USE OF DARWINIAN PARTICLE SWARM OPTIMIZATION TECHNIQUE FOR THE SEGMENTATION OF REMOTE SENSING IMAGES

Pedram Ghamisi, Micael S. Couceiro, Nuno M. F. Ferreira, Lalit Kumar

Geodesy & Geomatics Engineering Faculty, K. N. Toosi University of Technology, Tehran, Iran,

Institute of Systems and Robotics, University of Coimbra, Pólo II, Coimbra, Portugal Robo Corp, Electrical Engineering Department, Engineering Institute of Coimbra, Coimbra, Portugal

GECAD - Knowledge Engineering and Decision Support Research Center Ecosystem Management, School of Environmental and Rural Science, University of New England, Armidale

NSW 2351, Australia p.ghamisi@gmail.com; micaelcouceiro@isr.uc.pt; nunomig@isec.pt; lkumar@une.edu.au

Abstract—In this work, a novel method for segmentation of Remote Sensing (RS) images based on the Darwinian Particle Swarm Optimization (DPSO) for determining the n-1 optimal n-level threshold on a given image is proposed. The efficiency of the proposed method is compared with the Particle Swarm Optimization (PSO) based segmentation method. Results show that DPSO-based image segmentation performs better than PSO-based method in a number of different measures.

Keywords—multilevel segmentation, swarm optimization, remote sensing.

1. INTRODUCTION SEGMENTATION refers to the process of partitioning a digital image into multiple objects. In other words, image segmentation could assign a label to each pixel in the image such that pixels with the same label share certain visual characteristics. These objects are more meaningful than individual pixels as interpretation of images based on objects is more meaningful than that based on individual pixels. Image segmentation plays an important role in the analysis and understanding of images, thus being widely used for further image processing purposes such as classification and object recognition [1]. Several algorithms have so far been proposed in literatures that have addressed the issue of optimal thresholding such as ([2], [3]). One way for finding the optimal set of thresholds is the exhaustive search method. The exhaustive search method based on the Otsu criterion is simple, but it has a disadvantage that it is computationally expensive. Exhaustive search for optimal thresholds involves evaluations of fitness of combinations of thresholds [6] so this method is not suitable from a computational cost point of view. The task of determining

optimal thresholds for -level image thresholding could be formulated as a multidimensional optimization problem. Alternatively to the Otsu method, several biologically inspired algorithms have been explored in image segmentation such as [1] and [4]. The computational

time is one of the most important indicators along with fitness value which determine the ability of the algorithm. Provided that the data is large, the efficiency of the method is restricted to a great extent. RS data, in particular hyperspectral images, are considerably large most of the time so using a high speed and efficient algorithm is highly preferable. Moreover, in real-time applications, using a high speed algorithm is the main objective [8]. In [8], PSO has been shown to be significantly faster than bacterial foraging algorithm (BFA) and exhaustive methods. In this paper, a novel method for segmentation of remote sensing (RS) images based on DPSO is proposed. DPSO was introduced by Tillett et al. [6] for optimization of some primary test functions. We extended the concept of DPSO to RS image segmentation. It should be noted that this method is used for the first time in the field of RS. Therefore, the DPSO will be used to solve the Otsu problem for delineating multilevel threshold values. Further, for showing advantages of the new method, we compare the traditional PSO- with the DPSO-based segmentation method to determine the n-1 optimal n-level threshold on a given image.

2. PROBLEM FORMULATION

Multilevel segmentation techniques provide an efficient way to perform image analysis. However, the automatic selection of a robust optimum n-level threshold has remained a challenge in image segmentation. This section presents a more precise formulation of the problem introducing some basic notation. Let there be L intensity levels in each RGB component of a given image and these levels are in the range {0, 1, 2, …,L-1}. Then one can define:

, (1)

Where i represents a specific intensity level, i.e., 0 ≤ i ≤ L-1, C represents the component of the image, i.e.,

, N represents the total number of pixels in the

4295978-1-4673-1159-5/12/$31.00 ©2012 IEEE IGARSS 2012

image and denotes the number of pixels for the corresponding intensity level i in the component C. In other words, represents an image histogram for each component C, which can be normalized and regarded as the probability distribution . The total mean (i.e., combined mean) of each component of the image can be easily calculated as:

. (2)

Image thresholding (2-level) is the simplest and commonly used method of image segmentation that deals with determining a value of threshold (one threshold for each RGB component) to perform the operation expressed by:

, (3)

Where x and y are the width ( ) and height ( ) pixel of the image of size denoted by .This methodology enables to dichotomize the pixels of a given image into two classes and , which may represent the background and an object respectively, using a threshold level . The class contains allpixels having intensities less than or equal to , and the class contains all pixels having intensities greater than . The probabilities of occurrence of classes and are given by:

, (4)

. (5)

The mean of each class can be respectively calculated as:

, (6)

. (7)

The simplest and computationally more efficient method of obtaining the optimal threshold is the one that maximizes the between-class variance defined by:

. (8)

In other words, the problem of 2-level thresholding is reduced to an optimization problem to search for the thresholds thatmaximizes the three objective functions (i.e., fitness function) of each RGB component generally defined as:

. (9)

The 2-level thresholding can be extended to generic -level thresholding in which threshold levels are necessary in whichthe operation is performed as expressed in thefollowing equation:

. (10)

In this situation, the pixels of a given image will be divided into classes ,…, , which may represent multiple objects or even specific features on such objects (e.g., topological features).The between-class variance can be generally defined as:

, (11)

where represents a specific class in such a way that and are the probability of occurrence and mean of class ,

respectively.Once again, and just like in the 2-level threshold case, the objective function is the same as presented in equation (9) but should be rewritten as:

. (12)

Computing this optimization problem involves an increasingly computational effort as the number of threshold levels increase. This brings us to the following question: which kind of method should we use to solve this optimization problem for real-time applications? Many methods have been proposed in literature [5]. However, more recently, biologically inspired methods have been used as computationally efficient alternatives to analytical methods to solve optimization problems [8, 9]. Following section presents the methods used and compared in this work to solve the optimization problem defined in (12).

3. METHODOLOGY

3.1. Particle Swarm Optimization

The original PSO was developed by Eberhart and Kennedy in 1995 [7] in which candidate solutions are called particles. In each step of the algorithm, a fitness function is used to evaluate the particle success. To model the swarm, each particle moves in a multidimensional space according to position ( ) and velocity ( ) values which are highly dependent on local best ( ), neighborhood best ( ) and global best ( ) information:

, (13)

. (14)

The coefficients , and assign weights to the inertial influence, the global best and the local best when determining the new velocity, respectively. and are constant integer values, which represent “cognitive” and “social” components. The parameters and are random vectors with each component generally a uniform random number between 0 and 1. The intent is to multiply a new random component per velocity dimension, rather than multiplying the same component with each particle’s

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velocity dimension. The particles in the PSO are evaluated for the fitness function, which is defined as the between-class variance of the image-intensity distributionspreviously represented in equation 12 (section 3). In the beginning, the particles’ velocities are set to zero and their position is randomly set within the boundaries of the search space. To our specific situation the search space will depend on the number of intensity levels L, i.e., if the frames are 8-bit images then the particles will be deployed between 0 and 255.

3.2. Darwinian Particle Swarm Optimization

In search of a better model of natural selection using the PSO algorithm, the Darwinian Particle Swarm Optimization (DPSO) was formulated by Tillet et al [6], in which many swarms of test solutions may exist at any time. Each swarm individually performs just like an ordinary PSO algorithm in which natural selection (darwinian principle of survival of the fittest) is used to enhance the ability to escape from local optima. When a search tends to a local optimum, the search in that area is simply discarded and another area is searched instead. In this approach, at each step, swarms that get better are rewarded (extend particle life or spawn a new descendent) and swarms which stagnate are punished (reduce swarm life or delete particles). To analyze the general state of each swarm, the fitness of all particles is evaluated and the neighborhood and individual best positions of each of the particles are updated. If a new global solution is found, a new particle is spawned. A particle is deleted if the swarm fails to find a fitter state in a defined number of steps (Table 1).

Some simple rules are followed to delete a swarm, delete particles, and spawn a new swarm and a new particle: i) when the swarm population falls below a minimum bound, the swarm is deleted; and ii) the worst performing particle in the swarm is deleted when a maximum threshold number of steps (search counter ) without improving the fitness function is reached. After the deletion of the particle, instead of being set to zero, the counter is reseted to a value approaching the threshold number, according to:

. (15)

With being the number of particles deleted from the swarm over a period in which there was no improvement in fitness. To spawn a new swarm, a swarm must not have any particle ever deleted and the maximum number of swarms must not be exceeded. Still, the new swarm is only created with a probability of p = f / NS, with f a random number in [0,1] and NS the number of swarms. This factor avoids the creation of newer swarms when there are large numbers of swarms in existence. The parent swarm is unaffected and half of the parent's particles are selected at random for the child swarm and half of the particles of a random member of the swarm collection are also selected. If the swarm initial population number is not obtained, the rest of the particles are randomly initialized and added to the new swarm. A particle is spawned whenever a swarm achieves a new

global best and the maximum defined population of a swarm has not been reached.

Table 1: DPSO Algorithm Main Program Loop For each swarm in the collection

Evolve the swarm � Allow the swarm to spawn Delete “failed” swarms

Evolve Swarm Algorithm For each particle in the swarm

Update Particles’ Fitness Update Particles’ Best Move Particle If swarm gets better

Reward swarm: spawn particle: extend swarm life

If swarm has not improved Punish swarm: possibly delete particle: reduce swarm life

Like the PSO, a few parameters also need to be adjusted to run the algorithm efficiently: i) initial swarm population; ii) maximum and minimum swarm population; iii) initial number of swarms; iv) maximum and minimum number of swarms; and v) stagnancy threshold. In estimation problems previously studied in [7] and robotic exploration strategies developed in [14] the DPSO has been successfully compared with the PSO showing a superior performance. Therefore, next section presents the results obtained using the both PSO and DPSO that will be compared and discussed.

4. EXPERIMENTAL RESULTS PSO- and DPSO-based image segmentation which proposed in this paper was programmed in MatLab on a computer having Intel Core 2 Duo T5800 processor (2.00 GHz) and 3GB of memory.

Fig.1: Our test case study site

Our dataset was an 8km x 8km Worldview satellite image consisting of 8 bands. The pixel size was 2.4m x 2.4m. The image covered large sections of pine plantations, interspersed with native vegetation, grasslands, logged areas, barren soil and roads. This introduced a high level of natural variability to the segmentation problem. Unlike artificial objects, natural vegetation has multiple levels of variation. For example, within the pine plantation class, there are age differences, differences in reflectance due to slope, aspect and sun position, soil types, etc., and all these cause added complexities in the segmentation scheme. In this data set, bands 7, 5 and 3 are used for showing R, G, and B components respectively. Figure 1 shows our data. Table 2 depicts the initial parameters of DPSO and PSO.

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Table 2: Initial parameters of the DPSO and PSO

Parameter PSO DPSO Num of Iterations 150 150

Population 100 30 1 0.8 0.8 2 0.8 0.8

W 1.2 1.2 Vmax 4 1.5 Vmin -4 -1.5 Xmax 255 255 Xmin 0 0

Min Population - 10 Max Population - 50 Num of Swarms - 4

Min Swarms - 2 Max Swarms - 6

Stagnancy - 10

The CPU process time of each algorithm for 7-, 8- and 9-level thresholding was calculated as the average value of 20 different runs and being presented in Table 3. PSO is referred to as the fast optimization algorithm. However, as can be seen from Table 3, the computation time for PSO-based segmentation is significantly higher than the DPSO method. This happens since the PSO has a fixed population of 100 particles which, in other words, means 100 different solutions that need to be evaluated within the same swarm. The DPSO, on the other hand, is composed of multiple smaller swarms (between 2 and 6 swarms of 10 and 50 particles each), being faster than the PSO even with an equal or larger number of particles in the whole DPSO.

Table 3: CPU process time of each algorithm for different levels

Table 4 shows the optimal thresholds and corresponding fitness values (between-class variance) for each level of segmentation. Both fitness values and optimal threshold values were calculated for R, G, and B components separately. DPSO performs slightly better than PSO in terms of fitness value. It gives a better fitness because the PSO may get stuck in the vicinities of the global solution while the DPSO uses natural selection in order to avoid stagnation. It can be concluded that the DPSO is able to find better thresholds in less CPU time. Despite the minor differences between DPSO and PSO fitness values, i.e., the between-class variance, one should note that the DPSO-based thresholding is able to reach a slightly better solution significantly faster than the PSO. Consequently, we highly recommended using the proposed method for image segmentation, especially for more complex images.

5. CONCLUSION This paper proposed a new method for segmentation of RS Images which was based on Darwinian Particle Swarm Optimization. The new method was used for solving the Otsu problem for delineating multilevel threshold values and to overcome the disadvantages of PSO based methods. In this test case, the performance of DPSO and traditional PSO was compared using variables such as CPU time, optimal threshold value and corresponding fitness. Results indicate that DPSO is more efficient than PSO and has higher potential for finding the optimal set of thresholds with better fitness value in less CPU computation time than the PSO based method. It should be noted that in this paper, the concept of DPSO is being used in RS for the first time.

6. REFERENCES

[1] D. B. Fogel, “Evolutionary computation: Toward a new philosophy of machine intelligence, Second edition, Piscataway, NJ: IEEE Press, 2000. [2] A.D. Brink, “Minimum spatial entropy threshold selection”, IEE Proceedings on Vision Image and Signal Processing 142 (1995), 128-132. [3] N. Otsu, A threshold selection method from gray-level histograms. IEEE Trans. on Systems, Man, Cybernet, SMC-9, 62–66, 1979 [4] Y. Kao, E. Zahara,“ A hybridized approach to data clustering,” Expert Systems with Applications 34 (2008), 1754-1762. [5] M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” J. Electron.Imag., vol. 13, no. 1, pp. 146–168, Jan. 2004. [6] J. Tillett, T. M. Rao, F. Sahin, R. Rao, and S. Brockport, "Darwinian Particle Swarm Optimization," Proceedings of the 2nd Indian International Conference on Artificial Intelligence, pp. 1474-1487, 2005. [7] J. Kennedy and R. Eberhart, "A new optimizer using particle swarm theory," Proceedings of the IEEE Sixth International Symposium on Micro Machine, pp. 39-43, 1995. [8] R. V. Kulkarni, G. K. Venayagamoorthy. Bio-inspired Algorithms for Autonomous Deployment and Localization of Sensor Nodes, SMC-C(40), No. 6, pp. 663-675, November, 2010.

ACKNOWLEDGMENTS This work was supported by a PhD scholarship (SFRH/BD/73382/2010), by National Funds under the project: FCOMP-01-0124-FEDER-PEst-OE/EEI/UI0760/2011 both of the Portuguese Foundation for Science and Technology (FCT) and by FEDER Funds through the “Programa Operacional Factores de Competitividade - COMPETE” program.

Table 4: Fitness values and corresponding thresholds for R, G and B componentsLevel DPSO PSO DPSO PSO

7 4580.755373931023 3444.748953936530 3484.070584398548

4580.729185363865 3444.748953936530 3483.819662417987

28 65 99 134 171 214 24 46 72 111 159 213 31 61 88 120 160 213

28 64 98 133 170 214 24 46 72 111 159 213 27 55 84 117 160 212

8 4.608.810312490109 3.465.587793003639 3509.514760247274

4.608.733393981357 3.465.587793003639 3509.464498253156

24 56 86 116 148 182 220 20 39 62 91 127 171 218 23 51 77 104 135 174 219

24 55 85 115 146 180 220 20 39 61 91 127 171 219 24 50 78 104 135 174 219

9 4627.882493683985 3479.709454560466 3526.712254100473

4627.835589271379 3479.570796628618 3526.737869446567

21 49 76 102 128 157 188 225 17 36 53 75 105 141 182 226 20 44 68 91 116 144 181 224

19 48 75 101 128 156 187 223 17 35 53 72 101 137 179 222 20 44 66 87 112 141 178 222

Level DPSO PSO 7 19.83 24.78 8 22.46 28.03 9 25.36 31.25

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