Journal of Information & Computational Science 11:16 (2014) 5895–5903 Available at http://www.joics.com November 1, 2014 An Image Retrieval Algorithm Based on Improved Electromagnetism-like Mechanism Jianguo Jiang ∗, Juan Wang, Mingxiang Zang, Wenhong Zhou School of Electronic Engineering, Xidian University, Xi’an 710071, China Abstract In view of the advantages, such as the simplicity for understanding and high convergence rate of Electromagnetism-like Mechanism (EM) algorithm, an image retrieval algorithm based on improved EM is proposed in this paper. The novel algorithm assigns distinct weights to each block of the image, which represents the extent of human eyes’ preference to different areas when recognizing this image. The Chaos Search (CS) is used in local search in order to prevent the retrieval process from falling into a local optimum leading to a premature convergence. A genetic coefficient is added to the updating formula so that the particles are more likely to move into other feasible regions. The experimental results demonstrate that the improved EM algorithm can figure out the best matching image rapidly and accurately. Keywords: Electromagnetism-like Mechanism; Image Retrieval; Chaos Search; Global Optimization 1 Introduction Electromagnetism-like Mechanism (EM) algorithm [1, 2] is a new heuristic global optimization algorithm proposed by Birbil and Fang in 2003. The idea evolved from the attraction and elimination mechanism between the charged particles. This algorithm itself is very simple while in the same time it requires few resources but can converge to the optimal in a high rate. In recent years, EM algorithm has become a hot research topic for solving global optimization problems. With the rapid development of multimedia and Internet technology, the management of large amounts of images and image retrieval are becoming increasingly important. Conventional marking method [4, 5] has been unable to meet people’s desire. More and more researches pay their attentions on how to retrieve image quickly by visual features of image. In recent years, a lot of novel optimization algorithms are applied to image retrieval. Xu Li [6] proposed a image retrieval relevance feedback algorithm based on particle swarm optimization. In this method, initial results are generated randomly by using particle swarm algorithm, then particle swarm optimization evolutionary search process is combined with feedback, finally particle swarm algorithm runs repeatedly to achieve the purpose of retrieving target image by modifying the parameters based on ∗ Corresponding author. Email address: [email protected] (Jianguo Jiang). 1548–7741 / Copyright © 2014 Binary Information Press DOI: 10.12733/jics20104901 5896 J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 feedback result. However, the single feature and complex computation process of this algorithm resulting in low efficiency and accuracy. Shicai Yu [7] proposed an image retrieval method by using genetic algorithm and adjusting feature weight. This method uses group search technology, and adjusts the weight of new populations constantly. This method can improve the retrieval accuracy to some extent, but it is still not very satisfactory. At present, EM algorithm has not been applied to image retrieval, so in this paper, EM algorithm will be improved and applied to image retrieval. EM algorithm has the feature of leading search particles to local optimum of feasible regions which meets the need of image retrieval. The high convergence rate improves the probability of successfully retrieving the target image with high retrieval efficiency. EM algorithm can effectively avoid getting to premature local optimum which can make the search adaptively adjust the direction targeting the optimal soon. 2 2.1 Image Retrieval and Improved EM Algorithm Image Retrieval The central problem of image retrieval is to find the images relevant to that submitted by the user from the image library. Traditional image retrieval methods rely on artificial text annotation of the images. This method has disadvantages of strong subjectivity and time-consuming. Therefore, content-based image retrieval technology [4] emerges, which mainly considers the characteristics of image. The features [8] of an image are a description of some content of image and understanding by image retrieval systems. It largely determines the capabilities of retrieval systems. Broadly, the features of an image include text features and visual features. Text features include keywords and tagging, while visual features include color, texture, shape and spatial relationships. Color features are selected as retrieval features because color features computation are simple and color features are the most sensitive for human eyes when observing images. 2.2 Improved EM Algorithm EM is a heuristic global optimization algorithm which uses stochastic search. It generates an initial solution (i.e. the initial population) from feasible regions, and then imitates the attraction and elimination mechanism between the charged particles. The charge of particles and the search scope are determined according to objective function value of each solution. EM algorithm regards each solution as a charged particle, and then generates next populations on the basis of the update rules of the algorithm until the solution meets termination condition defined by users. EM algorithm mainly research unconstrained optimization problems, namely to find the optimal value of a real-valued function, the mathematical model is: { min f (x) (1) s.t. x ∈ [l, u] where f (x) is the objective function, [l, u] = {x ∈ Rn |lk ≤ xk ≤ uk , k = 1, 2, · · · , n}. J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 5897 But classical EM algorithm uses stochastic linear search [10, 11] in local search stage. It results in that the search process can easily fall into local optimum, and the particles’ moving step length is determined without considering the effects of particles’ merits and evolution algebra. Therefore, an improved algorithm named hybrid Chaos search Electromagnetism-like Mechanism algorithm (CEM) will be proposed in this paper. Hybrid chaos search is used in local search to avoid premature convergence. Then good point set [12] is used to generate initial population. And genetic variation coefficient is added to particle’s update formula so that the particles are more likely to move into the other feasible regions. 3 Image Retrieval Algorithm In applying the CEM algorithm to image retrieval, each image in the library is mapped to a particle of CEM algorithm. Each image’s feature vector is extracted and used to calculate the similarity (i.e. the value of objective function) to the target image. CEM algorithm finally outputs the particle with best objective function value. 3.1 Objective Function Construction Since color features are simple, they are selected to be used in CEM for image retrieval. As RGB color model aims hardware while HSV color model users, HSV color model is taken in order to reflect people’s understanding of images. Therefore, RGB color model has to be firstly converted to HSV color model [13, 14]. Assuming the resolution of image P is m × n, so the size of RGB vector is m × n × 3. If these data is considered as feature, a problem appears that feature dimension is too large and not identical. In order to solve this problem, the new method proposed in this paper preprocesses images first. The specific process is that each image with m × n resolution is divided into l × l blocks and each block contains ml × nl pixels. The blocking equation is as following: (i+1)× m l ∑ C(i, j) = (j+1)× n l ∑ i′ =i× m +1 j ′ =j× n +1 l l m l × n l C(i′ , j ′ ) (2) where i, j ∈ (1, 2, · · · , l), i′ ∈ (1, 2, · · · , m), j ′ ∈ (1, 2, · · · , n), C(i′ , j ′ ) represents h, s, v in point (i′ , j ′ ), C(i, j) represents the average h, s, v in block (i, j) after blocking. l is 4 in the experiments in this paper, so feature vector size of image P is 4 × 4 × 3, namely 48. Taking the different importance degrees when people observe different regions into account, the weight coefficients for different regions are designed. Each image is divided into 4 × 4 block, weight coefficients of the regions are shown in Table 1. As can be seen from Table 1, the more close the block is to the center, the larger weight coefficient it gets. It reflects that people pay more attention to center region when they observe objects; thereby the retrieval accuracy is enhanced. The particle in CEM algorithm is encoded with vector h, s, v in image P . The encoding equation follows: x12i+3j−15+r = Cr (i, j) × w(i, j) (3) 5898 J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 Table 1: Weight coefficients for each block 0.02 0.04 0.04 0.02 0.04 0.15 0.15 0.04 0.04 0.15 0.15 0.04 0.02 0.04 0.04 0.02 where i, j ∈ {1, 2, 3, 4}, r ∈ {1, 2, 3}, x12i+3j−15+r represents the independent variable in dimension 12i + 3j − 15 + r of the particle. When r is 1, 2 or 3, Cr (i, j) represents C(i, j) of h, s, v vector respectively. Image retrieval is to figure out the image most similar to the target from the library. Euclidean distance [15] is used to evaluate the similarity between two images, which is also being used to define the objective function. The equation is as: v u 48 u∑ f (x) = t (xi − xi∗ )2 (4) i=1 where xi∗ is dimension i of the particle that corresponds to the target image, while xi is dimension i of the particle that corresponds to be retrieved. Large f (x) means low similarity, therefore f (x) is computed as the target function of CEM. 3.2 3.2.1 Image Retrieval Process Initialization Good point set is used to generate m points {x1 , x2 , · · · , xm } as initial population from feasible region, where xi = {x1i , x2i , · · · , xni }(i = 1, 2, · · · , m), n is the number of dimensions of the problem which is set to 48 in this paper. Then the f (x) value of each particle is computed, the particle with the greatest f (x) is marked as xbest . 3.2.2 Chaos Local Search When EM algorithm is used to retrieve image, the search process of this algorithm is simple neighborhood linear search. The search range is small and the search step is constant which resulting in that the retrieval process will easily fall into local optima, thereby the retrieval speed and effect is affected. Since the ergodicity of the chaos can prevent search process falling into local optima, it is used in local search process of image retrieval. The basic idea of chaos is to introduce chaos status to optimization variable by using mapping model Logistic, and to enlarge the traversing range of chaos to the range of optimization variable, then search the optimal particle with chaos variable. The entire solution space will be inspected with ergodic track. When the termination condition is meet, the best status searched is close to the optimal solution to the problem. Specific process is described as following: Step 1: Let y = xbest which saves the current optimum. The solution space is mapped to the J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 5899 chaotic space with the following formula: zk (0) = yk (0) − lk , k = 1, 2, · · · , n uk − lk (5) Step 2: Logistic chaotic iteration is operated on variable z with the following formula: zk (t) = η · zk (t − 1) · (1 − zk (t − 1)) (6) where z ∈ [0, 1] is a chaos variable in the t-th search process (t = 1, 2, · · · , LSIT ER) and η is the control parameter. For η = 4, the system is in a complete chaotic state; Step 3: Map the chaotic space back to the solution space; yk (t) = lk + (uk − lk ) · zk (t) (7) Step 4: Calculate the objective function value f (y). If the new value is smaller than the previous one, update the particle until the termination criterion is meet. 3.2.3 Calculation of Total Force Vector The charge of each particle is evaluated as, f (xi ) − f (xbest ) qi = exp m −n ∑ (f (xk ) − f (xbest )) (8) k=1 Obviously, points that have smaller (better) objective values possess higher charges.Like electrical charges, the force exerted on a point via another point is calculated, and the total force exerted on a point is computed according to the superposition principle of electromagnetism theory. F ij and F i represent the force exerted on particle i from particle j and the total force exerted on particle i, respectively, and then: qi qj (xj − xi ) ||xj − xi ||2 , f (xj ) < f (xi ) Fij = (9) qi qj , f (xj ) ≥ f (xi ) (xi − xj ) ||xi − xj ||2 Fi = m ∑ Fij (10) j̸=i According to Equation (9), the direction of a particular force between two points is decided by their objective function values. And, between two points, the particle that has a better objective function value attracts the other one. Contrarily, the particle with worse objective function value repels the other. 5900 3.2.4 J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 Movement According to the Total Force In the standard EM algorithm, the effects of the quality of particles and the number of iterations on the feasible step length are not taken into consideration. In order to make the optimums become more accurate, an adaptive mobile operator is designed as following: ) ( 1 π i Φ = (1 − q ) sin √ · (11) t 2 where t denotes the order of the current iteration. The heredity makes the species remain relatively stable, while the variation makes it possible for the species to evolve. The idea of genetic variation in the theory of biological evolution is also introduced into the CEM algorithm. A genetic coefficient is added to the Equation (11), so that the particles are more likely to move to the other feasible regions. The balance between the global and local search ability can be arrived at by choosing an appropriate genetic coefficient. ( 1 π) F i xi = ωxi + (1 − q i ) sin √ · λ RN G (12) t 2 ||Fi || It can be seen from Equation (12) that (1 − q i ) makes the particle with (a worse ) objective π 1 function value move by a larger step. And with more and more iterations, sin √t · 2 makes the feasible step length smaller and smaller. Later in the evolution, the particles only move randomly in the neighborhood of the optimum. A more precise optimum may be found with the formula above. 4 Algorithm Description The image retrieval algorithm that using improved EM algorithm is described following: Step 1: Preprocess. Features of target image and the images to be retrieved from image library are extracted, region coefficients are set. The h, s, v of each block in the image and the value of the particle which corresponds to the image are computed; Step 2: Initialization. Good point set theory is used to generate initial population. Population scale and termination criteria are set including maximum number of iterations M AXIT ER, or the similarity of current optimal image with target image is less than threshold T , and the number of local search LSIT ER; Step 3: Use the improved local search method to locally search current optimal particle; Step 4: Compute the charge and the total force of each particle according to its target function values; Step 5: Update each particle according to the total force that it exerted; Step 6: Calculate the optimum for the updated population; Step 7: Judge that whether the result meets the termination criteria or not. If true, then search the particle that is nearest to the current optimal particle, and the image that corresponds to this particle is the result image; else go to Step 3. J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 5 5901 Simulation Results To illustrate the applicability of the improved EM algorithm for image retrieval, the test function following is used to verify the applicability according to definition of objective function: v u 48 u∑ f (x) = t (xi − xi∗ )2 (13) i=1 In order to test the retrieval effect of CEM algorithm, four groups are selected from Corel standard image library-flowers, dinosaurs, mountains and beaches-including 100 images each. The 100 images of each group are respectively used as target images. The representative images of each group are as Fig. 1. In the experiments, the parameters of EM and CEM are set as following: n = 48, m = 5, 10 and 20 represent different sizes of original population respectively, M AXIT ER = 100, LSIT ER = 50, δ = 1.0e − 2, and the threshold T is set to 1. Table 2 shows series of metrics including average Table 2: Results Set Flowers Dinosaurs Mountains Beaches m Alg Avg (iter) Avg (time) accuracy 5 EM 78.8 1.2924 96% 5 CEM 59.17 0.9482 100% 10 EM 70.6 0.5046 100% 10 CEM 54.52 0.8202 100% 20 EM 61.15 1.8819 100% 20 CEM 50.36 1.2924 100% 5 EM 100 1.7144 67% 5 CEM 83.19 1.3918 99% 10 EM 100 4.1854 79% 10 CEM 77.29 3.1189 100% 20 EM 99.77 9.9001 91% 20 CEM 73.6 6.2075 99% 5 EM 46.33 0.7913 96% 5 CEM 44.02 0.7111 99% 10 EM 39.34 1.396 98% 10 CEM 38.96 1.4029 99% 20 EM 33.59 2.9224 95% 20 CEM 35.09 2.9554 99% 5 EM 39.34 0.6604 80% 5 CEM 38.06 0.6328 98% 10 EM 34.38 1.2267 78% 10 CEM 31.26 1.1350 96% 20 EM 30.85 2.6335 76% 20 CEM 26.72 2.3128 94% 5902 J. Jiang et al. / Journal of Information & Computational Science 11:16 (2014) 5895–5903 (a) Flower (b) Dinosaur (c) Mountain (d) Beach Fig. 1: (a), (b), (c) and (d) are respectively representative images of flowers, dinosaurs, mountains and beaches image library number of iterations (Avg(iter)), average retrieval time (Avg(time)) and accuracy under different sizes of original population with each picture in the four sets taken as the target. Obviously in Table 2 that for most of the images, the accuracy of CEM is always better than that of EM and at the same time CEM costs less time than EM, which means CEM is more effective than EM. On the other hand, CEM proposed in this paper also outperforms both the PSO-based algorithm presented in [6, 9] and GM-based algorithm [7] on accuracy of image retrieval. 6 Conclusion A novel CEM-based method for image retrieval is proposed in this paper. It combines EM algorithm and image retrieval. 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