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Pattern Recognition Letters 28 (2007) 788–796 www.elsevier.com/locate/patrec

Object segmentation using ant colony optimization algorithm and fuzzy entropy q
Wenbing Tao
b

a,b,*

, Hai Jin

a,b

, Liman Liu

c

a Cluster and Grid Computing Laboratory, School of Computer, Huazhong University of Science and Technology, Wuhan 430074, China Service Computing Technology and System Laboratory of Ministry of Education, Huazhong University of Science and Technology, Wuhan 430074, China c O2 Micro, Wuhan 430074, China

Received 8 December 2005; received in revised form 5 November 2006 Available online 19 January 2007 Communicated by Y.J. Zhang

Abstract In this paper, we investigate the performance of the fuzzy entropy approach when it is applied to the segmentation of infrared objects. Through a number of examples, the performance is compared with those using existing entropy-based object segmentation approaches and the superiority of the fuzzy entropy method is demonstrated. In addition, the ant colony optimization (ACO) is used to obtain the optimal parameters. The experiment results show that, compared with the genetic algorithm (GA), the implementation of the proposed fuzzy entropy method incorporating with the ACO provides improved search performance and requires significantly reduced computations. Therefore, it is suitable for real-time vision applications, such as automatic target recognition (ATR). Ó 2006 Elsevier B.V. All rights reserved.
Keywords: Infrared object segmentation; Ant colony optimization; Fuzzy entropy; Performance evaluation; Global thresholding

1. Introduction Image segmentation is one of the most important and most difficult low-level image analysis tasks. Automatic target recognition (ATR) often uses segmentation to separate the desired target from the background. Thresholding is one of the most popular segmentation approaches because of its simplicity. However, the automatic selection of a robust, optimum threshold that separates different objects or separates an object from background has remained a challenge. Excellent reviews on early thresholding methods can be found in (Sahoo et al., 1988; Pal and

The work was supported by the National Natural Science Foundation of China (Grant No. 60603024) and the National Science Foundation for Post-doctoral Scientists of China (Grant No. 2005037198). * Corresponding author. Tel.: +86 27 8754 1924; fax: +86 27 8755 7354. E-mail address: [email protected] (W. Tao). 0167-8655/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.patrec.2006.11.007

q

Pal, 1993), and the latest development in this topic is summarized in (Sezgin and Sankur, 2004). Of all the thresholding methods, entropy-based method is widely studied and is considered effective. Pun (1980, 1981) described a method that maximizes the upper bound of the posteriori entropy derived from the histogram. Kapur et al. (1985) proposed the selection of the optimum threshold by maximizing the sum of entropies of the segmented regions. Li and Lee (1993) and Li and Tam (1998) proposed to minimize the cross-entropy between the input gray-level image and the output binary image as indicative of preservation of information. Yen et al. (1995) defined the entropic correlation and obtain the threshold that maximizes it. Sahoo et al. (1997) determines the optimum threshold by maximizing the posteriori entropy subject to certain inequality constraints that characterize the uniformity and shape of the segmented regions. Brink’s method (1996) maximizes the sum of the entropies computed from two autocorrelation functions of the thresholded image histograms.

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Fuzzy sets play a significant role in many deployed systems because of their capability to model nonstatistical imprecision (Ebanks, 1983). A fuzzy entropy is a function on fuzzy sets that becomes smaller when the sharpness of its argument fuzzy set is improved. The notion of entropy, in the theory of fuzzy sets, was first introduced by Luca and Termini (1972). There have been numerous applications of fuzzy entropies in image segmentation. Cheng et al. (1998) proposed fuzzy homogeneity vectors to handle the grayness and spatial uncertainties among pixels, and to perform multilevel thresholding. Cheng et al. (2000) presented a thresholding approach by performing fuzzy partition on a two-dimensional histogram based on the fuzzy relation and the maximum fuzzy entropy principle. Shelokar et al. (2004) considered the fuzzy memberships as an indication of how strongly a gray value belongs to the background or to the foreground. The optimum threshold is found as the threshold that minimizes the sum of the fuzzy entropies. In (Cheng et al., 1999), Cheng and Chen defined a new approach to fuzzy entropy and implemented genetic algorithm to find the optimal combination of the fuzzy parameters. Zhao et al. (2001) presented an entropy function by the fuzzy c-partition (FP) and the probability partition (PP) which was used to measure the compatibility between the PP and the FP. By using a simple monotonic function to approximate the memberships of the bright, the dark and the medium, Zhao et al. derived a necessary condition for the entropy function to be maximized, i.e., pd = pm = pb = 1/3, and deduced an algorithm for threelevel thresholding. Based on the idea of Zhao et al., Tao et al. (2003) designed a new three-level thresholding method for image segmentation. A new fuzzy entropy through probability analysis, fuzzy partition and entropy theory is defined. The image is partitioned into three parts, namely the dark, the gray, and the white part, whose member functions of the fuzzy region are, respectively, Z-, P-, and S-functions. To obtain the optimal thresholds, Tao et al. utilized genetic algorithm to find the optimal combination of all the fuzzy parameters. In this paper, we examine the performance of the fuzzy entropy (Tao et al., 2003) for the segmentation of infrared objects. The performance is compared with the existing entropy-based object segmentation methods. To obtain the optimal threshold it is required to find the optimal combination of all the fuzzy parameters. Therefore, the segmentation problem can be formulated as an optimization problem. In addition, we use the ant colony optimization (ACO) method to effectively obtain the optimal combination of the fuzzy parameters. ACO is a branch of a larger field referred to as Swarm Intelligence (SI). SI is the property of a system whereby the collective behaviors of simple agents interacting locally with their environment cause coherent functional global patterns to emerge (Bonabeau et al., 1999). It is the behavioral simulation of social insects such as bees, ants, wasps and termites. This behavioral simulation came about for

many reasons—optimization of systems and learning about self-organization are two of many reasons why scientists are interested in simulating these insects. More specifically, ACO simulates the collective foraging habits of ants—ants venturing out for food, and bringing their discovered food back to the nest. Ants have poor vision and poor communication skills, and a single ant faces a poor probability of longevity. However, a large group, or swarm, of ants can collectively perform complex tasks with proven effectiveness, such as gathering food, sorting corpses or performing division of labor. They have been successfully applied to a large number of difficult combinatorial problems like the quadratic assignment (Maniezzo and Conlorni, 1999), communication strategies (Dorigo et al., 1996), the traveling salesman problems (Chu et al., 2004), productionsequencing problem (Patrick, 2001), feature selection (Jensen and Shen, 2005), and clustering (Shelokar et al., 2004). This paper investigates how ACO may be applied to the image segmentation based on fuzzy entropy. This paper is organized as follows. In Section 2, for the integrity of this paper, we simply describe the object segmentation method based on probability analysis and fuzzy entropy, which is similar to the method presented in (Tao et al., 2003). In Section 3, how to use ACO approach to find the optimal combination of all fuzzy parameters is presented. In Section 4, we evaluate the performance of the proposed thresholding approach using a wide variety of real images and compare it with leading techniques from the literature. Finally, Section 5 concludes this paper. 2. Maximum fuzzy entropy based on probability partition Let D = {(i, j) : i = 0, 1, . . . , M À 1; j = 0, 1, . . . , N À 1} and G = {0, 1, . . . , l À 1}, where M, N and l are three positive integers. Let I(x, y) be the gray level value of the image at the pixel (x, y) and Dk = {(x, y) : I(x, y) = k, (x, y) 2 D}, k = 0, 1, . . . , l À 1. Denote T as the threshold, which segments an image into the background and a target. In a gray levels image, the domain D of the original image is classified into two parts, Ed and Eb. Ed is composed of pixels with low gray levels and Eb is composed of pixels with high gray levels. P2 ¼ fEd ; Eb g is an unknown probabilistic partition of D, whose probability distribution is described as p d ¼ P ðE d Þ; pb ¼ P ðEb Þ ð 1Þ

We use the membership functions (see Fig. 1) to approximate the memberships of the dark ld and the bright lb of an image with 256 gray levels. The membership function have three parameters a, b and c. In other words, the threshold T depends on a, b and c, which are the parameters of the membership functions. For each k = 0, 1, . . . , 255, let Dkd ¼ fðx; y Þ : I ðx; y Þ 6 T ; ðx; y Þ 2 Dk g Dkb ¼ fðx; y Þ : I ðx; y Þ > T ; ðx; y Þ 2 Dk g then the following equations hold:

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Fig. 1. Membership function graph.

pkd ¼ P ðDkd Þ ¼ pk à pdjk pkb ¼ P ðDkb Þ ¼ pk à pbjk

ð2Þ

Then the total fuzzy entropy function is given as H ð a; b; c Þ ¼ H d þ H b ð 7Þ

It is clear that pdjk and pbjk are the conditional probability of a pixel that is classified into the class ‘d’ (dark) and ‘b’ (bright), respectively, under the condition that the pixel belongs to DK with pdjk + pbjk = 1 (k = 0, 1, . . . , 255). Let the grade of a pixel whose gray level value is k belonging to the class ‘d’ (dark) and ‘b’ (bright) be equal to its conditional probability pdjk, pbjk, respectively. Then the following equations hold: pd ¼ pb ¼
255 X k ¼0 255 X k ¼0

The total fuzzy entropy varies along with the three variables a, b, c. We can find a combination of a, b, c such that the total fuzzy entropy H(a, b, c) achieves the maximum value. Then the most appropriate threshold to segment the image into two classes can be computed as following: ld ðT Þ ¼ lb ðT Þ ¼ 0:5 ð 8Þ

pk à pdjk ¼ pk à pbjk ¼

255 X k ¼0 255 X k ¼0

pk à ld ðk Þ ð3Þ pk à lb ðk Þ

As is shown in Fig. 1, threshold T is the point of intersection of the ld(k) and lb(k) curve. Based on formulas (4) and (5), the solution can be given as following: ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a þ ðc À aÞ Ã ðb À aÞ=2 ða þ cÞ=2 6 b 6 c T ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c À ðc À aÞ Ã ðc À bÞ=2 a 6 b 6 ða þ cÞ=2

The two membership functions are shown in Fig. 1. We choose the Z(k, a, b, c)-function as the membership function ld(k) of the class ‘d’ (dark) and choose the S(k, a, b, c)-function as the membership function lb(k) of the class ‘‘b’’ (bright). The two membership functions are shown in the following: 8 1; k6a > > > 2 > > ð k À a Þ > > ; a<k6b <1 À ð c À aÞ Ã ð b À a Þ ð4Þ ld ðk Þ ¼ 2 > ðk À cÞ > > ; b<k6c > > > ð c À aÞ Ã ð c À bÞ > : k>c 8 0; 0; k6a > > > > > ðk À aÞ2 > > ; a<k6b < ð c À aÞ Ã ð b À aÞ lb ðk Þ ¼ ð5Þ 2 > ðk À c Þ > > 1 À ; b < k 6 c > > > ð c À aÞ Ã ð c À bÞ > : 1; k>c The three parameters a, b, c satisfy the condition 0 6 a 6 b 6 c 6 255. Each class fuzzy entropy function is given as following:   255 X pk à ld ðk Þ pk à ld ðk Þ Hd ¼ À à ln pd pd k ¼0 ð6Þ   255 X p à l ðk Þ pk à lb ðk Þ b k Hb ¼ À à ln pb pb k ¼0

3. Ant colony optimization approach SI provides a basis with which it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model. Those SI techniques that solve discrete optimization problems are based on the behavior of real ant colonies and are classified as ant colony optimization (ACO) techniques (Bonabeau et al., 1999). Ants are capable of finding the shortest route between a food source and their nest without the use of visual information and hence possess no global world model, adapting to changes in the environment. The key to such effectiveness is pheromone—a chemical substance deposited by ants as they travel. Pheromone provides ants with the ability to communicate with each other. Ants essentially move randomly, but when they encounter a pheromone trail, they decide whether or not to follow it. If they do so, they deposit their own pheromone on the trail, which reinforces the path. The probability that an ant chooses one path over another is governed by the amount of pheromone on the potential path of interest. Because of the pheromone, trails that are more frequently traveled by ants become more attractive alternative for other ants. Subsequently, less traveled paths become less likely paths for other ants. With time, the amount of pheromone on a path evaporates. Prior to the establishment of the most desirable pheromone trails, individual ants will use all potential paths in

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equal numbers, depositing pheromone as they travel. But the ants taking the shorter path will return to the nest first with food. The shorter pathway will have the most pheromone because the path has fresh pheromone and has not yet evaporated, and will be more attractive to those ants that return to the food source. There is, however, always a probability that an ant will not follow a well-marked pheromone trail. This probability (although small) allows for exploration of other trails, which is beneficial because it allows discovery of shorter or alternate pathways, or new sources of food. Given that the pheromone trail evaporates over time, the trail will become less detectable on longer trails, since these trails take more time to traverse. The longer trails will hence be less attractive, which benefit to the colony as a whole.

The entropy model presented before is essentially a function optimization problem: J ¼ max H ðxÞ; x ¼ ðx1 ; x2 ; . . . ; xn ÞT ; x & X

where H(x) is the optimized multidimensional function, x is the n-dimension solution vector, and X is the definition field. In this paper, we choose n = 3, that is, x = (a, b, c)T and 0 6 a 6 b 6 c 6 255, where T denotes transpose. We can use the ant colony algorithm to optimize the fuzzy entropy principle. We consider every possible solution x = (a, b, c)T as one ant and some ants are chosen randomly. The best ant which corresponds to the optimal solution of the fuzzy entropy function H(x) is marked.

Time begin

Choose the first ant k=1

Evaluate the ants’ value and record the best ant g

Evaluate ant value. If k(ant)<aver(ant), generate new ant k again. Else transit to ant j (1<=j<= K) according to the transition rule.

Begin Generate K ants no

Does the transition happen? yes In the neighborhood of ant j with a radius of r, randomly search the better ant to update ant j. Copy the ant j to the best ant g if j(ant>g(ant). Update ant k with ant j

Segment object by threshold T

Continue to choose the next ant k=k+1 Compute optimal threshold T by the best ant k>K Update Pheromone and neighbor radius r=0.9r

k<=K

Return the best ant g

yes

Time end ?

no

Fig. 2. ACO-based fuzzy entropy object segmentation overview.

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For every ant i, its evaluation function value is defined as the corresponding object function value Hi. The transition probability of an ant i choosing to travel to ant j at time t is denoted as following: ½sj ðtފa  ½DH ij Šb pij ðtÞ ¼ X a b ½sl ðtފ  ½DH lj Š l 2K ð9Þ

c 6 255. We can make some mathematical processing to solve it. The results obtained from b1 ¼ b c1 ¼ b1 þ ð255 À b1 Þ Ã ðc=255Þ a1 ¼ b1 Ã ða=255Þ Satisfy 0 6 a1 6 b1 6 c1 6 255. Therefore, we can evaluate the ant value based on a1, b1, and c1. 4. Experimental results A set of images was used to evaluate the performance of the proposed algorithm as well as some of the commonly used algorithms presented in the literature. To make the performance evaluation and comparison meaningful and effective, most of our test images are real images. Each image includes distinct object and the background, and the object can be exactly distinguished from the background by some suitable threshold. Especially, some infrared object images are selected to examine our algorithm for the reason that infrared sensors have good night vision performance and are widely applied in automatic target recognition (ATR). Infrared images reflect the thermal radiations of the targets and the background, and the objects can be distinguished by their gray levels. In this section, we present some contrastive experimental results, including illustrative examples and performance evaluating tables, which clearly demonstrate the advantages of the proposed method. To make purposeful yet effective comparisons, the selected thresholding methods for comparison are all entropy-based thresholding methods. They are Pun entropy method (Pun, 1980), Kapur entropy method (Kapur et al., 1985), Li entropy method (Li and Tam, 1998), Yen entropy method (Yen et al., 1995), Sahoo entropy method (Sahoo et al., 1997), Shanbag fuzzy entropy method (1994), and Cheng fuzzy entropy method ´ ndez-Garcı ´a et al., 2004), (Cheng et al., 1999). In (Ferna several empirical measures are presented to evaluate color edge detectors. In our paper, our primary interest is the integrality and the accuracy of object segmentation. Therefore, we use the absolute error ratio as the main comparison criterion. The absolute error ratio is defined as the ratio between the absolute error, ndiff, and the total number of pixels, N, of an image, i.e., ndiff rerr ¼ Â 100% ð12Þ N The absolute error ndiff is defined as the absolute difference in the number of object pixels between the optimally thresholding image and the thresholding image obtained by each method. The optimally thresholding image and the corresponding threshold value are manually obtained using visual inspection. The experimental results of five examples are shown in Figs. 3–7. Each figure shows the original gray-level image, ð11Þ

where K is the number of ants, sj(t) is the amount of virtual pheromone at time t and DHij = Hj À Hi is the heuristic desirability for ant i to choose ant j. The choice of parameters a and b are determined experimentally. Their values are chosen in range [0, 1] and are evaluated by experiments. In this paper, we set both a and b to 1. Depending on the definition of the optimality for the particular application, the pheromone may be updated accordingly. In our application, the amount of pheromone of ant j increases when another ant travels to it and decreases with time. The pheromone is updated according to the following formula: sj ðt þ 1Þ ¼ ð1 À qÞ Á sj ðtÞ þ Dsj ðtÞ ð10Þ

where Dsj(t) = sj(0) = 1 if the ant j has been traversed, and Dsj(t) = 0 otherwise. The value of q is a decay constant used to simulate the evaporation of the pheromone with time. The overall process of the ACO fuzzy entropy approach can be summarized in Fig. 2, where k(ant) denotes the value of the fitness function of ant k and aver(ant) denotes the average value of the fitness function of all generated ants. It begins by generating a number of ants randomly. Every ant is a possible solution x = (a, b, c)T and 0 6 a 6 b 6 c 6 255. We use Eq. (7) to evaluate these ants and record the best ant. The outer circulation is time and the inner circulation is the number of the generated ants. For every ant k, first decide if transit to another ant j according to the transition rule, and if the transition happen then perform neighborhood random search m (in this paper m = 5) time so as to find the better ant to update ant j. After that, update ant k with ant j. Lastly, update pheromone and neighbor radius after inner circulation ends. Return the best ant after time ends. The time complexity of the ant-based fuzzy entropy algorithm is O(HKR), where H is the time, K is the number of ants and R is the radius of the neighborhood random search. After all ants’ iteration finish, the process halts and outputs the best ant encountered. The three parameters H, N and R decide not only the time complexity of the algorithm, but also the accuracy of the solution. Obviously, larger values of parameters H, N and R lead to more accurate solution, but require higher computations. Therefore, we should choose suitable values of parameters H, N and R to tradeoff the accuracy of the solution and the computation efficiency. The parameters are related to the specific applications and are usually decided by experiments. Notice that it is possible that the randomly generated ants do not follow the increasing order 0 6 a 6 b 6

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Fig. 3. Top row, from left to right: original ship image (182 · 253), manually thresholding image (T = 201), thresholding result by the proposed method (T = 211), results by Kapur method (T = 148), results by Li method (T = 101). Bottom row, from left to right: results by Pun method (T = 106), Sahoo method (T = 148), Yen method (T = 155), Cheng method (T = 172), Shanbag method (T = 140).

Fig. 4. Top row, from left to right: original tank image (148 · 106), manually thresholding image (T = 175), thresholding result by the proposed method (T = 182), results by Kapur method (T = 140), results by Li method (T = 61). Bottom row, from left to right: results by Pun method (T = 49), Sahoo method (T = 134), Yen method (T = 141), Cheng method (T = 138), Shanbag method (T = 151).

Fig. 5. Top row, from left to right: original air plane1 image (200 · 150), manually thresholding image (T = 163), thresholding result by the proposed method (T = 162), Kapur method (T = 144), and Li method (T = 101). Bottom row, from left to right: results by Pun method (T = 120), Sahoo method (T = 139), Yen method (T = 147), Cheng method (T = 185), Shanbag method (T = 174).

the optimally thresholding image, the thresholding images using the proposed as well as other methods used in the comparison. The images used for comparison include an

offing infrared image with one ship object (Fig. 3), a ground infrared image with one tank object (Fig. 4), an air infrared image with a small plane objects (Figs. 5

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Fig. 6. Top row, from left to right: original person image (320 · 210), manually thresholding image (T = 167), thresholding result by the proposed method (T = 157), Kapur method (T = 124), and Li method (T = 49). Bottom row, from left to right: results by Pun method (T = 59), Sahoo method (T = 122), Yen method (T = 122), Cheng method (T = 138), Shanbag method (T = 117).

Fig. 7. Top row, from left to right: original air plane2 image (200 · 150), manually thresholding image (T = 186), thresholding result by the proposed method (T = 178), Kapur method (T = 116), and Li method (T = 101). Bottom row, from left to right: results by Pun method (T = 84), Sahoo method (T = 112), Yen method (T = 119), Cheng method (T = 162), Shanbag method (T = 119).

and 7), and a night infrared image with a person (Fig. 6). The deviations from the optimum threshold value are shown in Table 1 for different algorithms. It is evident from Figs. 3–7 and Table 1 that the proposed algorithm provides better segmentation performance than the other techniques. The values of the absolute error for different algo-

rithms are compared in Table 2. Note that in all the four examples, the proposed algorithm can effectively extract the infrared object from the background and the performance is close to the optimum one obtained by manual thresholding. The experiment results show that the proposed method provides the best thresholding performance

Table 1 Comparison of threshold values and error ratio (%) for the images shown in Figs. 3–7 Figure Ref. value T0 Ship Tank Plane1 Person Plane2 201 175 163 167 186 Thresholding algorithms Kapur T 148 140 144 124 116 Error 3.85 0.82 0.09 3.07 33.7 Li T 101 61 101 49 101 Error 64.74 43.84 98.27 61.03 50 Pun T 106 49 120 59 84 Error 59.5 59.28 67.46 53.31 67.73 Sahoo T 148 134 139 122 112 Error 3.85 1.25 0.19 3.57 38.2 Yen T 155 141 147 122 119 Error 2.82 0.76 0.09 3.57 33.7 Cheng T 172 138 185 138 162 Error 1.27 0.99 0.13 1.05 4.28 Shanbag T 140 151 174 117 119 Error 5.55 0.38 0.02 5.1 33.7 Proposed T 211 182 162 157 178 Error 0.21 0.09 0.02 0.26 0.03

Table 2 Comparison of object error pixels for the images shown in Figs. 3–7 Figure Ship Tank Plane1 Person Plane2 Size of images 182 · 253 148 · 106 200 · 150 320 · 210 200 · 150 Ref. ob. pixels 497 181 60 3110 11 Kapur 1773 128 28 2065 10 120 Li 29 810 6878 29 480 41 011 14 998 Pun 27 391 9300 20 239 35 824 19 120 Sahoo 1773 196 57 2401 11 467 Yen 1300 119 28 2401 10 120 Cheng 585 155 39 708 1284 Shanbag 2556 60 7 3429 10 120 Proposed 94 14 5 177 10

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among all the methods being compared. Fig. 8 shows the membership function curves of the three images. The respective point of intersection of ld-curve and lb-curve is the optimal threshold T. In the implementation of the proposed fuzzy entropy segmentation method based on ACO, the following para-

meters are used: total time T = 20, number of the ants K = 20, neighbor initial radius R = 10, and decay constant q = 0.2. The execution time of segmenting an image is about 30 ms when a Pentium PC of 1.7 GHz CPU is used. However, when the proposed fuzzy entropy method by the genetic algorithm (GA) is used, the corresponding

Fig. 8. (a) The membership function curves of the ship image with a = 108, b = 254, c = 255 and maximal fuzzy entropy H = 9.1889. (b) The membership function curves of the tank image with a = 7, b = 252, c = 255 and maximal fuzzy entropy H = 9.7837. (c) The membership function curves of the plane image with a = 129, b = 150, c = 218 and maximal fuzzy entropy H = 5.3679. (d) The membership function curves of the person image with a = 4, b = 198, c = 252 and maximal fuzzy entropy H = 9.8101. (e) The membership function curves of the plane image with a = 12, b = 247, c = 255 and maximal fuzzy entropy H = 7.2667.

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execution times to get the same performance takes more than 260 ms. The following parameters are used for the GA: MaxGen (maximal generation number) = 100, PoPs (population size) = 50, Pc (probability of cross-over) = 0.8, and Pm (probability of mutation) = 0.01. Therefore, using ACO to implement fuzzy entropy optimization is much more effective than using GA. 5. Conclusion The automatic selection of a robust, optimum threshold to separate different objects, or to separate an object from the background, has remained a challenge in image segmentation. Entropy-based method is a wide-studied and effective category thresholding strategy. Fuzzy entropy is a function on fuzzy sets that becomes smaller when the sharpness of its argument fuzzy set is improved. In recent years, there have been numerous applications of fuzzy entropies in image segmentation. In this paper, we have investigated the infrared object segmentation performance of the fuzzy entropy principle proposed in (Tao et al., 2003), which has been proved to be the extension of KSW entropy (Kapur et al., 1985). Therefore, we compare the proposed fuzzy entropy segmentation method with the present typical object segmentation approaches based on entropy or fuzzy entropy principle, including KSW entropy. The results of the performance evaluation using a number of examples show that the proposed fuzzy entropy segmentation method provides best segmentation performance among all compared entropy-based thresholding method. Additionally, we have designed an ant colony optimization (ACO) strategy to find the optimal combination of all the parameters. The experiment results show that the implementation of the proposed fuzzy entropy principle by ACO has more highly effective search performance than genetic algorithm (GA) and therefore, is suitable for real-time vision applications, such as automatic target recognition. References
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