Enhanced Hemisphere Concept for Color Pixel Classification

2016 International Conference on Multimedia Systems and Signal Processing Enhanced Hemisphere Concept for Color Pixel Classification Van Ng Graduate School of Information Sciences Tohoku University Sendai, Japan e-mail: vannth@riec.tohoku.ac.jp Terumasa Aoki New Industry Hatchery Center (NICHe) Tohoku University Sendai, Japan e-mail: aoki@riec.tohoku.ac.jp Abstract Most of current clustering methods are designed for general purpose other than a specific color pixel classification use. Color Line model representation emerged as the ultimate method for clustering pixels using RGB color components. However, this method is strongly sensitive to the adjustment of input parameters, which cannot conform to the frequent change of image structures and compositions. In this paper, we address this problem by introducing a hemisphere-grid based method for RGB pixel classification. Our method minimizes the reliance on user provided parameters as well as it can dynamically estimate the proper number of clusters. The properly clustering results prove the robustness and advantages of our method in classifying color pixels for unfamiliar input images. Keywords-hemisphere-grid; RGB clustering; adaptive clustering I. INTRODUCTION Most of the current clustering methods dedicate for the generic applications rather than color pixel classification purpose. First introduced in [1], fuzzy c-means clustering algorithm attempts to minimize the mean square errors between the number of clusters and the distances to cluster centroids, and simultaneously updates the set of membership degrees for each data pattern with respect to prospective clusters. The output is a matrix with each row is the membership degrees of data points corresponding to set of available clusters. Since, original fuzzy method requires desired number of clusters, the work in [2] tries to address this obstacle by automatically estimating the number of partitions using Xie-Beni formula [3]. With the similar purpose, the authors in [4] proposed a fuzzy-objectivefunction-based method that uses ant colonial optimization to find the optimal clusters and quantized RGB channel as initial clusters. Although, ant algorithm is an optimal method but high computational complexity that needs a lot of effort to reduce computing cost by using quantized pixel colors and settlements for proper quantizing levels. k-means method [5] can effectively cluster data patterns to the most proper partitions if a reasonable number of expected clusters is provided. k-means tends to detect the hyper-spherical shaped clusters while in the real case, clusters often take any shape and size. Challenging this drawback, M. Su and C.-h. Chou [6] explore the symmetrical distance instead of using Euclidean distance to measure the dissimilarity between data patterns. The obtained clusters from this method are robust for the data set containing nonspherical-shaped clusters. Besides, k-means algorithm heavily suffers from the initial conditions, which randomly places the cluster centers and proceeds by iteratively relocating the centers to minimize the clustering errors. In order to extricate this situation, A. Likas, N. Vlassis and J. J. Verbeek [7] proposed a global search that incrementally adds up one optimal center in each searching cycle until reaching the expected number k. The method guarantees that in every search for a new center, an optimal result is obtained without the random initialization of centroid locations. Another method presented by S. Guha and R. Rastogi [8] as the derivation of k-mediod algorithm where the authors initially consider every single point as the representative of their occupied clusters. In each successive step, the two closest representatives are merged to one cluster until obtaining k clusters using distance between them as the measurement. Even if achieving the high performance for clustering generic input data, these methods still contain some drawbacks that make it difficult to apply for image processing such as color pixels classification under the frequent change of image color and scenes. Recently, Color Line representation [9] was presented as an ultimate method for RGB color pixel classification. This method exploits the geometric information of pixels in RGB space to build a Color Line model in which pixels having similar color elongate around their representative lines. Basically, Color Line method assumes that the plotted RGB points aligned surrounding their skeleton lines in RGB space. However, the problem occurs since the distribution of color vectors in RGB space does not always satisfy this assumption. In many cases, pixels gather and arrange in the non-line-like-shaped, or the spatial distances between pixels are very narrow that leads to incorrect formation of Color Line model. In order to tackle those limitations, in this paper, we present a robust clustering algorithm for RGB pixels that enhances hemisphere concept introduced in Color Line approach. The proposed method can simultaneously preserve spatial relation of data patterns and automatically adapt to the frequent change of cluster size and shape. Besides, as the target to investigate a devoting clustering method for image processing applications, our method can apply for not only the line-like RGB distribution model but also the arbitrary pixels arrangement with the flexible size and shape of the clusters. 978-1-5090-4519-8/16 $31.00 2016 IEEE DOI 10.1109/ICMSSP.2016.15 31

In the rest of this paper, Section II presents our contribution and the detailed algorithm then, the experimental results are presented in Section III. Finally, the conclusion and future work are expressed in Section IV. II. HEMISPHERE-GRID BASED RGB PIXEL CLASSIFICATION Hemisphere was originally introduced in [9] with the purpose to separate the RGB color space to equal-width slices limited by a couple of neighbor hemisphere surfaces for Color Line model constructions. Each color line consists of two color points located on neighbor hemisphere surfaces and it represents a color cluster. Pixels around this color skeleton are gathered into one cluster under a Gaussian distribution model. However, Color Line approach presumes the number of hemispheres as equal to 5 and an empirical distance threshold for all input images while these parameters are strongly sensitive to the changing of input data so that this method is unable to preserve its robustness for the unfamiliar images. Figure 1. Polar-like coordinate system In order to address these limitations, we enhance the hemisphere concept in the context of polar-like coordinate system to exploit their advantages. While log-polar system [10] considers both l 2 -norm and angle of pixel coordinates, our approach only takes the RGB l 2 -norm into account as the basement for further algorithm. As demonstrated in Fig. 1, we investigate hemisphere slices in the context of polar-like coordinate system that produces a hemisphere grid for geometrically separating the pixels in RGB space into proper clusters. In other words, we use the hemisphere grid as the hyperplane to define boundary of clusters and preserve the scale between pixel color tuples. To sum up, our method introduces two major improvements for Color Line model: Automatically estimate the number of hemispheres needed to slice RGB space properly instead of using empirical number of 5 as suggested in Color Line model proposal. Automatically estimate the distance threshold to assess pixels into proper clusters in each hemisphere slice, while in Color Line method, this parameter is provided by user, and it is often vulnerable to the change of input images in spite of that it strongly impacts to the clustering results. A. Hemisphere Slice Estimation In the Color Line method, authors suggested to use predefined number of hemispheres equals to 5 with that 3- dimensional RGB space is divided into 5 equally-widthslices for every input image. Since, pixel distribution changes differently from image to image, this use of a constant number cannot keep the robustness in most cases. We overcome this issue by using l 2 -norm to estimate dynamically this parameter in each use case. Our work is toward color pixels classification, so that, initially labelling pixels to subspaces G i with respect to their color scale is the intuitive preprocessing process. As a result, G i collects only the similar color scale pixels those are served for further steps. We conduct a learning algorithm to estimate the most appropriate number of hemispheres for each subspace as following. Learning the number of hemispheres algorithm bases on the assumption that the boundary region of clusters should contain less pixels than their center regions. Therefore, we use the ratio between number of pixels in center and surface of hemisphere as the factor to detect a new hemisphere candidate. The initial radius is equal to the minimum l 2 -norm of RGB coordinates in G i. Learning process iteratively increases the radiuses with the step size equals to 2 n (n is the number of vector dimensions, in this case, n=3). In each iteration it i, the average number of pixels gathering at the surface and center of each hemisphere slice are computed, denoted as n s and n c respectively. Then, the decision cost is calculated by equation d c = n c /n s. A new hemisphere slice is established if the decision cost d c is lower than its preceding value, which indicates the boundary region between a pair of neighbor clusters. Once the number of hemispheres is defined for each subspace, the corresponding radii also can be identified accordingly. Eventually, we have created a hemisphere-grid system (virtually) that acts as hyperplanes for pixel classification process. B. Distance Threshold Estimation and Pixel Classification Distance threshold is used to calculate depth-of-thevalley distance in Color Line method for pixels classifier. This parameter stands for the size of each cluster so that it seems be unnatural if it is fixed as any particular number as in Color Line approach. In our algorithm, we consider the angle between two furthest points in center regions of each hemisphere slice regarding origin O as the distribution angle θ depicted in Fig. 2. In the primarily classifying step we consider only the pixels at the center regions of each hemisphere slice and use this estimated θ to compute the depth distance d v (Fig. 2) connecting each pixels and the rest ones alternatively. Since this depth measurement handles not only the distance between two points but also the angle between them which bears the spatial relation and geometric positions for the further use. Pixels are distributed to the same clusters if their depth distance d v is below than the threshold distance. The result of this step is primary cluster containing only the centering pixels with a respective kernel. For other pixels locating outside of hemisphere center regions, we compute the distance from them to obtained 32

kernel pixels and assess the corresponding cluster with the minimum distance. As a result, we obtain the list of clusters for input pixels with respect to their RGB components that each partition has a kernel point as its representative. Color Line method vary drastically demonstrating the difficulty to manipulate this parameter in reality. Our proposed algorithm shows its capability to address this obstacle since it does not need any user effort in providing this threshold while still achieve high precision in classifying color pixels. TABLE I. MSE LEVELS OF RECONSTRUCTED COLOR IMAGE USING COLOR LINE METHOD WITH VARIOUS MANIPULATED NUMBER OF HEMISPHERES AND OUR METHOD.ASSHOWN IN THE TABLE,OUR PROPOSED METHOD ACHIEVES IMPRESSIVE LOWER VALUE OF MSE THAN OTHER RESULTS OBTAINED UNDER COLOR LINE METHOD Figure 2. Valley depth distance and distribution angle θ III. EXPERIMENTAL RESULT To assess our proposed method, we perform various experiments under different settling conditions. We use the color images from Berkeley Segmentation Dataset [11] as the input data. In our experiment, color deduction process was performed efficiently. This process reconstructs an output image, which is composed of fewer known-color pixels than an input image. Color is propagated from cluster kernel to other belonging pixels to obtain reconstructed images. By measuring MSE (Mean Squared Error) of input image (ground truth) and output images (reconstructed images), we can compare the performance of color classification methods objectively. 900.00 800.00 700.00 600.00 500.00 400.00 300.00 200.00 100.00.00 MSE Proposed method tan(θ)=1.02 tan(θ)=1.05 tan(θ)=1.08 1 2 3 4 5 6 7 8 9 1011121314151617181920 Input image index Figure 3. MSE levels of reconstructed color image using Color Line method with various manipulated number of hemispheres comparing with results from our method (blue line) We make the testify to show the reliance on distance threshold of Color Line model by keeping the number of hemisphere equals to recommended value of 5 and manually adjust the distance threshold equals to 1.02, 1.05 and 1.08. MSE levels from these different conditions are plotted in Fig. 3. As shown in this graph, obtained MSE levels using Input MSE of output images using Color Line with respective number of hemispheres Proposed method (N h=5) (N h=7) (N h=9) (N h) N h MSE 1 322.16 126.59 209.76 209.91 9 11.00 2 22.60 18.28 11.99 70.50 4 5.68 3 62.81 35.95 27.07 35.95 7 17.46 4 30.57 19.16 32.34 34.22 8 8.51 5 36.63 28.32 17.80 36.63 5 5.90 6 31.33 25.11 30.07 38.23 6 7.48 7 93.56 69.77 46.32 20.33 12 6.07 8 62.01 26.42 21.67 26.42 7 8.96 9 48.01 50.47 38.53 51.91 8 6.02 10 133.49 180.85 19.36 19.36 9 8.13 11 21.69 21.36 16.16 26.17 6 6.95 12 25.40 19.51 12.63 25.48 6 6.73 13 101.43 56.07 52.67 104.55 4 18.70 14 136.83 116.93 62.65 116.93 7 11.23 15 262.79 160.57 87.04 97.10 6 11.06 16 45.64 27.40 29.07 29.07 9 7.41 17 60.35 25.58 19.89 60.35 5 9.89 18 55.97 41.12 28.04 41.12 7 8.37 19 83.27 53.68 69.88 53.67 8 11.73 20 79.45 34.21 28.51 155.80 3 6.50 Color Line method use the number of hemisphere slice equals to 5 for every input images. However, with the changing of image compositions, this number is not always suitable. We perform four experiments using Color Line method to classify RGB pixels with manipulated number of hemisphere equals to 5, 7, 9 and the estimated number from our method (N h ) alternately. The obtained MSE levels are summarized in Table I. As shown in this table, our method yields impressively lower MSE than all other cases using Color Line method. This result proves that our proposal can achieve the strong accuracy and the ability to estimate 33

appropriate number of hemispheres suits for unfamiliar images. more suitable for RGB pixel classification than general clustering method such as k-means. TABLE II. MSE LEVELS OF RECONSTRUCTED COLOR IMAGES USING K- MEANS WITH VARIOUS MANIPULATED NUMBER OF CLUSTERS AND RESULTS FROM OUR METHOD.AS SHOWN IN THIS TABLE,OUR PROPOSED METHOD ACHIEVES LOWER VALUE OF MSE THAN OTHER RESULTS OBTAINED USING K-MEANS METHOD MSE of output images using k-means with Proposed respective number of clusters method Input (N (N c) (N c+5) (N c-5) (N c- c+10) N 10) c MSE 1 10.04 9.06 12.68 10.13 11.81 89 5.68 2 18.97 19.77 25.95 21.52 26.30 51 17.46 3 14.39 14.03 12.99 12.30 13.74 87 5.90 4 9.96 12.74 15.86 10.40 19.67 54 6.95 5 27.44 26.15 33.10 24.18 41.58 47 18.70 6 13.10 14.10 14.96 13.97 15.64 122 7.41 7 25.64 20.19 33.87 17.64 29.18 33 9.89 8 14.52 17.24 12.43 11.62 18.31 125 8.37 9 14.61 16.12 15.12 12.09 14.94 53 6.50 10 12.32 10.33 11.43 7.93 15.31 68 4.81 11 15.19 11.60 13.09 12.55 11.87 102 7.05 12 15.73 13.37 17.09 13.80 22.43 46 8.18 13 13.62 11.83 14.41 13.00 16.02 42 7.34 14 10.33 11.38 9.96 11.00 10.62 123 7.16 (a) (b) 15 19.20 17.97 18.65 15.57 18.82 104 8.22 16 17.13 15.84 17.51 14.44 19.30 90 8.10 17 31.08 27.04 24.99 24.50 33.06 74 13.54 18 15.56 12.05 13.37 15.09 13.83 157 7.94 19 16.36 15.76 24.50 11.04 22.10 37 7.39 20 21.41 20.41 26.35 21.06 33.34 42 14.19 We also perform clustering process for RGB pixels using k-means algorithm that takes the estimated number of clusters from our method as parameters. Furthermore, we increase and decrease these numbers by 5 ((N c +5), (N c -5) columns) and 10 ((N c +10), (N c -10) columns) iteratively. The obtained MSE values are shown in Table 2. In all cases, even if the number of clusters is equal, greater or lower than estimated numbers, our method keep holding the lower values of MSE. Especially, under the condition that the number of clusters provided for k-means algorithm larger than estimated values from our method Table II column ((N c +5) and (N c +10)), our approach still can keep its ability to achieve the smaller levels of MSE. These prove the robustness of our algorithm and good estimation of the number of clusters. Besides, these achievements also indicate that our method is not only more flexible but also (c) (d) Figure 4. Input image (a) and reconstructed color from experiments using proposed method (5 hemispheres, 104 clusters), Color Line representation (9 hemispheres, 89 clusters) and k-means (114 clusters). Even using a larger number of hemispheres (Color Line method) or higher number of clusters (k-means), our method still keeps its robustness proved by the more similarity of reconstructed color image with the original one. Fig. 4 depicts reconstructed color images using our proposed method, Color Line, and k-means approaches respectively. As shown in this figure, our method holds the better clustering result without providing number of hemispheres or clusters as the input parameter. In other two methods, there exist the incorrectly reconstructed regions marked as red circles while the output obtained from our method is mostly similar (blue circles) to the original image. IV. CONCLUSION AND FUTURE WORK In this paper, we presented the hemisphere-grid based clustering algorithm as the enhancement of Color Line representation model, which could automatically estimate the necessary parameters using the distribution of pixels in 3-dimensional RGB space. Our method showed its robustness, flexibility and adaptability with the change of input image texture and composition. In our proposed 34

method, we initially classify pixels into the subspaces with respect to their color channel ratios. For each subspace, we introduced a new algorithm for self-estimating the most appropriate number of clusters as well as the distance threshold parameters, which are used to classify data points to appropriate clusters. The algorithm to estimate these parameters strongly relies on the distribution characteristic of pixels in 3-dimensional space. So that, with the frequent change in texture and composition of the input images represented as the distribution characteristic of pixel positions in RGB space, our method could still keep its robustness and capability to produce outstanding clustering achievements. For the future work, we would like to extend our achievement not only for pixel clustering but also for segmentation approaches. For this purpose, we aim at developing a hemisphere-cut segmentation method, which can consider geometric criteria underlying pixels color and feature coordinates to define the appropriate segment boundaries. The success of this method expects to have a wide range of applications in image processing field such as text, pictogram, force and background extraction applications. Besides, we will also develop an optimal method for image matching where input image pixels can automatically be classified into proper clusters and efficiently matched between corresponding regions. This approach expects to reduce the redundancy as well as to maintain the precision of matching task. Also successfully developing an effective matching algorithm can be applied for automatic colorization applications due to the important role of matching task in this field. REFERENCES [1] J. C. Bezdek, R. Ehrlich, W. Full, FCM: The fuzzy c-means clustering algorithm, Computers & Geosciences 10 (2-3) (1984) 191 203 [2] S. Das, A. Konar, Automatic image pixel clustering with an improved differential evolution, Applied Soft Computing Journal 9 (1) (2009) 226 236. [3] X. L. Xie, G. Beni, A validity measure for fuzzy clustering (1991). [4] Z. Yu, O. C. Au, R. Zou, W. Yu, J. Tian, An adaptive unsupervised approach toward pixel clustering and color image segmentation, Pattern Recognition 43 (5) (2010) 1889 1906. [5] An efficient k-means clustering algorithm: analysis and implementation, IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (7) (2002) 881 892. 16 [6] M. Su, C.-h. Chou, A modified version of the K-means algorithm with a distance based on cluster symmetry, Pattern Analysis and Machine Intelligence 23 (6) (2001) 674 680. [7] A. Likas, N. Vlassis, J. J. Verbeek, The global k-means clustering algorithm, Pattern Recognition 36 (2) (2003) 451 461. [8] S. Guha, R. Rastogi, Cure: an efficient clustering algorithm for large database, Information Systems 26 (1) (2001) 35 58 [9] I. Omer, M. Werman, Color lines: image specific color representation, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004. 2.17 [10] E. L. Schwartz, Computational anatomy and functional architecture of striate cortex: A spatial mapping approach to perceptual coding, Vision Research 20 (8) (1980) 645 669. [11] Berkerley segmentation dataset, https://www.eecs.berkeley.edu/research/projects/cs/vision/bsds/, access: 2016-05-18. 35