Anis Ladgham* Abdellatif Mtibaa

Transcription

1 Int. J. Signal and Imaging Systems Engineering, Vol. X, No. Y, XXXX Fast and consistent images areas recognition using an Improved Shuffled Frog Leaping Algorithm Anis Ladgham* Electronics and Microelectronics Laboratory, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia and Department of Electrical Engineering, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia *Corresponding author Anis Sakly Department of Electrical Engineering, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia and Research Unit: Industrial Systems Study and Renewable Energy (ESIER), National Engineering School of Monastir (ENIM), University of Monastir, Monastir, Tunisia Abdellatif Mtibaa Electronics and Microelectronics Laboratory, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia and Department of Electrical Engineering, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia Abstract: Improved Shuffled Frog Leaping Algorithm (IMSFLA) is a novel optimal algorithm of automatic recognition of areas of greyscale-based images. It is as an efficient improvement of the original Shuffled Frog Leaping Algorithm (SFLA). SFLA is a newly developed evolutionary algorithm with good global search capability. In this new paradigm, we propose a new fitness function. It is computationally simple and assists to quickly discover the adequate threshold in a continuous range of grey levels. And more, the new method is enhanced by the cloning of the fitter particles at the expense of the worst particles. The performance of IMSFLA is evaluated towards an Artificial Bee Colony algorithm (ABC) based method, two Genetic algorithm (GA) based method and Artificial Fish-Swarm (AFS) based method for many benchmark images and IMSFLA outperforms these algorithms. Keywords: recognition; SFLA; IMSFLA; fitness function; imaging. Reference to this paper should be made as follows: Ladgham, A., Sakly, A. and Mtibaa, A. (XXXX) Fast and consistent images areas recognition using an Improved Shuffled Frog Leaping Algorithm, Int. J. Signal and Imaging Systems Engineering, Vol. X, No. Y, pp.xxx xxx. Copyright 200X Inderscience Enterprises Ltd.

2 A. Ladgham, A. Sakly and A. Mtibaa Biographical notes: Anis Ladgham did his schooling in the National School of Engineering of Monastir (ENIM). In 2010, he graduated with a National Diploma of Engineering in Electrical engineering from ENIM. In July 2011, he received the Master degree from ENIM. He is currently a PhD researcher in the Electronics and Microelectronics Laboratory (EμE) at the Faculty of Sciences of Monastir. His research interests include medical image processing, embedded systems and soft computing. Anis Sakly received the Electrical Engineering diploma in 1994 from National Engineering School of Monastir (ENIM), then the PhD degree in Electrical Engineering in 2005 from National Engineering School of Tunis (ENIT). Since 2012 he has been a Professor at ENIM. His research interests are in analysis, synthesis and implementation of intelligent control systems, particularly soft computing-based control approaches. Abdellatif Mtibaa received his PhD degree in Electrical Engineering at the National School of Engineering of Tunis. Since 1990 he has been an Assistant Professor in Micro-Electronics and Hardware Design with Electrical Department at the National School of Engineering of Monastir. His research interests include high level synthesis, rapid prototyping and reconfigurable architecture for real-time multimedia applications. 1 Introduction The automatic recognition of the regions of images or recognition of the threshold separating them is the main act for image segmentation. The latter is an essential construction step for various image analysis and processing tasks. It becomes required for subsequent image description. It is one of the most complex stages. The problem is how to partition an image into its homogeneous regions, objects or labels (Gonzalez and Woods, 2002). Thresholding is a tool widely used. It is typically practical and computationally efficient. The leading objective here is to distinguish objects from background in an image. The most popular approaches of image thresholding are classified into two classes: the first is based on grey levels and the second is based on textures. However, it is often difficult to determine an accurate discrimination for a field of textures especially when the image contains fields of similar regions. Brief, we are facing a problem of estimation of thresholds. Generally, approaches that lead to good results are commonly costly in terms of calculation time (Otsu, 1979). A simple and an effective method remains an interesting and urgent issue for several research topics. Recently, the development of nature-inspired computations remedies for this problem. The latter have received an increasing amount of attention and therefore many approaches have been suggested by many researchers in recent decades (Ma et al., 2011; Chen and Zuo, 2002; Ma et al., 2009; Hammouche et al., 2010; Yin, 1999; Chen and Zuo, 2002; Pan and Wu, 2009; Chander et al., 2011; Zhang and Liu, 2006; Du et al., 2005). This paper aims at the automatic recognition of threshold of an image based on grey levels and moreover proposes a new meta-heuristic technique for sample images. Due to their flexibility and their simplicity, meta-heuristics have developed for all image processing tasks, including images denoising, digital watermarking, images compression, images segmentation, images classification (Chen and Zuo, 2002; Pan and Wu, 2009; Chander et al., 2011; Zhang and Liu, 2006; Du et al., 2005; Li et al., 2011; Ladgham et al., 2012, 2013). The most popular meta-heuristics are the Evolutionary Algorithms (EAs) (Goldberg, 1989) and the Swarm Intelligence (SI) (Kennedy and Eberhart, 1995). EAs such as the Genetic Algorithm (GA) and SI such as the Particle Swarm Optimisation (PSO) algorithm and Artificial Fish Swarm (AFS) algorithm. AFS and PSO are based on collective intelligence and they are inspired from the foraging behaviour of animals and GA is an evolutionary algorithm which is inspired from natural selection and survival of the best adapted in nature. Similar to the existing nature-inspired algorithms, Eusuff and Lansey (2003) proposed a new emerging optimisation algorithm SFLA. It observes, imitates and models the behaviour of collection of frogs looking for the location containing the maximum quantity of available food. This food is placed on discrete stones randomly located in a lake. SFLA is a memetic meta-heuristic based on evolution of memes, performed by interactive individuals and global communication of information between the frogs population. The suitability and effectiveness of this algorithm have been demonstrated by its application in image processing (Bhaduri, 2009; Ladgham et al., 2013; Wang et al., 2010; Gu et al., 2012; Horng, 2013), flow shop scheduling problem (Alireza et al., 2008), continuous function optimisation (Luo et al., 2009), watermarking scheme (Li et al., 2011) and traditional travelling salesman problem (Luo et al., 2008), etc. The already algorithm has been clearly demonstrated to be better than PSO and GA and it has been proved its success in the optimisation of various complex functions. The overall objective of this manuscript is to apply our algorithm, which is inspired from SFLA, to search for the thresholds of sample images such as the satellite images (SAR images) or medical images. These two kinds of images can be infected with many types of noise such as speckle noise, Gaussian noise and Salt-and-pepper noise. The latter deteriorate inevitably the quality of images. For this, noisy images must be filtered before applying our algorithm. We use a novel and a computationally simple fitness function that can evaluate with accuracy all frogs to give the adequate threshold. This proposed method is called the Improved Shuffled Frog Leaping Algorithm (IMSFLA).

3 Fast and consistent images areas recognition using an ISFLA The remaining of this paper is organised as follows. In Section 2, the principle of SFLA optimisation is briefly presented. Section 3 presents the proposed IMSFLA approach. Performance evaluation and comparative results are given in detail in Section 4. Finally, some conclusions are made in Section 5. 2 Shuffled Frog Leaping Algorithm (SFLA) optimisation Figure 1 Flowchart of SFLA Begin Initialise : number of memplexes number of evolution steps within each memplex Shuffled Frog Leaping Algorithm (SFLA) is a newly developed nature-inspired method (Eusuff and Lansey, 2003) which is characterised by great capability in global search and easy implementation. SFLA combines the advantages of a gene-based memetic algorithm GA (Yin, 1999; Chen and Zuo, 2002) and social behaviour-based particle swarm optimisation PSO (Pan and Wu, 2009; Chander et al., 2011; Zhang and Liu, 2006; Du et al., 2005; Hamdaoui et al., 2013). In GA, chromosomes are represented as a string consisting of a set of elements called genes. GA implements a local search before crossover and mutation to determine new descendents. New descendants that get better results than original descendants replace the original ones, thus continuing the evolutionary process. In PSO, individual solutions called particles are analogous to the GA chromosomes. However PSO doesn t apply crossover or mutation to determine a new particle. Each particle changes its position and its velocity based on its individual best solution and on the global best solution until a global optimal solution is found. The SFLA principle came from a virtual population of frogs in which individual frogs are equivalent to GA chromosomes and they represent a set of solutions. The whole population of frogs is divided into many subsets called memplexes. Each frog is distributed to a different memeplex. Frogs of each memplex are described as a memetic vector with the same structure but different adaptabilities. They have their own strategy to explore the environment and they can communicate and transmit information to improve their strategies. After a predefined number of memetic evolution, the exchange of information between memplexes takes place in the shuffling stage. In this stage, the evolution towards a particular interval must be free from all prejudices. Memetic evolution and shuffling are carried alternately until reaching the convergence criterion otherwise until a stopping criterion. SFLA have demonstrated effectiveness in several optimisation problems that are computationally expensive to solve using other methods, i.e. water distribution and ground water model calibration problems (Huynh, 2008). The flowchart of Figure 1 gives briefly and in order the steps of the original SFLA. Generate population (P) randomly Evaluate P with the fitness function Sort P in descending order Partition P into m memplexes Iterative update of the worst frog of each memplex Shuffle the memplexes Convergence criteria satisfied Determine the best solution End The application of SFLA starts firstly by creating arbitrarily an initial population X ( i = 1, 2 F) of F frogs. All i particles are sorted in descending order and divided into m memplexes, each memplex contains p frogs, the frog that is ranked first moves to the first memplex, the second moves to the second memplex, the p th frog to the p th memplex and the ( ) 1 th p + returns to the first memplex. Particles having the best and the worst fitness in each memplex are identified respectively by X b and X w. The best particle in the whole population is identified by X g (the global best). During the

4 A. Ladgham, A. Sakly and A. Mtibaa evolution of memplexes, worst frogs jump to reach the best ones in the memeplex evolution process using equations (1) and (2): ( ) S = rand X X (1) w w. b w IX = X + S ; S < Smax (2) where IX w indicates the improved worst solution, S indicates the jump step of the worst frog, S max is the maximum jump distance and rand is an arbitrary number in the range [ 0,1 ]. Equations (1) and (2) are repeated for a predefined number of iterations in order to obtain a better result than X w. If these equations do not improve the worst solution, X b is replaced by X g and adopted to equation (3) and the process of evolution is repeated. ( ) S = rand X X (3). g w If the worst solution is not improved using equations (1) and (3), a new solution is generated arbitrarily to replace the worst one. After a specified number of memeplex evolution stages, all frogs of all memeplexes are recollected, and resorted in descending order based on their fitness. Then frogs are divided into different memeplexes again, and then the process of evolution is done. Finally, if a global solution or a fixed iteration number is reached, the algorithm stops. by the evaluation of the memplexes. And the evolution of particles of each memplex is replaced by the evolution of memplexes. Poor memplex is concerned by the amelioration at each shuffling iteration. Figure 2 Flowchart of IMSFLA Begin Initialise : number of memplexes number of evolution steps Generate population (P) randomly Divide P into m memplexes Evaluate the memplexes with the fitness function Sort memplexes in descending order Iterative update of the worst memplex 3 Images areas recognition based on IMSFLA Recently, SFLA has been used in order to recognise the optimal thresholds in images. For example, it is used in colour image segmentation using Clonal Selection (Bhaduri, 2009). It is used to improve the algorithm of segmentation by Otsu (Wang et al., 2010). The use of SFLA to optimise the Otsu algorithm reduces significantly the computation time and gives better results than using only Otsu, but it always remains expensive in terms of time and resources. Also Gu et al. (2012) proposed a new image segmentation algorithm in combination with Shuffled frog-leaping algorithm and FCM clustering, this algorithm could overcome the disfigurement caused by FCM algorithm. Horng (2013) used the original SFLA to search the adequate thresholds. Even though, basic SFLA may give good results but it may present some problems such as coincidence in a local optimum that may cause raise in computation time. IMSFLA remedies to these troubles. It can give best qualities and lower execution times. Indeed, the problem of local optima is cancelled by our algorithm since the process of evolution to the best solution in a memplex is replaced by a random recombination of positions of frogs in each memplex. The process of evolution is limited to the evolution to the global best solution. Here, the global best solution is the best memplex. The steps of IMSFLA are given in the flowchart (Figure 2). Observing this flowchart, we can see that the phase of evaluation of the particles by the fitness function is replaced Shuffle the memplexes Convergence criteria satisfied Determine the best solution End In IMSFLA, memplexes are the equivalents of the GA chromosomes. Each memplex contains 8 frogs generated arbitrarily and modelling the decision variables. Each frog is really a number coded on 8 bits (each frog has a continuous value between 0 and 255). To simplify the calculation and evaluation of these frogs, low value frogs are converted to 0 and high value frogs are converted to 1. The proposed fitness function is computationally simple; it helps to evaluate memplexes rapidly. The original image must be filtered to reduce the amount of noise, especially with a real SAR image. We use a correlation to filter images with a 5-by-5 averaging filter containing equal weights.

5 Fast and consistent images areas recognition using an ISFLA Figure 3 Flowchart of the fitness function 3.1 Fitness function In addition to modifications affected in the body of the original SFLA algorithm to overcome the problems of quality and high execution time, the major contribution of this work is the establishing of the new evaluation function. To calculate this function, a weight P j is computed for each particle x(, i j ) of the memplex j according to its location in its Memplex. Then we calculate the sum of these weights SP for frogs of each i Memplex according to equations (4) and (5). Pi p i = 2 xi (, j) (4) i= p p 1 2 SPj = Pi = 2 x i,1 + 2 x i,2 + + x i, p i= 1 p ( ) ( ) ( ) (5) After this, the sum SP i obtained is standardised using equation (6): 255 SPj N( j) = (6) ( p 1) 2 The standardised sum N(j) is calculated for each memplex, each sum is compared with the intensities of pixels of the (m, n) original image. These comparisons allow determining the fitness function of each memplex as shown in the flowchart of Figure 3. Parameters used in the pseudo-code of the fitness function are hnum and hsum which are respectively the number of particles having intensities upper than N(i) and the sum of their intensities. lnum and lsum are respectively the number of particles having intensities lower than N(i) and the sum of their intensities. 3.2 Steps of IMSFLA Upon the right choice of threshold, we can classify the pixels of a given image into two classes: one composed of pixels related to an object and another to the background. In IMSFLA, the optimal threshold vector is selected by a discriminate criterion to maximise the fitness function of each memplex. As the SAR images are concerned, our algorithm may suppress the influence of speckle noise. Main steps of our method are briefly explained as below: Step 1: Filtering the original image Employ a low-pass filter (averaging filter) in which we use a correlation to filter images with a 5-by-5 matrix containing equal weights to reduce the noise in the original image. The principle is to replace each pixel by the average of pixels in a square window surrounding this pixel. It is a trade-off between noise removal and detail preserving. Step 2: IMSFLA evaluation i Initial population of frogs The initial population initpop contains F frogs. The latter is divided into m memplexes, each memplex contains p frogs (i.e. F = m.p). The frogs are really the elements of a matrix. Each row of the matrix modes one memplex. Each column gives the frogs of the corresponding memplex. The initial population is created randomly as indicated in equation (7): x11 x 1m initpop = xp 1 x pm To gain in terms of computational time, these frogs are first decoded into binary numbers (0 and 1), the low value frogs (having intensities lower or equal to 0.5) are replaced by 0 and the high value ones (having intensities upper than 0.5) are replaced by 1. ii Sorting and distribution For each population, the evaluation of memplexes is done using the fitness function. Then, memplexes are ranked in (7)

6 A. Ladgham, A. Sakly and A. Mtibaa descending order according to their fitness values as shown in section 3.1. Best and worst memplexes are named M b and M w respectively. M b is the memplex with the high fitness value. M w is the memplex with the less fitness value. iii Memplexes evolution To improve the worst solution, an equation similar to the PSO is used. In our algorithm, we want to make this worst solution better than the best one. This amelioration takes place by swapping randomly the positions of the internal frogs in the worst memplexe, e.g. equation (8): S1 rand( 1, p).( Mb Mw) where rand ( 1, ) = (8) p is a random vector which elements are between 0 and 1. The new solution is given in equation (9). This new solution is also evaluated by the fitness function. If a better solution than the previous is produced, it will be memorised, else equation (8) is repeated for a predefined number of times. IM = M + S (9) w w 1 If these equations produce a better solution, it replaces the worst memplex. If they do not, then M b of equation (8) is changed by M j other than M b and M w and adapted to equations (10) and (11): ( ) ( ) S2= rand 1, p. Mj Mw ; 1 < j < m (10) IM = M + S (11) w w 2 If these equations produce a better solution, it replaces the worst memplex. If they do not improve it, then a new solution is randomly generated to replace the worst one. iv Shuffling After improving the worst solution, it takes the rank of the last best solution. Memplexes are sorted in descending order again based on their fitness, and then step iii is repeated. Indeed, we want to ameliorate the new worst solution by using the same strategy used with former worst solution. The shuffling stage is repeated until a terminal condition is reached. v Terminal condition If a predefined solution is reached, the algorithm stops. Increasing the value of the terminal condition is useless because our developed algorithm IMSFLA shows that it stabilises and gives a precise result rapidly from the first iterations. The threshold t is the rounded value of the standardised coefficient N(j) of the best memplex. Step 3: Thresholding After reaching the terminal condition, the filtered image I is segmented with the optimal threshold t and obtain the final segmented image. 4 Experimental results In order to testify the efficiency of the IMSFLA, aspects including the recognition effect under noisy and non noisy situations and calculation efficiency are taken into consideration. The algorithm is coded in Matlab 7.9 and executed on a personal computer with characteristics: Windows 7 with PIV GHz CPU and 3 G RAM. 4.1 Comparisons of recognition performance In the already study, images used are with 256 greyscale. Firstly, we compare the efficiency of the IMSFLA with other meta-heuristics such as the Artificial Bee Colony (ABC) based algorithm (Ma et al., 2011), the Genetic algorithm (GA) based (Chen and Zuo, 2002) and the Artificial Fish Swarm (AFS) based algorithm (Pan and Wu, 2009). The ABC algorithm, the AFS algorithm and the GA are briefly detailed in Tables 1, 2 and 3 step by step. Table 1 Pseudo-code of the ABC algorithm Step 1: Initialisation Step 2: Move the employed bees onto the food sources and evaluate their nectar amounts. Step 3: Place the onlookers depending upon the nectar amounts obtained by employed bees. The onlooker bees determines and evaluates the nectar amount and compares it with the neighbours and replaces it with best pixel value Step 4: Send the scouts for exploring abandoned food sources. Step 5: Memorise the best food sources obtained so far. Step 6: If a termination criterion not satisfied go to step 2; otherwise stop the procedure and display the best food source obtained so far. Table 2 Pseudo-code of the AFS algorithm Step 1: Initialise the position matrix X i and the velocity V i of each particle as follows: x = x + ( x x )* rand() im min max min vim = vmin + ( vmax vmin )* rand() Step 2: Evaluate the fitness function value of each particle. Step 3: Find parameters P i of each particle and P g. Step 4: Update the position and the velocity of each particle using equations (2) and (1). Step 5: Stop if the stopping criteria is satisfied or go to Step2. Table 3 Pseudo-code of the genetic algorithm Step1: Choose the initial population of individuals Step2: Evaluate the fitness of each individual in that population Step3: Repeat on this generation until termination (time limit, sufficient fitness achieved etc.): Select the best-fit individuals for reproduction. Breed new individuals through crossover and mutation operations to give birth to offspring Evaluate the individual fitness of new individuals Replace least-fit population with new individuals

7 Fast and consistent images areas recognition using an ISFLA The latter are applied to some typical images including a non-noisy coins image, a noisy one (containing Gaussian noise with mean 0 and variance 0.01 and speckle noise with variance 0.005) and a real SAR image. Secondly, our method is compared with another Genetic Algorithm (Ma et al., 2009) using a medical image of globules of blood. Finally, IMSFLA is compared with the original SFLA. The results of the visual qualities of recognition of the adequate thresholds are given in Figures 4, 5 and 6 respectively. Figure 4 Comparative experiments on images areas recognition: (a) Noise-free coins image; (b) coins image polluted by synthetic noise; (c) SAR image; (d) recognition of (a) by our method; (e) recognition of (b) by our method; (f) recognition of (c) by our method; (g) recognition of (a) by Ma et al. (2011); (h) recognition of (b) by Ma et al. (2011); (i) recognition of (c) by Ma et al. (2011); (j) recognition of (a) by Chen and Zuo (2002); (k) recognition of (b) by Chen and Zuo (2002); (l) recognition of (c) by Chen and Zuo (2002); (m) recognition of (a) by Pan and Wu (2009); (n) recognition of (b) by Pan and Wu (2009); (o) recognition of (c) by Pan and Wu (2009)

8 A. Ladgham, A. Sakly and A. Mtibaa Figure 5 Comparative experiments on image areas recognition: (a) blood image; (b) our method; (c) GA method (Ma et al., 2009) (a) (b) (c) Figure 6 Comparative experiments on image area recognition: (a) camera image; (b) original SFLA; (c) our method. (a) (b) (c) For IMSFLA, we suppose that the number of memeplexes used is 3, the number of frogs in each memeplex is 3, so the population size is 9 and the number of iterations is 10. In ABC, the population size is 10, the number of iterations is 30 and the limit time for abandonment is 10. In GA, the population size is 50, the number of iterations is 70, the binary digits of variable are 16, the crossover probability is 0.7 and the mutation probability is In AFS algorithm, the visual distance of artificial fish is 50, the crowding index is 0.5, the maximal moving step is 3, the try times is 5, the population size is 30 and the maximum iteration is 100. Our algorithm presents the smallest number of particles and the smallest number of iterations. In Figure 4, it is obvious to see that there are a lot of noise and over-segmentation phenomenon in the resulted images achieved by the GA algorithm of (Chen and Zuo, 2002). The AFS algorithm (Pan and Wu, 2009) provides with a medium effect in case of the noise-free coins image but its performance degrades once noise is implicated. In particular, it provides dimpled seashore when the real SAR image is performed. Compared with these two methods in (Chen and Zuo, 2002; Pan and Wu, 2009), no matter whether the image is polluted by noise or not, our method always obtains satisfying binary images with clear contours and continuous edges. The ABC algorithm of (Ma et al., 2011) does not lose its performance by adding noise to the coins image but it is noticeable that the contours of the SAR image do not define precisely the regions of the image, our method obtains precise edges and continuous seashore. Figure 5 shows that the two methods (IMSFLA and GA (Ma et al., 2009)) detect the same number of globules. Although, IMSFLA gives a resulted image whose blood globules are more rounded and precise especially for locations inside globules. Figure 6 shows the results of automatic areas recognition of the camera image using IMSFLA and the original SFLA. In this experiment, we use the new fitness function in IMSFLA and in the basic SFLA. It is obvious that IMSFLA gives better visual results than the basic SFLA. Also, SFLA consumes 17.20s but IMSFLA consumes only 5.52s. Figures 7 9 give the traces of thresholds of IMSFLA, ABC, GA and AFS algorithms. These traces model in part against the convergence time and the manner of converge (stable convergence or non-stable convergence). From the curves given in Figures 7 9, the convergent performance of the algorithms can be ordered as IMSFLA > ABC > AFS > GA. Figures 7 9c shows that the first GA algorithm of (Chen and Zuo, 2002) do not stabilise until the last iterations. Figures 7 9b and d shows that AFS and the second GA algorithms stabilise but after a number of harmonics. Our algorithm in Figures 7 9a stabilise quickly without making harmonics. It is clear that IMSFLA keeps the best performance for all the test images especially for the SAR image where the quality of our algorithm exceeds obviously the others. Moreover, IMSFLA converges very quickly and it stabilises from the earliest iterations.

9 Fast and consistent images areas recognition using an ISFLA Figure 7 Traces of thresholds in case of Figure 4a: (a) Threshold trace of IMSFLA algorithm; (b) threshold trace of ABC (Ma et al., 2011); (c) threshold trace of GA algorithm (Chen and Zuo, 2002); (d) threshold trace of AFS algorithm (Pan and Wu, 2009) (see online version for colours) (a) (b) (c) (d) Figure 8 Traces of thresholds in case of Figure 4b: (a) Threshold trace of IMSFLA algorithm; (b) threshold trace of ABC algorithm (Ma et al., 2009); (c) threshold trace of GA algorithm (Chen and Zuo, 2002); (d) threshold trace of AFS algorithm (Pan and Wu, 2009) (see online version for colours) (a) (b)

10 A. Ladgham, A. Sakly and A. Mtibaa Figure 8 Traces of thresholds in case of Figure 4b: (a) Threshold trace of IMSFLA algorithm; (b) threshold trace of ABC algorithm (Ma et al., 2009); (c) threshold trace of GA algorithm (Chen and Zuo, 2002); (d) threshold trace of AFS algorithm (Pan and Wu, 2009) (see online version for colours) (continued) (c) (d) Figure 9 Traces of fitness and thresholds in case of Figure 4c: (a) Threshold trace of IMSFLA algorithm; (b) threshold trace of ABC algorithm (Ma et al., 2009); (c) threshold trace of GA (Chen and Zuo, 2002); (d) threshold trace of AFS algorithm (Pan and Wu, 2009) (see online version for colours) (a) (b) (c) (d)

11 Fast and consistent images areas recognition using an ISFLA 4.2 Comparisons of recognition time Tables 4 6 give a comparison of recognition times spent in the results given in Figure 4. The best results in the Tables 4 6 are in bold. These results indicate that our method is considerably faster than the other methods given by (Ma et al., 2011; Chen and Zuo, 2002; Pan and Wu, 2009). Table 4 Comparison on recognition time of Figure 4a Method SI scheme Threshold Time(s) Our method IMSFLA The method in Ma et al. (2011) ABC The method in Chen and Zuo (2002) GA The method in Pan and Wu (2009) AFS Table 5 Method Comparison on recognition time of Figure 4b SI scheme Threshold Time(s) Our method IMSFLA The method Ma et al. (2011 ABC The method in Chen and Zuo (2002) GA The method in Pan and Wu (2009) AFS Table 6 Comparison on recognition time of Figure 4c Method SI scheme Threshold Time(s) Our method IMSFLA The method in Ma et al. (2011) ABC The method in Chen and Zuo (2002) GA The method in Pan and Wu (2009) AFS Comparison of convergence speed To compare the convergence speed of our method over the other methods (Ma et al., 2011; Chen and Zuo, 2002; Pan and Wu, 2009), we compare their performance illustrated by their fitness trace when all the population sizes are 20, all the maximum iterations are 30 and the other parameters are the same as those in Section 4. Figure 10a illustrates that IMSFLA converges stably at the 3 rd iteration. Figure 10b indicates that the ABC algorithm in (Ma et al., 2011) converges at the 11 th iteration. Figure 10c shows that the GA algorithm in (Chen and Zuo, 2002) does not converge during the 30 iterations, so it cannot find the adequate threshold. In Figure 10d, AFS converges at the 12th iteration, comparable to ABC algorithm given in Figure 10d. We can say that IMSFLA is not only the faster but also the most stable. Figure 10 Comparisons on convergence speed: (a) Fitness trace of IMSFLA algorithm; (b) fitness trace of ABC (Ma et al., 2011); (c) fitness trace of GA (Chen and Zuo, 2002); (d) fitness trace of AFS algorithm (Pan and Wu, 2009) (see online version for colours) (a) (b) (c) (d)

12 A. Ladgham, A. Sakly and A. Mtibaa 5 Conclusion In this paper, we proposed a rapid method, called IMSFLA, for the automatic recognition of areas of several images such as SAR images. This approach simulates the behaviour of shuffled frogs seeking foods to develop the algorithm that search the adequate thresholds of images. The IMSFLA method has demonstrated its adaptability to converge rapidly and to give good qualities of recognition of thresholds of images. The results are promising and they encourage further researches for applying this algorithm in complex and real-time image analysis problems. References Alireza, R.V., Mostafa, D., Hamed, R. and Ehsan, S. (2008) A novel hybrid multi-objective shuffled frog-leaping algorithm for a bicriteria permutation flow shop scheduling problem, International Journal of Advanced Manufacturing Technology, Vol. 41, Nos. 11/12, pp Bhaduri, A. 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