Image Segmentation Using Semi-Supervised k-means

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1 I J C T A, 9(34) 2016, pp Internationa Science Press Image Segmentation Using Semi-Supervised k-means Reza Monsefi * and Saeed Zahedi * ABSTRACT Extracting the region of interest is a very chaenging task in Image Processing. Image segmentation is an important technique for image processing which aims at partitioning the image into different homogeneous regions or custers. Lots of genera-purpose techniques and agorithms have been deveoped and widey appied in various appication areas. In this paper, a Semi-Supervised k-means segmentation method is proposed. First, an image threshoding has been performed to get the optima threshod vaue of the image which categorizes the image in to two main parts. This optima threshod vaue is then used to abe the objects in the image to be initiaized as initia custer centroids in Semi-Supervised k-means agorithm. At the end of custering, a mask of abeed parts of image has been created. To evauate the resuts and compare them with k-means simpe agorithm, PSNR criteria of the images are used. Evauations show that this method has better accuracy in comparison with the unsupervised k-means. Keywords: optima threshoding, k-means, semi-supervised k-means, PSNR 1. INTRODUCTION Image segmentation is an important technique for image processing which aims at partitioning the image into different homogeneous regions or custers.most computer vision and image anaysis probems require a segmentation stage in order to detect objects or divide the image into regions which can be considered homogeneous according to a given criterion, such as coor, motion, texture, etc. Custering is the search for distinct groups in the feature space. It is expected that these groups have different structures and that can be ceary differentiated. The custering task separates the data into number of partitions, which are voumes in the n-dimensiona feature space. These partitions define a hard imit between the different groups and depend on the functions used to mode the data distribution. The goa of the semi-supervised image segmentation is to obtainthe segmentation from a partiay abeed image.sankari et a [1] presented a segmentation agorithm based on Semi-Supervised custering which integrates imited human assistance. Instead of mouse cicks [2], the user seected some window area by mouse, the seected object inside the window used to be segmented and dispayed.paiva et a [3]proposed Semi-Supervised image segmentation based on novety seection method as the preprocessing step to reduce the number of data points whie retaining the fundamenta structure of the data. They took advantage of the fact that neighboring points in the features space convey approximatey the same information.sun et a [4] proposed a region based Semi-Supervised custering image segmentation method. They assumed the adjacent or nearby regions in abeed image beong to the same custer. They used abeed andassigned unabeed datawith different weights during the iterative custering process. They aso introduced a penaty function when abeed data were incorrecty segmented. Wang et a [5]proposed a Semi-Supervised image segmentation method based on Leve Set and the interactive information betweenuser and system as the prior knowedge. They introduced a mode which was based on active contour without edge and prior shape. As the reason of imprecise prior shape user inputs, the weighted area agorithm based on the gradient and Lapace was introduced. * Department of Computer Engineering, Ferdowsi University of Mashhad (FUM), Mashhad, Iran, E-mai: monsefi@um.ac.ir; szahedi@stu.um.ac.ir

2 596 Reza Monsefi and Saeed Zahedi In this paper,it is taken advantage of the Semi-Supervised k-means agorithm for image segmentation based on optima threshoding technique to initiaize centroids of Semi-Supervised k-means. At the end, the experimenta resuts on BEREKELY image Dataset are demonstrated and compared by means of PSNR criteria to evauate the quaity of the proposed method. Resuts show the efficiency of the proposed method. The rest of this paper is as foows. In part 3, the bock diagram of the proposed method is shown and the optima threshoding and Semi-Supervised k-means agorithm are depicted in parts 3.1 and 3.2, respectivey. Then the experimenta resuts and concusion parts are iustrated in the end parts. 2. IMAGE SEGMENTATION AND K-MEANS CLUSTERINGALGORITHMS K-Means agorithm is an unsupervised custering agorithm that cassifies the input datapoints into mutipe casses based on their inherent distance from each other. The agorithmassumes that the data features form a vector space and tries to find natura custering inthem. The points are custered around centroids µ i, i = 1...k which are obtained byminimizing the objective k 2 ( j i ) (1) i1 xis j V x µ where there are k custers S i, i = 1,2,, k and µ i is the centroid or mean point of a thepoints x j S i. As a part of this project, an iterative version of the agorithm was impemented. The agorithmtakes a 2 dimensiona image as input. Various steps in the agorithm are as foows: 1. Compute the intensity distribution(aso caed the histogram) of the intensities. 2. Initiaize the centroids with k random intensities. 3. Repeat the foowing steps unti the custer abes of the image do not changeanymore. 4. Custer the points based on distance of their intensities from the centroid intensities. 5. Compute the new centroid for each of the custers. ( i ) (i) 2 c : argmin x µ j (2) ( i) 1{ c j} x µ i : 1{ (3) j} m i1 ( i) m i1 c( i) where k is a parameter of the agorithm (the number of custers to be found), i iterates overthe a the intensities, j iterates over a the centroids and µ i are the centroid intensities. 3. PROPOSED METHOD The bock diagram of the proposed method is shown beow: Figure 1: The bock diagram of proposed method

3 Image Segmentation using Semi-Supervised k-means 597 At the beginning of the proposed method, the image is converted to the grey-eve image which can faciitate the segmentation process. Then the foowings steps are appied to get the abeed image as the resut of the Semi-Supervised k-means agorithm Optima Threshoding The simpest threshoding methods repace in an image with a back pixe if the image intensity I i,j is ess than some fixed constant T (that is, I i,j <T), or a white pixe if the image intensity is greater than that constant. In this part, it is aimed to get the optima threshod of the image which is used to create the initia abeed image as the initia centroids of k-means agorithmfor prior knowedge of the abeed data.the optima threshoding technique is based on Rider [6] iterative proposed method and contains steps beow: Step 1: mean intensity of the image from histogram is firsty computed as the initia threshod vaue. Step 2: Then the sampe mean of the data is taken by the achieved threshod. Step 3: Repeat step 2 iterativey ti the condition T(i) T(i 1) is confirmed. Rider et a. [6] proposed a method for image threshoding based on two-cass Gaussian mixture modes. At iteration n, a new threshod T n is estabished using the average of the foreground and background cass means. Iterations terminates when the changes T n T n+1 become sufficienty sma. T opt m f ( Tn ) mb ( Tn ) im (4) n 2 Tn m ( n) gp( g), m ( T ) f b n g0 G gtn 1 gp( g) Where g is the peak of the image histogram, and p is the probabiity density function of the image.m f and m b is the mean intensity of the foreground and background of the image, respectivey. Figure 2: The resut of Optima Threshoding 3.2. Semi-supervised k-means Agorithm K-means custering (MacQueen, 1967) [7, 8] is a method commony used to automaticaypartition a dataset into k custers. The agorithmsof k-means and Semi-Supervised k-means are presented in detai in figure.3 and figure. 4:

4 598 Reza Monsefi and Saeed Zahedi K-means Agorithm Input: a dataset X = {x 1, x 2,, x N }, number of custers k Output: k-partitioning of { X} k of X 1 1. Seect k data points as the initia custer centers randomy {µ 1, µ 2,..., µ k } 2. Each data point X i is assigned to its cosest custer center. 3. Each custer center µ is custered to be the mean of its constituent data points. 4. Repeat 2 and 3 k-means objective function is optimized Figure 3: The K-means agorithm Semi-Supervised K-means Agorithm k Input: a dataset X={x 1, x 2,, x N }, number of custers k, a set 1 S of abeed data Output: k-partitioning of { X} k of X 1 1. Seect k data points as the initia custer centers 1 { µ 1, µ 2,..., µ k }, µ x S, 1,..., x k S 2. Each data point X i is assigned to its cosest custer center. 3. Each custer center µ is custered to be the mean of its constituent data points. 4. Repeat 2 and 3 k-means objective function is optimized Figure 4: The Semi-Supervised K-means agorithm It is we known that the most chaenge of k-means agorithm is seection of theinitia custer centers. The traditiona k-means agorithm randomy seects k datapoints as initia custer centers from unabeed dataset, which eads to the chances of itgetting stuck in poor oca optima. In this paper, it is taken advantage of Semi- Supervised k-meansagorithm [9] which uses a set of abeed data to initiaize custer centers in the first step of k-means agorithm. Here, it is tried to create a set of abeed data by using an optima threshoding technique to obtain the proper threshod. Then, the mean of the maximum intensity of the image histogram and this optimum threshod is used to initiaize custer centers.other steps of the agorithmcontinues unti itsconvergence. At the end, a mask of abeed data was then obtained as the resut of Semi-Supervised k-means Image Segmentation by taking advantage of the weighted centroids computed by this agorithm. 4. EXPERIMENTAL RESULTS Peak signatonoise ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum possibe power of a signa and the power of corrupting noise that affects the fideity of its representation. Because many signas have a very wide dynamic range, PSNR is usuay expressed in terms of the ogarithmic decibe scae. PSNR is most commony used to measure the quaity of reconstruction of ossy compression codecs.the signa in this case is the origina data, and the noise is the error introduced by compression. When comparing compression codecs, PSNR is an approximation to human perception of reconstruction quaity. Athough a higher PSNR generay indicates that the reconstruction is of higher quaity, in some cases it may not. One has to be extremey carefu with the range of vaidity of this metric; it is ony concusivey vaid when it is used to compare resuts from the same codec and same content[10]. The proposed method has been impemented using MATLAB. The segmentation resuts have been shown as the foowing in comparison to the k-means image segmentation agorithm for some sampes of images of

5 Image Segmentation using Semi-Supervised k-means 599 the BEREKELY Image Dataset. The PSNR criteria are shown of each of the agorithms. In figure 5(a) and (b) the comparison of resuts are shown by using two sampe images of the BEREKELY image Dataset. PSNR is the proportion between maximum attainabe powers and corrupting noise that infuence simiarity of image pixes. The PSNR is usuay used as measure of quaity rebuiding of image. The signa in this case is origina data and the noise is the error imported. High vaue of PSNR signifies the big Quaity of image. It is expained via the Mean Square Error (MSE) and anaogous deformity metric, the Peak Signa to Noise Ratio. Here Max is maximum pixe vaue of image when pixe is represented by using 8 bits per sampe. This is 255 bar coor image with three RGB vaue per pixe.the higher the PSNR vaues, the better the quaity of image. 2 PSNR 10.og10 MAX I MSE (5) 20.og10 MAXI MSE 20.og10( MAXI) 10og10( MSE) As it can be seen in figure 4. (a) and (b), the promising resuts are achieved by taking advantage of the Semi-Supervised k-means image segmentation. 5. CONCLUSION Image segmentation is an important technique for image processing which aims at partitioning the image into different homogeneous regions or custers.in this paper, a semi-supervised k-means segmentation method is proposed. First, an image threshoding has been performed to get the optima threshod vaue of the image which categorizes the image in to two main parts. This optima threshod vaue is then used to abe the objects in the image to be initiaized as initia custer centroids in semi-supervised k-means agorithm. At the end of custering, a mask of abeed parts of image has been created. To evauate the resuts and compare them with k-means simpe agorithm, PSNR criteria of the images is used. Evauations show that this method has better accuracy in comparison with the unsupervised k-means. REFERENCES [1] Sankari. L, Chandrasekar.C, Semi-supervised Image Segmentation using Optima Hierarchica Custering by Seecting Interested Region as prior Information Journa of Goba Research in Computer Science, vo.2, No. 11, [2] Yuntao.Qian, Wenwu.Si A Semi-supervised Coor Image Segmentation Method IEEE proceedings, vo.5, [3] Paiva. R. C, Tasdizen.T, Fast Semi-supervised Image Segmentation by Novety Seection, ICASSP, IEEE [4] Sun. T, Ren. Z, Ding. Sh, Region-Based Semi-supervised Custering Image Segmentation, Internationa Conference on Natura Computation, IEEE [5] T. W. Rider and S. Cavard, Semi-Supervised Segmentation based on Leve Set Springer. pp ,2012. [6] T. W. Rider and S. Cavard, Picture threshoding using an iterativeseection method, IEEE Trans. Syst. Man Cybern. SMC-8, [7] Basu. S, Banerjee. A., Mooney, R.J. Semi- supervised custering by seeding. In: Proc. Ofthe 19th Internationa Conference on Machine Learning, pp , [8] Wagstaff. K, Cardie. C, Rogers. S: Constrained k-means custering with backgroundknowedge. In: Proceedings of the 18th Internationa Conference on Machine Learning, pp Morgan Kaufmann Pubishers Inc., San Francisco, [9] Wang, X, Wang.Ch, Shen.J, Semi-supervised k-means custering by optimizing Initia Custer Centers.WISM, Springer, pp , [10] Huynh-Thu, Q.; Ghanbari, M. Scope of vaidity of PSNR in image/video quaity assessment. Eectronics Letters 44 (13): 800,2008.

6 600 Reza Monsefi and Saeed Zahedi Figure 5 (a): Resuts of k-means and Semi-Supervised k-means from image sampe 1 of BEREKELY Image Dataset

7 Image Segmentation using Semi-Supervised k-means 601 Figure 5 (b): Resuts of k-means and Semi-Supervised k-means from image sampe 2 of BEREKELY Image Dataset