velocity Vmax.
The velocity on that dimension is limited to Vmax, if the sum of accelerations would cause the velocity on that dimension to exceed Vmax, which is a parameter specified by the user.
DATA CLUSTERING :
Data clustering is a popular approach for automatically finding classes, concepts, or groups of patterns. The term “clustering” is used in several research communities to describe methods for grouping of unlabeled data. These communities have different terminologies and assumptions for the components of the clustering process and the context in which clustering is used. This paper looks into the use of Particle Swarm Optimization (PSO) for cluster analysis. In standard PSO the non-oscillatory route can quickly cause a particle to stagnate and also it may
prematurely converge on suboptimal solutions that are not even guaranteed to local optimal solution. In this paper a modification strategy is proposed for the particle swarm optimization (PSO) algorithm and applied in the data sets This paper provides a method for particles to steer clear off from local stagnation and the local search is applied to improve the goodness of fitting[11]. The effectiveness of this concept is demonstrated by cluster analysis. Results show that the model provides enhanced performance and maintains more diversity in the swarm and thereby allows the particles to be robust to trace the changing environment. [12]
Proposed PSO for Data clustering
Initial Population
One particle in the swarm represents one possible solution for clustering. Therefore, a swarm represents a number of candidate utions for the data set. At the initial stage,each particle randomly chooses k different data set from the collection as the initial cluster centroid vectors and the data sets are assigned to cluster based clustering solutions for the data set. At the initial stage,each particle randomly chooses k different data set from the collection as the initial cluster centroid vectors and the data sets are assigned to cluster based on one iteration.[13]
Local search
After finding the solutions of N particles, a local search is performed to further improve fitness of these solutions. Local search helps to generate better solutions, if the heuristic information can not be discovered easily. Local search is applied on all generated solutions or on a few percent N. In this work, local search is performed on 20% of the total solutions. So in the test data set of N data, local search is applied on the 20% of solutions based on roulette-wheel selection. The requirement is that the fittest individuals have a greater chance of selection than weaker ones. In the local search procedure, the objective function values selected particles are computed again. These solutions can be accepted only if there is an improvement on the fitness, namely, if the newly computed objective function value is lower than the first computed value, newly generated solution replaces the old one.
Personal best & Global best positions of particle:
The personal best position of particle is calculated as follows
The particle to be drawn toward the best particle in the swarm is the global best position of each particle. At the start, an initial position of the particle is considered as the personal best and the global best can be identified with minimum fitness function value.
Finding new solutions
According to its own experience and those of its neighbors, the particle adjusts the centroid vector position in the vector space at each generation. The new velocity is calculated based on equation (1) and changing the position based on equation(2)
5. Experiment Results
In this section, results from the proposed PSO method on well-known test data sets are reported. The choice of the parameter values seems not to be critical for the success of the methods; it appears that faster convergence can be obtained by proper fine-tuning. The balance between the global and local exploration abilities of the proposed system is mainly controlled by the inertia weight, since the positions of the particles are updated according to the classical PSO strategy. A time decreasing inertia weight value, i.e., start from 0.9 and gradually decrease towards 0.4, proved to be superior to a constant value. The optimal solution (fitness) is determined with N=20, c1= 2.1 & c2 = 2.1.. The Results obtained from test data sets by the proposed system are shown in Table 1 & Table 2 respectively. In this section, the proposed PSO-based lifting Method is simulated and verified. The following images of size512 x 512 is used: Rice image , Boy image , IC board image and Vegetable image.The results were promising as the PSNR is high when compared to other methods.The encoding and decoding time is also less when compared to other methods as PSO is used.Therefore the computational complexity is improved when compared to existing methods.
Table1 : For Rice image
Compr ession Ratio
With Particle swarm optimization Technique
Without Particle swarm optimization Technique PSNR Encodin
g time
Decoding
time PSNR
Encodin g time
Decoding time
34.65 42.12 .655 .154 37.21 2.39 1.94
40.12 38.34 .623 .165 36.05 1.59 1.86
45.25 36.45 .594 .172 35.16 1.57 1.81
52.85 34.72 .517 .178 34.23 1.34 1.75
58.98 29.18 .492 .075 24.45 1.30 1.56
65.58 20.74 .373 .058 18.95 1.24 1.51
70.57 18.04 .323 .052 15.56 .965 1.45
Table 2 :For vegetable image
Comp ressio n Ratio
With Particle swarm optimization Technique
Without Particle swarm optimization Technique
PSNR Encodin g time
Decodin
g time PSNR
Encoding
time Decoding time
34.65 41.55 .635 .153 36.45 2.37 1.92
40.12 40.04 .613 .145 35.75 1.49 1.83
45.25 38.12 .592 .143 35.23 1.43 1.80
52.85 35.03 .509 .151 34.45 1.31 1.69
58.98 30.04 .482 .072 24.12 1.23 1.52
65.58 24.02 .364 .054 18.25 1.19 1.47
Input image Reconstructed image
Conclusion:
The advantages of the PSO are very few parameters to deal with and the large number of processing elements, so called dimensions, which enable to fly around the solution space effectively. On the other hand, it converges to a solution very quickly which should be carefully dealt with when using it for combinatonial optimization problems.. In the proposed method,the lifting scheme (LS) , is combined with PSO. Results of the proposed method are good when compared to existing methods in terms of compression ratio,PSNR , encoding time, decoding time.The computational complexity is also reduced as PSO is used.The quality of the reconstructed image is promising when compared to existing methods.
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