Image Enhancement using Accelerated Particle Swarm Optimization

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Image Enhancement using Accelerated Particle Swarm Optimization

Swagat Kumar Behera

  1. Tech Scholar, Dept of ECE, CUTM

    Bhubaneswar, Odisha, INDIA

    Dr. Satyasis Mishra Associate Professor, Dept. of ECE, CUTM

    Bhubaneswar, Odisha, INDIA

    Debaraj Rana

    Asst. Professor, Dept of ECE, CUTM

    Bhubaneswar, Odisha, INDIA

    Abstract This paper proposes a new variant of Particle Swarm Optimization (PSO) called Accelerated Particle Swarm Optimization (APSO) in gray level image enhancement application. Image enhancement is mainly done by maximizing the information content of the enhanced image with intensity transformation function. In this paper image enhancement is considered as an optimization problem and APSO is used to solve it. APSO is simpler to implement and it has faster convergence when compared to the PSO algorithm. Hence as an alternative to PSO based image enhancement algorithm, APSO is introduced in this present paper. In this present work a parameterized transformation function is used, which uses local and global information of the image. Here an objective criterion for measuring image enhancement is used which considers entropy and edge information of the image. We have achieved the best enhanced image according to the objective criterion by optimizing the parameters used in the transformation function with the help of APSO. The enhancement is done using three techniques: Histogram equalization (HE), Contrast stretching (LCS) and APSO. Different gray level images are taken and processed through these techniques, simulated in MATLAB. Results obtained using all these techniques are in good agreement and are compared using performance graphs and image based enhancement results. Simulation result proves that APSO based image enhancement algorithm is superior to the traditional techniques.

    Keywords Accelerated Particle Swarm Optimization; Contrast stretching; Histogram equalization; Image enhancement; Particle Swarm Optimization Introduction (HEADING 1)

    1. INTRODUCTION

      Digital Image Processing involves the modification of digital data for improving the image qualities with the aid of computer. The processing helps in maximizing clarity, sharpness and details of features of interest towards information extraction and further analysis. Image enhancement is a technique in which an image is processed to bring out specific features of an image.

      It can be categories into following: enhancement by point processing, enhancement in the spatial domain, enhancement

      where f(i, j) is the gray value of the (i, j)th pixel of the input image and g(i, j) is the gray value of the (i, j)th pixel of the enhanced image. T is the transformation function defined over some neighborhood of (i, j) [12]-[5]. Histogram transformation is considered as one of the fundamental processes for contrast enhancement of gray level images [3] which facilitates subsequent higher level operations such as detection and identification. Linear contrast stretching employs a linear transformation that maps the gray-levels in a given image to fill the full range of values [1].

      In this paper we have performed gray-level image contrast enhancement by APSO. In comparison to PSO, APSO has a first convergence and give good result. At the same time PSO takes more time to converge to better optima [8]. The resulted gray-level enhanced images by APSO are found to be better as compared to the traditional methods of image enhancement.

    2. LIST OF FUNCTIONS USED

      In order to implement enhancement operation, we have taken a transformation function and a fitness function. The transformation function is used to generate a new intensity value of original image and produce an enhanced image. To evaluate the quality of the enhanced image simultaneously, a fitness function is used.

      A. Transformation Function

      Here we have applied Local enhancement method on a pixel considering intensity distribution among its neighboring pixels. Local information is extracted from a user defined window of size. The transformation is defined as:

      , = , , × , + (, )

      (2)

      In eq. (2) a, and c are two parameters, , is the local mean of the , pixel of the input image over a n×n window and , is enhancement function which takes both local and global information into account [5]. Expression for local mean and enhancement function are defined as:

      in the frequency domain and pseudo-color image processing [4]. We have concentrated on spatial domain and carried out our work. Spatial domain techniques are performed to the image plane itself and they are based on direct manipulation of pixels in an image.

      The enhancement process can be denoted by

      g(i, j) = T [ f (i, j)] (1)

      , = 1

      ×

      = .

      , +

      (, )

      =1 =1

      (4)

      (3)

      where k, and b are two parameters, G is the global mean and , is the local standard deviation of , pixel of the input image over a n×n window, which are defined as:

      combining PSO with other existing algorithms are also increasingly popular. In a PSO system, particles fly around in a multidimensional search space. During flight, each particle adjusts its position according to its own experience, and the

      = 1

      ×

      (, )

      =1 =1

      (5)

      experience of its neighboring particles, making use of the best position encountered by itself and its neighbors. Thus, a PSO system combines local search with global search, attempting to balance exploration and exploitation.

      , = 1

      ×

      ( , , )2

      =1 =1

      (6)

      1. PSO Algorithm

        PSO algorithm is a population-based search algorithm. It is based on the simulation of the social behavior of birds within

        Thus, the transformation function is

        a flock. In PSO, each single solution (individual bird) is a particle. All of the particles have fitness values which are

        , = .

        , +

        , × , + (, ) (7)

        evaluated by the objective function to be optimized the randomness and to get a better solution, and have velocities which direct the flying of these particles. The particles fly through the problem space by following the personal and

        Using eq. (7), contrast of the image is stretched considering local mean as the center of stretch. Four parameters, a, b, c, k are introduced in the transformation function to produce large variations in the processed image.

      2. Fitness Criterion

      One of the requirements of the APSO based image enhancement is to choose a criterion that is related to a fitness function. The proposed technique needs the enhanced image to have a relatively high intensity of the edges. Consequently, the fitness criterion is proportional to the number and intensities of the pixels in the edges that might give an over- sized credit to an image that doesnt have a natural contrast.

      In fact, we need a fitness criterion to evaluate the quality of the processed image with uniform intensity distribution. The fitness function shown in eq.(8), [5]-[6] is used for an

      global best particles.

      The swarm is initialized with a group of random particles or population and it then searches for optima by updating through iterations. In all iteration, each particle is updated by following two best values. The first one is the best solution of each particle achieved so far. This value is known as pbest solution. Another one is that, best solution experience by any particle among all generations of the swarm. This best value is known as gbest solution. These two best values are responsible to drive the particles to move to new better position.

      After finding the two best values, a particle updates its velocity and position with the help of the following equations [11]:

      +1 = . + 1 × ×

      enhancement criterion:

      = ((())) ×

      __

      ×

      +1 × × (9)

      × ( ) (8)

      +1 = + +1 (10)

      In the above mentioned equation is the enhanced

      where and denotes the position and velocity of

      image of the original image produced by the transformation

      function defined in eq. (7). () is the sum of × pixel

      particle at time instance t , is inertia weight at

      intensities of Sobel edge image . __ is the number of edge pixels as detected with the Sobel edge detector. The Sobel detector used here is an automatic threshold detector [13]-[14]. Lastly, ( ) measures the entropy of the image.

    3. ACCELAERTED PARTICLE SWARM OPTIMIZATION (APSO)

      PSO is an optimization algorithm developed by J. Kennedy and R. C. Eberhart in 1995 [10]-[11]. This optimization algorithm is a multi-agent based search strategy [8], modeled on the social behavior of organisms such as flocking bird. PSO has generated much wider interests, and forms an exciting, ever-expanding research subject, called swarm intelligence. It is an optimization tool provides a population based search procedure in which individuals called particles change their position with time. PSO has been applied to almost every area in optimization, computational intelligence, and design/ scheduling applications. There are at least two dozens of PSO variants, and hybrid algorithms by

      instant of time, 1 and 2 are positive acceleration constants, and rand is the random values generated in the range [ 0,1], sampled from a uniform distribution. is the best solution of individual particle over its flight path, gbest is the best particle obtained over all generations so far[10]-[16]-[17]-[18].

      B. APSO Algorithm

      The particle swarm optimization uses both the current global best, and the individual best, . The reason of using the individual best is to increase the diversity in the quality solutions. A simplified version which could increase the convergence of the algorithm is to use the global best only. Thus, in the accelerated particle swarm optimization (APSO) [7], the updated velocity vector is generated by a simpler formula

      +1 = + + (11)

      Where is from [0, 1] of d dimension, where d is the dimension of the parameter set. The update position is given by

      +1 = + +1 (12)

    4. PROPOSED METHODOLOGY

      In order to increase the convergence criteria further, we update the position as

      The original image is read by executing the algorithm. The local mean, global mean and standard deviation are

      +1 = (1 ) + ( ) +

      (13)

      calculated by the eq.(3), eq.(5) and eq.(5) in order to produce

      an enhanced image, that is described in eq.(7), which holds

      Typically, = 0.1 0 .5 and = 0.2 0 .7. A further improvement is done by reducing randomness in every iteration. = 0.7t , where t [0, max_iteration].

      START

      INITIALIZE POPULATION, VELOCITY FOR EACH PARTICLE

      EVALUATE FITNESS OF EACH PATICLE

      FOR EACH PARTICLE SET PERSONAL BEST FITNESS = pbest

      GLOBAL BEST FITNESS = max(pbest) = gbest

      UPDATE VELOCITY,POPULATION OF EACH PARTICLE

      NEW POPULATION = POPULATION + VELOCITY

      EVALUATE FITNESS OF NEW POPULATION

      IF CURRENT FITNESS >

      pbest

      SET pbest = CURRENT FITNESS

      EVALUATE max ( pbest )

      IF max(pbest)> gbest

      SET gbest = max (pbest)

      both global and local information of the input image. The function containing four parameters a, b, c, and k are used to produce different result. These four parameters have their defined range which is mentioned in the parameter setting section.

      Now our aim is to find the best set of values for these four parameters which can produce the optimal result and to perform this work APSO has been used. P number of particles are initialized, each with four parameters a, b, c, and k by the random values within their range and corresponding random velocities. It means position vector of each particle has four components a, b, c, and k, using these parameter values, each particle generates an enhanced image. Quality of the enhanced image is then calculated by the fitness function defined in eq. (8). Fitness values of all the enhanced images generated by all the particles are calculated. From these fitness values pbest and gbest are found. In APSO, pbest and gbest are highly responsible to drive each particle (solution) to the direction of best location using the eq. (11), eq. (12) and eq.(13).

      In each step (iteration) groups of P number of new particles are generated. From every generation pbest and gbest are found according to their fitness values. With the help of these best values, component wise new velocity of each particle is calculated to get the new solution. In this way new positions of particles are created for generations. When the process is completed the enhanced image is created by the particle, as it provides the maximum fitness value and the image is displayed as the final result. The detail flow chart is given in figure 1.

      1. Proposed Algorithm

        Algorithm for APSO based image enhancement

        Initialize population size (P), max iteration, dimension (d), window size (n).

        Read the image. Convert it into gray image. Calculate Mean eq.(3), Global Mean eq.(5), Standard Deviation. eq.(6)

        for each particle i=1 to P do

        Initialize parameters a,b,c and k (randomly within their range) and corresponding random velocities.

        STOPPING CRITERIA

        STOP

        Fig. 1 Flow Chart for Optimization

        end for

        SET POPULATION = pbest, VELOCITY = UPDATED VELOCITY

        Generate enhanced image using eq. (7) Calculate fitness functional value using eq. (8)

        //Set pbest=pop and pbest_value=fitness as the personal best

        //solution of ith particle achieved so far among.

        //gbest_value=max(fitness) and gbest=popi i.e the solution of

        // ith particle having maximum fitness.

        While ( t < maximum iteration) do for each particle i=1 to P do

        =0.7t

        = [ 0.2, 0.7]

        = (1, )

        Update velocity using eq. (11)

        Update population using eq. (12) and eq.(13) Calculate fitness using eq. (8)

        If F((Ie)i) > F(pbesti) then pbesti=popi pbest_valuei= F((Ie)i)

        // popi is the ith particle

        In experimental result we tested the algorithm for varieties of test image which include some indoor to outdoor scene image for better performance.

        1. Objective Evaluation:

          The objective criterion taken into consideration is the quality of the image, entropy, edge information of the enhanced image. In APSO we can get a higher number of edge information, optimum fitness and a good entropy value

          end if

          //set gbest as the global best solution achieved

          //so far among all generation.

          If F((Ie)i) > F(gbest) then

          gbest=popi

          gbeat_value = new_max_fitness

          TABLE 2

          ENTROPY, EDGE INFORMATION AND FITNESS OF THE ENHANCED IMAGES

          tr>

          Image

          Criteria

          HE

          LCS

          APSO

          Keyboard

          Entropy

          5.6147

          5.3453

          0.8649

          Edge Info.

          24933

          5947

          103480

          Fitness

          0.6459

          0.1364

          0.4624

          Bean

          Entropy

          5.2044

          3.6742

          0.7739

          Edge Info.

          22589

          1173

          60552

          Fitness

          0.9826

          0.0306

          0.4544

          Bus

          Entropy

          5.9451

          5.7653

          0.2998

          Edge Info.

          2382

          3040

          49972

          Fitness

          0.1418

          0.1800

          0.2169

          Toy

          Entropy

          5.9720

          4.5753

          0.6919

          Edge Info.

          2615

          2786

          56804

          Fitness

          0.1195

          0.0982

          0.4413

          Outdoor

          Entropy

          5.6222

          5.0861

          0.7787

          Edge Info.

          3783

          3355

          51717

          Fitness

          0.1752

          0.1390

          0.4551

          end if

          end for

          end while

        2. Parameter setting

      The result of APSO algorithm is parameter dependent. Fine tuning of the parameters can provide better result than other optimization algorithms. Parameters , and are positive acceleration constants or learning parameters, given

      = 0.1 0.5 and = 0.2 0 .7. Here, we have taken = 0.7t.. In this study there are four problem specific parameters, a, b, c, and k. The ranges of these parameters are the same as a [0.8,1.5], b [1, 22], c [ 0.01, 0.6 ], and k [ 0.5, 2]. The

      ranges of velocities for each parameter are velocity maximum

      = [0.1 2 0.1 0.1] and velocity minimum = [ -0.1 -2 -0.1 –

      0.1].

    5. RESULTS AND DISCUSSIONS

      The proposed method is tested on many gray-level images. Here we put results of only five images due to space limitation. Results of the proposed method is compared with three other methods, namely (i) linear contrast stretching (LCS), (ii) histogram equalization (HE). All the algorithms are evaluated using the same evaluation function, and the results are put in Table-2. The description of the input images and details about size of the image, Edge information (E), Entropy (H) and Fitness (F) are given in the Table 1.

      TABLE 1

      DETAILS ABOUT THE ORIGINAL IMAGES

      Image

      Size

      E

      H

      F

      Keyboard

      378×384

      2165

      6.0266

      0.0547

      Bean

      280×280

      1151

      5.2823

      0.0451

      Bus

      182×290

      2206

      6.5466

      0.1434

      Toy

      220×317

      2165

      7.6170

      0.1237

      Outdoor

      224×300

      3201

      6.4513

      0.1674

      1. (b)

        (c)

        Fig. 2 (a) Original Image (b) APSO output image (c) Performance Plot

        In average we have tested by taking 50 populations with around 50 iterations. Some of the results have shown below which shows that in average around it takes 15 to 20 iterations to converge in to the optimal parameters. The performance plot shows the relationship between numbers of iteration to the corresponding fitness values.

        (a) (b)

        (c)

        Fig. 3 (a) Original Image (b) APSO output image (c) Performance Plot

        (a) (b)

        (c)

        Fig. 4 (a) Original Image (b) APSO output image (c) Performance Plot

        1. (b)

          (c)

          Fig. 5 (a) Original Image (b) APSO output image (c) Performance Plot

          1. (b)

        (c) (d)

        Fig. 6 Resulted Outputs (keyboard)

        (a) (b)

        (c) (d)

        Fig. 7 Resulted Outputs (bean)

        (a) (b)

        (c) (d)

        Fig. 8 Resulted Outputs (outdoor)

        The output results showed in figure 6, 7 and 8. Here we have compared the output result with histogram equalization and linear contrast stretching with APSO based proposed method. Here the figures (a) are the original image, (b) are histogram equalized image, (c) are contrast stretching image and (d) are APSO output.

    6. CONCLUSION

In this paper we have propose an APSO based automatic image enhancement technique for gray level images. Results of the proposed technique are compared with some other image enhancement techniques, like linear contrast stretching and histogram equalization based image enhancement. We found better result compared to other techniques mentioned above. In APSO, the most important property is that, it can produce better result with proper tuning of parameters. But in case of contrast stretching and histogram equalization, they always produce only one enhanced image for a particular input image.

In future we have planned to compared this APSO with other optimization methods like ACO, Water cycle algorithm etc.

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