Cellular Learning Automata-Based Color Image Segmentation using Adaptive Chains

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1 Cellular Learning Automata-Based Color Image Segmentation using Adaptive Chains Ahmad Ali Abin, Mehran Fotouhi, Shohreh Kasaei, Senior Member, IEEE Sharif University of Technology, Tehran, Iran Abstract This paper presents a new segmentation method for color images. It relies on soft and hard segmentation processes. In the soft segmentation process, a cellular learning automata analyzes the input image and closes together the pixels that are enclosed in each region to generate a soft segmented image. Adjacency and texture information are encountered in the soft segmentation stage. Soft segmented image is then fed to the hard segmentation process to generate the final segmentation result. As the proposed method is based on CLA it can adapt to its environment after some iterations. This adaptive behavior leads to a semi content-based segmentation process that performs well even in presence of noise. Experimental results show the effectiveness of the proposed segmentation method. 1. Introduction Segmentation is an important task in image and video processing that plays an important role in understanding images or videos. Applications such as content-based image and video retrieval, video indexing, extraction of region of interest (ROI) in an image or scene, and medical image processing are some examples which show the significance of segmentation process in the processing. A variety of techniques are reported in the literature for segmentation purposes these are based on statistical information [1], energy minimization [2], graph cut [3], and unsupervised segmentation [4]. Most existing segmentation techniques (such as clustering-based techniques) work well on a homogenous regions. In this paper, a new algorithm has been proposed that combines color and texture information of input images with CLA to segment input images. In many existing segmentation techniques, some criteria are defined at first and then the segmentation process is applied based on these criteria and image neighboring information. Criteria definition and neighboring information can be easily simulated and implemented by CLA. Our proposed method is done in two soft and hard segmentation steps. In Soft segmentation step a CLA analyzes the input color image and tries to decrease color differences among pixels at same region iteratively and generate a soft segmented image. This soft segmented image is delivered to a hard segmentation system. This system labels and segments the soft segmented image based on a threshold and generate final segmented image. The paper is organized as follows. Learning automata and cellular automata are described in Section 2. Proposed color image segmentation algorithm is addressed in Section 3. Experimental results are discussed in Section 4. Finally, concluding remarks are given in Section Cellular Learning Automata Cellular automata (CA) are a collection of cells that each adapts one of a finite number of states. Single cells change in states by following a local rule that depends on the environment of the cell. The environment of a cell is usually taken to be a small number of neighboring cells. Fig. 1 shows two typical neighborhood options. Figure 1.(a) Von Neumann, (b) Moore adjacency [5]. Figure 2. Feedback connections of automata and its environment [5]. A learning automata (LA) is an automaton that interacts with a random environment, having as goal to improve its behavior. It is connected to the environment in a feedback loop, as shown in Fig /09/$ IEEE 452

2 The functionality of the learning automata can be described in terms of a sequence of repetitive feedback cycles in which the automata interacts with an Environment. The automata choose an action that triggers a response (reinforcement signal) from the Environment. Such a response can be either a reward or a penalty. The automata uses this response and the knowledge acquired in the past actions to determine which the next action is. The automaton updates its action probability vector depending upon the reinforcement signal received at that stage. Various learning algorithms have been reported in the literature. Below, a learning algorithm, called L R-P, for updating the action probability vector is given. Let i be the action chosen at time k as a sample realization from probability P(k) distribution and (k) is the environment response to that action. In L R-P algorithm, the action probability vector is updated according to ρ + 1 = + (1 ) i (n ) ρi (n) α ρi (n) for ( k) = 0 + 1) = (1 ) j : j i j (n j (n) β ρ α ρ ρ + 1 = (1 ) i (n ) b ρi (n) for ( k) = 1 + 1) = b b j : j i j (n r 1 j (n) β ρ ρ (1) (2) where i (n+1) is the selection probability of action i, and a and b are the decreasing and increasing factor of actions. When (k)=0 the environment rewards the chosen action of LA and when (k)=1 the environment penalizes the chosen action. Parameter 0<b<a<1 represent the step length and r is the number of actions for LA [6]. LA have been used successfully in many applications such as telephone and data network routing [7] and solving NP-complete problems [8] to mention a few. A CLA is a mathematical model for dynamical complex systems that consists of a large number of simple learning agents [9]. A CLA is a CA in which a learning automaton will be assigned to its every cell. The learning automaton residing in each cell determines the state of the cell on the basis of its action probability vector. Like CA, there is a rule that governs CLA. The rule of CLA and the actions selected by the neighboring LAs of any cell determine the reinforcement signal to the LA residing in that cell. A number of applications for CLA have been developed recently; such as image processing [5] and modeling of commerce networks [11]. 3. Proposed Segmentation Technique This paper has proposed an algorithm that combines color and adjacency information of image regions with CLA to segment regions in color images. Fig. 3 illustrates the overall structure of the proposed segmentation method. The details of each process are described below. Figure 3. Overall structure of proposed segmentation method CLA-Based Segmentation The main idea for using CLA to segment regions is to use the adjacency relation among regions for better segmentation. CLA propagate the adjacency information of adjacent regions to all directions and segment each region based on its overall color and texture information. To do so, first a 2-D CLA with dimensions of input image is created. Each LA related to its pixel in input color image. Then, a dynamic structure LA with L R-P learning algorithm is allocated to each cell of CLA. Moore neighborhood is considered for the cells. Each learning automaton takes eight actions. Each action is related to eight neighbors of the central LA in a 3 3 adjacency which has a selection probability. Selection probability of each action shows the similarity of the central pixel to its neighbors. Selection of an action by central LA means that the central pixel in input image and the selected neighbor lie in the same region. Fig. 4.a shows the adjacency structure in action selection. Since a single pixel is noise and cannot form a region, there is no action related to the central LA. The initial probability map associated with CLA is calculated as follows. First, for each pixel I(x,y) at location (x,y) of image I (with red, green, and blue values r, g, and b, respectively), The RGB Euclidian distance between the color of that pixel and all its neighbors in a 3 3 block around it is calculated by 2 D i (x,y) = (I(x,y,k)-,y,k)) k= r,g,b i (x' ' (3) 453

3 where I i (x,y ) is the ith adjacent pixel at location (x,y ) and k shows the channels (red, green and blue) of color image. D i (x,y) is the RGB Euclidian distance between I(x,y) and its ith neighbor [5]. Now, these RGB distances are converted to action selection probability for CLA. The initial probability map P i (x,y) is calculated by S (x,y) i 1 P i (x,y) = 8 j = 1 S (x,y) j where S i (x,y) = D (x,y) i (4) where P i (x,y) is the selection probability of the ith action by LA and P i (x,y) means that the pixel at that location is similar to its ith neighbor with probability P i (x,y). Fig. 4.b and 4.c shows a typical 3 3 image and the action selection probability of the central LA at location (2,2) obtained by (4). Therefore, a learning automaton with eight actions is assigned to each pixel of input image. Each action shows the similarity probability of that pixel to its eight adjacent pixels. Similarity probability P i (x,y) related to each adjacent shows the probability which the central pixel and its ith adjacent lie in the same region. Each LA selects an action from its action list based on their probability. Then, each learning automaton is rewarded or penalized based on the selected action of the central LA and its neighbors. A rule analyzes the selected action of adjacent automata and makes a decision to reward or penalize the central LA. The rule is as follows. At first, the average RGB Euclidian distances among each pixel and its neighbors is calculated and is named D m (x,y). It is considered as the distance between the central pixel and its ith neighbor which is selected in action selection step. The rule to reward or penalize the central learning automata is If c D i (x,y) D m (x,y), Then Reward Else Penalize. Figure 4. A typical image and action selection probability of central LA. Constant c controls the hardness of applied rule. If the inequality is met, the central learning automaton is rewarded by means of its learning algorithm described in (1) and (2), and otherwise the central LA is penalized by means of its learning algorithm. It needs an algorithm to propagate color information in each segment which is described in detail next section Chain Extraction When CLA complete one step, pixels in the same segment propagate their color information together. This causes pixels to reach a stable state and near pixels lie in the same segment. In this section, a chain detector algorithm is proposed which extracts sequential similar pixels as a chain and updates their color information based on all chain members information. Consider the input image as I and the output image as I. First, for each pixel a chain of sequential pixels is extracted from that location and pixels of chain determine the color of that pixel. Fig. 5 shows the pseudo code for the chain extraction process related to each pixel. pixels_list is a list which holds chain members related to the pixel at location (x,y). The list is empty and current cell is initially equal to (x,y). First, the current cell is added to pixel_list and then based on the selected action of the current cell; the adjacent pixel is processed and will be added to the list if it does not fire the stop condition. Then, the current cell is set to the adjacent cell and the process is repeated until it reaches the chain expansion stop condition. Chain expansion process is stopped as the rule penalizes current cell or a cycle is detected in chain. Fig. 6 shows two examples of the chain extraction process. Black blocks are the start points of chains and gray blocks are trajectory of extracted chains. Arrows show the adjacency relation and the direction of chain elements. Red arrows show the illegal moves and fire the stop condition in the chain extraction process. Extract_Chain (x, y) Set current cell to (x,y). Assign pixels_list to an empty set. Repeat Add current cell to pixels_list. Set to selected action in current cell. Set current cell to (x,y ) which (x,y ) is the neighborhood of current cell corresponds to action. Until (LA in current cell is penalized or a cycle is detected in pixels_list) Return pixels_list. End Extract_Chain Figure 5. Pseudo code for chain extraction. Figure 6. Two typical extracted chains. On the right side of Fig. 6, the chain extraction process is continued until a learning automaton is penalized and on the left side it is continued until a cycle is detected. Next section explains how the chain elements update the color value of chain start point. 454

4 3.3. Color Propagation In chain extraction process, a chain is extracted for each pixel. Chain elements are the pixels most similar to the pixel at location (x,y). After a chain is extracted for each pixel, elements of that chain combine their color information and update color value of that pixel. Pixels of each chain combine their color info by weighted average of its elements color value and update color value of that pixel by L( x, y) i = 1 ( w I{ L ( x, y)}) I '(x,y) = i i (5) L( x, y) i = 1 w i where I is the input image, I is the output soft segmented image, L(x,y) is the list of chain elements corresponding to pixel at location (x,y),. is the number of chain elements, L i is the i th chain element and w i is the weight related to the i th chain element which determines the effectiveness ratio of the ith chain pixel. Weights w i are designed to have an descending behavior. This is true and significant that the initial chain elements is more important and must have higher weights and the final chain elements are less important and must have lower weights. Equation (6) shows a typical descending function and Fig. 7 shows its behavior on a sample chain. w i = 1 i :1... M x x + y y (6) 2 i c i c where (x i,y i ) is location of the i th chain elements and (x c,y c ) is the location of current cell. Figure 7. (a) A typical chain. (b) A typical 2-D descending weightening function and chain corresponding weight. As described above, (5) tries to eliminate differences among pixels of each segment and converges the representative color of each segment to a stable color. A problem which reduces the performance of weighting algorithm is the existence of small edges which form the texture of each segment. Small edges can generate effective values on the weighting process and mislead the segmentation algorithm. Discrete normalized Gaussian filter (7) has been used to reduce the effect of texture on the result. exp( ( m2 + n2 ) 2σ 2 ) h( m, n; σ ) = (7) i jexp( ( i2 + j 2 ) 2σ 2 ) Where m and n denote the rows and columns of filter h and are zero in filter central point. After K iterations of CLA, chain detection and color propagation, once the Gaussian filter is used to enhance the segmentation quality. The filter smoothes the texture of each segment and reduces the effect of noise and small edges. The effectiveness of adjacent pixels will be increased as the standard deviation () is increased. Effectiveness rate of adjacent pixel is directly associated to the parameter. As CLA iterations increase, the effectiveness of the filter is decreased by reducing parameter. Decrement of is done by σ σ t = F σ ( ) σ 1 t 1 T (8) where T = N K, 1 and F ( 1 > F ) are the initial and final standard deviations, respectively. N is the maximum number for CLA iterations Hard Segmentation Till now, soft image segmentation has been applied on input images and a soft segmented image has been generated. This soft segmented image is an image which has been analyzed by CLA and pixels of the same segment are very close together. Now, a hard segmentation is applied on the soft segmented image. A threshold is selected as the maximum RGB distances between pixels of a segment. IF the RGB distance among two adjacent pixels be smaller than, these two pixels are considered to belong to the same segment and will get the same label else, they are considered to belong to different segments and their segment labels will be different. After segment labeling, the average color of the same labeled pixels is considered as the color representative of that segment. This work results in a hard segmented image. Final result is very sensitive to. Different values for result in different segmented images with different number of segments. Change in value will result in different generated segments. A small leads the total number of segments in the final result to be high. If has a large value (greater than maximum RGB distances in soft segmented image), the whole soft segmented image will be considered as one segment. It is worth mentioning that other existing segmentation algorithms have one or more free parameters as well. For example, the K-means algorithm needs to know the total number of clusters and in JSEG [4] there is a parameter named as region merge threshold which is defined between 0 and 1. This parameter determines the final segmentation result. 455

5 4. Experimental Results Our segmentation method was carried out on a 2 GHz processor with 1024 MB RAM on Windows XP professional platform. MATLAB 7.1 and image processing toolbox have been used. The proposed method was tested on Berkeley segmentation dataset. The Moore neighborhood with r=2 has been considered for CLA cells. The learning algorithm of each dynamic structure learning automata employed the L R-I algorithm with a=0.040 and b= The process is stopped when CLA iterations reaches a maximum iteration number and F have been considered as 1 and 0.5. Note that if F be very small then the filter will be very short and hence the adjacency relation will not be considered in the soft segmentation process. Gaussian filter is applied to CLA processed image each 10 iterations. Fig. 8 shows the result of proposed method and compares it with JSEG and the k-means methods on some typical images. Fig. 9 shows the robustness of proposed method at presence of noise. The first row in Fig. 9 shows the original image and segmentation result. The second and third rows show the Salt & Pepper and Gaussian noisy image and segmentation results for K- means, JSEG and proposed method. Table I shows the average time complexity of our proposed method and the others on dataset. Table 1. TIme Complexity comparison. Method K-Means JSEG Proposed Method Time (Sec) Conclusion A new technique for image segmentation is proposed in this paper which segments color images using soft and hard segmentation processes. In soft segmentation, a CLA analyzes the input image and closes pixels of each region together and delivers it to hard segmentation process. This process applies a threshold on the soft segmented image and generates the final segmentation result. One advantage of the proposed method is that it is based on CLA that has an adaptive behavior with its environment after some iteration. This leads to have a semi content-based segmentation process. Another advantage of the proposed method is that it can work well in presence of noise. Here, a new viewpoint has been introduced to the problem of image segmentation method and some learning algorithms has been used to segment color images based on their color and content information. 6. References [1] J.P. Wang, "Stochastic Relaxation on Partitions with Connected Components and Its Application to Image Segmentation", IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 6, pp , [2] W.Y Manjunath, and B.S. Ma, "Edge Flow: a Framework of Boundary Detection and Image Segmentation", Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp , [3] J. Shi, and J. Malik, "Normalized Cuts and Image Segmentation", IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp , [4] Y. Deng, and B.S. Manjunath, "Unsupervised Segmentation of Color-Texture Regions in Images and Video", IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 8, pp , [5] A.A. Abin, M. Fotouhi, and S. Kasaei, "Skin Segmentation based on Cellular Learning Automata," 6 th International Conference on Advances in Mobile Computing & Multimedia (MoMM2008), pp , [6] K.S. Narendra, and M.A.L. Thathachar, Learning Automata: An Introduction, New York, Printice-Hall, [7] P.R. Srikantakumar, and K. S. Narendra, "A Learning Model for Routing in Telephone Networks", SIAM Journal of Control and Optimization, vol. 20, no. 1, pp , [8] B.J. Oommen, and E.V. de St Croix, "Graph Partitioning Using Learning Automata", IEEE Transactions on Computers. vol. 45, no. 2, pp , [9] M.R. Meybodi, and H. Beigy, "New Learning Automata- Based Algorithms for Adaptation of Backpropagation Algorithm Parameters", International Journal of Neural Systems, vol. 12, no. 1, pp , [10] M.R. Meybodi, H. Beigy, and M. Taherkhani, "Cellular Learning Automata and its Applications", Sharif Journal of Science and Technology, vol. 19, no. 25, pp , [11] M. R. Meybodi and M. R. Khojasteh", Application of Cellular Learning Automata in Modeling of Commerce Networks," Proceedings of 6th Annual International Computer Society of Iran (CSICC2001), pp ,

6 Figure 8. (a) Input image. Segmentation results of (b) K-means, (c) JSEG, (d) proposed method. Figure 9. (a) Noisy input image. Segmentation results of (b) K-means, (c) JSEG, (d) proposed method. 457

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