Multi-threshold Image Segmentation with Improved Artificial Fish Swarm Algorithm Block-coding and Antenna Selection ´ Lagunas M. Jiang, N. Mastorakis, D. Yuan, M. A.
Publication: Vol.: No.: Date:
European Computing Conference (ECC) September 2007
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Multi-threshold Image Segmentation with Improved Artificial Fish Swarm Algorithm Mingyan Jiang 1, 2 , Nikos E. Mastorakis 3 , Dongfeng Yuan 2 , and Miguel Angel Lagunas 1 1
3
Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Av. del Canal Olímpic s/n, 08860 Castelldefels (Barcelona), Spain {mingyan.jiang, m.a.lagunas }@cttc.es 2 School of Information Science and Engineering, Shandong University Jinan, 250100 China {jiangmingyan, dfyuan }@sdu.edu.cn Military Insitutes of University Education (ASEI), Hellenic Naval Academy Terma Chatzikyriakou 18539, Piraues, GREECE
[email protected]
Abstract. Some improved adaptive methods about step length are proposed in the Artificial Fish Swarm Algorithm (AFSA) which is a new heuristic intelligent optimization algorithm. The experimental results show that proposed methods have better performances such as good and fast global convergence, strong robustness, insensitive to initial values, simplicity of implementation, we apply the method in the image processing for the multi-threshold image segmentation compared with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), the properties are discussed and analysed in the end. Keywords: Adaptive step length, Multi-threshold, Image segmentation, AFSA, GA, PSO
1 Introduction In resent years, with the rise of artificial intelligence and artificial life, the research of swarm intelligence aroused great concern of numerous scholars, and some new-type bionic algorithms with the swarm intelligence are become hot research topics such as the Genetic Algorithm (GA) [1], the Particle Swarm Optimization (PSO) algorithm [2], the Ant Colony Optimization (ACO) algorithm [3], the Bees Algorithm (BA) [4], and Artificial Fish Swarm Algorithm (AFSA) [5]. Their applications in many kinds of scientific research fields show their good properties and practical value. They have some common characters and also have their unique characters. AFSA as a new optimization algorithm becomes a very hot topic, it offers new ideas to solve the optimization problem in signal processing [6], complex function optimization [7], neural network classifiers [8], network combinatorial optimization [9], multi-user detection in communication [10][11], sequence code estimation [12], and some
2 Mingyan Jiang P1, 2P , Nikos E. Mastorakis P3P , Dongfeng YuanP 2P , and Miguel Angel Lagunas P1
applications [13]. In these applications, the algorithm reflects good performances and becomes a prospective method in solving optimization problems. Its basic idea is to imitate the fish behaviours such as praying, swarming, following with local search of fish individual for reaching the global optimum, it is random and parallel search algorithm, it has the good ability to overcome local extrema, obtain the global extrema and has fast convergence speed. In this paper, we proposed some adaptive step methods and apply one in image processing.
2 The Artificial Fish Swarm Algorithm
2.1 The Artificial Fish The Artificial Fish (AF) realizes external perception by its vision. X is the current state of a AF, Visual is the visual distance, and X v is the visual position at some moment. If the state at the visual position is better than the current state, it goes forward a step in this direction, and arrives the X next state; otherwise, continues an inspecting tour in the vision. The greater number of inspecting tour the AF does, the more knowledge about overall states of the vision the AF obtains. Certainly, it does not need to travel throughout complex or infinite states, which is helpful to find the global optimum by allowing certain local optimum with some uncertainty. 2.2 Five Basic Behaviors of AF Fish usually stay in the place with a lot of food, so we simulate the behaviors of fish based on this characteristic to find the global optimum, which is the basic idea of the AFSA. Five basic behaviors of AF are defined [5][12] as follows: (1). AF_Prey: This is a basic biological behavior that tends to the food; generally the fish perceives the concentration of food in water to determine the movement by vision or sense and then chooses the tendency. (2). AF_Swarm: The fish will assemble in groups naturally in the moving process, which is a kind of living habits in order to guarantee the existence of the colony and avoid dangers. (3). AF_Follow: In the moving process of the fish swarm, when a single fish or several ones find food, the neighborhood partners will trail and reach the food quickly. (4). AF_Move: Fish swim randomly in water; in fact, they are seeking food or companions in larger ranges. (5).AF_Leap: Fish stop somewhere in water, every AF’s result will gradually be the same, the difference of objective values (food concentration, FC) becomes smaller within some iterations, it might fall into local extrema, change the parameters randomly to the still states for leaping out current state. The detail behaviors pseudocode can be seen in [6].
Multi-threshold Image Segmentation with Improved Artificial Fish Swarm Algorithm
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2.3 The improved adaptive step length in AFSA In the AFSA, there are many parameters that have impacts on the final optimization result, In this paper, we only consider the parameter Step, With the increase of the Step, the speed of convergence is accelerated. However, when the increase of the Step is out of a range, the speed of convergence is decelerated, and sometimes the emergence of vibration can influence the speed of convergence greatly. Using the adaptive step may prevent the emergence of vibration, increase the convergence speed and enhance the optimization precision. In the behaviors of AF_Prey, AF_Swarm and AF_Follow, which use the Step parameter in every iteration, the optimized variables (vector) have the various quantity of Step*rand( ) , Step is a fixed parameter, rand( ) is a uniformly distributed function. We give some adaptive Step methods as follows (t means iteration time). (1). Stept +1 = α i Stept , α =0.9~0.99 and Stept =1 = Step (2). Prior period of iteration, using Step*rand( ); later period, using method (1). β iN − t (3). Stept +1 = Step , β =(1.1~1.5), N is the all iteration times. N The method (1) can insure the precise result when the iteration is in the optimal research range, but might trap in local extrema. Method (2) can balances above problems. Method (3) has a relation with the iteration time, and gradually decreases the Step, so decreases the various quantities of optimized variables in each iteration time. Using the adaptive step, we can select the Step more randomly which can guarantee the fast convergence, the result’s precision and stability. For example, using fixed Step=2 and adaptive step ( β =1.2) of method (3), we optimize a nonlinear function with many local extreme points by AFSA and improved AFSA, the function f ( x, y ) = x sin(2π x) − y sin(2π y ) + 1 , and x, y ∈ [−1, 2] .The comparison result is shown in Fig.1. With the adaptive step, convergence speed is faster and the result is more stable especially when the optimized variables are many.
3 Image Segmentation by improved AFSA
3.1 The Multi-threshold image segmentation The image segmentation is key pre-step for the object identification; there are many conventional segmentation methods such as the maximum variance between clusters method, maximum entropy (ME) threshold method, minimum error threshold method, etc. The principle of image segmentation based on ME [14] is: the image gray t
level ∈ [0, l − 1] , t is the threshold for the image segmentation, Pt = ∑ pi and pi is the i =0
probability of i gray level of image. Select the optimal t; make the image entropy
4 Mingyan Jiang P1, 2P , Nikos E. Mastorakis P3P , Dongfeng YuanP 2P , and Miguel Angel Lagunas P1 t
H (t ) = −∑ i =0
problem
pi pi l −1 pi p ln − ∑ ln i be maximal. Extending to multi-threshold, the Pt Pt i = t +1 1 − Pt 1 − Pt
is:
select t1
H (t1 , t2 ,..., tk ) = −∑ i =0
multi-threshold
,
tk
t2
pi p p p ln i − ∑ i ln I − ... − Pt0 Pt0 i =t1 +1 Pt1 Pt1
make
i = l −1
pi
∑P i = ti
ln
tk
the
pi Ptk
image
be
entropy
maximal.
We
optimize and select 2, 3 thresholds with improved AFSA for image segmentation.
O ptim ized function value
4.5
4
3.5
3 Adaptive Step Fixed Step 2.5
2
0
5
10
15
20
25
30
35
40
45
50
Iteration time
Fig.1. Convergence speed with adaptive step and fixed step
3.2 The Parameter Selection and Results The parameter selection: fish number is 15, try_number is 3, iteration is 50, Step is 10, Visual is 10, crowded factor δ is 0.8 and the result is shown in the Fig.2.
(a). Source image (b). Single threshold (c). Two thresholds (d). Three thresholds
Multi-threshold Image Segmentation with Improved Artificial Fish Swarm Algorithm
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Fig.2. The image segmentation with 1, 2 and 3 thresholds respectively
We also use the GA and PSO for the population size is 20, iteration number parameter selection: the number of 100, wmax =0.9, wmin =0.4, learning factor
same problem, the GA parameter selection: is 100, Pc is 0.8 and Pm is 0.05, the PSO particles is 20, the iteration number is c1 = c2 = 2 , the result is shown in Table 1.
4 Discussion and Conclusion
4.1 Discussion From the principle of the optimization algorithm, the AFSA is a neighborhood search, with the aid of heuristic search strategy, and has the ability of the global optimization. The AFSA has no special requirements to the object function and initial values, so the initial value can be set with stochastic values or fixed values, and other parameters can be set in a wide range. In brief, the algorithm has strong adaptability. Table 1. The comparison of GA, PSO and improved AFSA
Method 2-threshold ME Time 3-threshold ME Time _____________________________________________________________________ GA 82,151 12.613 17.24s 58,115,162 15.571 20.91s PSO 80,151 12.613 8.67s 59,109,162 15.590 9.96s AFSA 80,151 12.613 4.19s 60,109,162 15.590 6.9s
In the Table 1, with the optimized threshold results of image segmentation by GA, PSO and improved AFSA, we can see that the properties of AFSA are better than PSO, and the properties of PSO are better than GA. But how to compare them fairly is a problem, the AFSA has low computing complexity, faster convergence speed and more precision, the future work is consideration of establishing the theory standard and adjusting method of other parameters such as adaptive Visual, crowded factor effect etc. Fish fast recognition and decision mechanism can be considered into the algorithm and some other improved ideas can be seen in [10][13]. 4.2 Conclusion We propose three adaptive step methods in the AFSA and analyze the properties of improved method, and then we use it in the multi-threshold image segmentation, and compare it with the GA and PSO method. The results show that the AFSA can obtain
6 Mingyan Jiang P1, 2P , Nikos E. Mastorakis P3P , Dongfeng YuanP 2P , and Miguel Angel Lagunas P1
better performance than the GA and PSO. The some improved methods and ideas are proposed, the applied performance can be better, the AFSA can obtain the optimal or sub-optimal results on theory, it is believed that the AFSA can be used in some other complicated optimization applications in the fields such as control, communication, signal processing and pattern recognition, etc. Acknowledgments. This work is supported by the National Natural Scientific Foundation of China (No. 60672037), the Natural Science Foundation of Shandong Province of China (No. Y2006G06), and the Catalan Government (Generalitat de Catalunya, Spain) under grant SGR2005-00690.
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