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PAPER IDENTIFICATION NUMBER < Since the Herlev dataset [19] is publicly available, the second topic has also attracted much attention. Mao-Yang et al. [4] proposed an edge-based method to extract cell contours in single-cell cervical smear images. They employed a trim-meaning filter and a bi-group enhancer to remove noise and enhance the obscure edges in cell images, respectively. Then, they proposed a mean vector difference enhancer using the GVF vectors [21] to further brighten the obscure edges. The cell contours are finally obtained by automatic thresholding [22] and morphological operations. Li et al. [2] proposed to extract cell contours using the Radiating GVF (RGVF) Snake model. The edge and region information are combined to solve the cell segmentation problem. A spatial K-means clustering algorithm is used for rough extraction of the cell nucleus and cytoplasm. Then, a stack-based refinement method is proposed to compute the radiating edge map. The GVF Snake model [21] is finally employed to extract the cell contour. High accuracy of the segmentation result has been shown in their work. However, their approach may be only suitable for the segmentation of single-nonoverlapping cells. Due to the challenge of cell overlapping, most of the recent studies [2, 4, 11, 12] only dealt with images with single-nonoverlapping cells. To the best of our knowledge, accurate segmentation of overlapping cervical cells has not been sufficiently addressed. The aim of this paper is to address the problem of partially overlapping cells segmentation in high resolution cervical smear images (e.g., the Herlev dataset [19]). Since the cervical cell generally has an irregular shape, the active contour model (Snake model) is a suitable tool for cervical cell image segmentation [2, 8, 23]. The dual active contour model [8] and the RGVF Snake model [2] have been proposed for segmentation of cervical cell images. The common idea of these two models lies in the fact that the nucleus is in the center of the whole cell and surrounded by the cytoplasm, and they both analyze the cell structure from a center-radial direction, which is an effective way to solve the problem of cell image segmentation. The work presented in this paper is inspired by these two models as well as the hysteresis thresholding method in the Canny [24] edge detector. Based on carefully investigating the cell contour structure from a center-radial direction, we summarize the characteristics of the cell contour points and propose a novel cell segmentation method in this paper. We first approximately represent the cell contour as a set of sparse contour points. Inspired by the hysteresis thresholding method [24], we further divide these contour points into two categories: the strong contour points (between the cytoplasm and the background) and the weak contour points (in the cell overlapping regions). Then, we consider the cell segmentation as a contour points locating problem and propose a dynamic sparse contour searching (DSCS) algorithm to search for the weak contour points based on the strong contour points. Finally, we combine the DSCS algorithm with the GVF Snake model [21] to obtain accurate cell segmentation results. In the rest of this paper, Section II summarizes the characteristics of cell contours in detail and presents the main idea as well as the framework of our method. Section III and Section IV describe the details of the individual
2 steps of the proposed segmentation method. Section V analyzes the performance of the proposed method on two cervical smear image datasets. Conclusions and future work of this paper are presented in Section VI. Due to the fact that recent studies [2, 3, 7] have already obtained high accuracy of nuclei segmentation results and the main challenge in our work is the segmentation of the whole cell in overlapping cells images, we do not show the nuclei segmentation results in this paper. II. OVERVIEW OF THE PROPOSED SEGMENTATION FRAMEWORK In cervical smear images, there are a large number of overlapping cells that make the cervical cell segmentation a challenging problem. Fig. 1 shows some cell images with overlapping cells from the Herlev dataset [19]. The difficulties for segmentation of such kind of images are mainly caused by three aspects: 1) There are plenty of small artifacts dispersedly distributed in the whole image; 2) The color (or intensity) in the cell region is not uniformly distributed due to cell overlapping and uneven illumination; and 3) Cell contours belonging to different cells in the overlapping regions intersect with each other and it is even a time-consuming task for human to distinguish the true cell boundaries.
Fig. 1. Cervical smear images containing overlapping cells.
To address the aforementioned difficulties and extract accurate cell contours, we investigated the GVF Snake [21] model for cervical cell segmentation. Because the Snake [25] is an elastic shape model, which is suitable for the description of cell contours, we use the GVF Snake as the final step of our segmentation method. However, there are two problems to be solved when applying the GVF Snake to segmentation of overlapping cells: one is how to automatically estimate the initial contour; the other is how to enhance the true edges of the cell and suppress the false edges caused by other unconcerned overlapping cells and artifacts. The aim of solving these two problems is to make the Snake converge to the true cell boundary. In this paper, we solve these two problems and propose an initial contour estimation method based on a DSCS algorithm. The main idea of our segmentation framework is briefly summarized as follows. After investigating the geometric structure of cell contours, we summarize their characteristics and make three assumptions to approximately describe a cell contour below: Assumption 1: A cell contour is composed of a set of contour points, and the nucleus is surrounded by these points. If we draw a radial line starting from the nucleus center, there would be one contour point on this line. We use the polar coordinates ( r , q ) as the representation of cell contour points and set the nucleus center as the origin. For a contour point pi , qi represents the angle between its corresponding radial line and a reference radial axis,
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m max{ f gde } f gde (i, j ) = í (8) others ïî0 , where m is a weight, and max{ f gde } is the maximum of f gde .
a2 Fig. 7. Illustration of the difference between the gradient vectors at different cell contour points.
In our method, the Sobel operator [27] is first employed to calculate the gradient edge map of the cell image denoised by the non-local means filter in Section III-A. Let W (i, j ) be the corresponding window of pixel (i, j ) with 3 ´ 3 pixels, then r the gradient g (i, j ) at pixel (i, j ) is r g (i, j ) = ( M x * W (i, j ), M y *W (i, j ) ) (5) r 2 2 g (i, j ) = ( M x * W (i, j )) + ( M y * W (i, j )) (6) where * is the operator of convolution, M x and M y are two
3 ´ 3 Sobel convolution masks.
(a)
(b)
(c)
effectively enhanced, whereas the false edges belonging to other unconcerned overlapping cells and artifacts are mostly suppressed. It should be noted that there may be a few parts of the cell contour that are not convex, and these parts are not enhanced. However, the main aim of our edge enhancement method is to suppress the false edges belonging to other unconcerned cells, and the loss of a few true cell edges may not significantly influence our method, because in the final step, we use the original edge map as well as the enhanced edge map for the final contour extraction, as described in eq. (19). In order to further suppress the false edges, we redefine f gde
(d)
Fig. 8. (a) Original cell images. (b) Sobel edge map. (c) Enhanced edge map by our method. (d) Extracted basic contours.
Then, the enhanced edge map is defined as: cos a + cos a r f gde (i, j ) = g (i, j ) × (7) 2 r where a is the angle between the gradient g (i, j ) and the corresponding radial line (as Fig. 7 shows). Fig. 8(c) shows some edge enhancement results of our method. We can find that most of the true edges belonging to the center cell are
m is used to suppress the false weak edges and make the rest steps more robust. Since a large value may result in the loss of many true cell edges, m is supposed to be a small value. IV. ACCURATE CELL CONTOUR EXTRACTION The major difficulty in overlapping cells segmentation is the correct segmentation of the cell overlapping regions. Our edge enhancement method described in the previous section can make the true cell contour more distinct, but it is still a difficult problem to effectively extract the whole cell contour. Recent studies [2, 10] have attempted to use the rough boundary of the whole cell region (including all other overlapping cells) or a circle that encloses the cell as the initial contour of the GVF Snake model. However, such initial contours obtained by these methods are far away from the true cell boundaries. Therefore, the GVF Snake is prone to be disturbed by the interferential edges in the cell overlapping regions and can hardly converge to the true cell boundary. In order to estimate the initial contour as close as possible to the true cell boundary, we propose a DSCS algorithm to achieve this objective in this section. A. Basic contour extraction In Section II, we have made three assumptions to describe a cell contour. According to Assumption 3, the cell contour can be divided into two parts: the strong contour and the weak contour. The strong contour is more obvious than the weak contour. Although the weak contour is unobvious, it is, to some extent, connected with the strong contour in the enhanced edge map (see Fig. 8). Based on this fact, the main idea of our contour extraction is that we first extract the strong contour and set it as the basic contour, and then the proposed DSCS algorithm is performed to gradually locate the weak contour points starting from the basic contour points. The basic contour belongs to the strong contour that lies between the cell cytoplasm and the background. Therefore, we first extract the background in the pre-segmentation result and further extract its rough boundary using morphological operators. Let f bkg be the background and Ñf bkg be the rough boundary of the background, then
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PAPER IDENTIFICATION NUMBER < boundaries. From Fig. 8(c), we can find that most of the true edges of the cell contour are enhanced by our edge enhancement method in Section III-C, but there are still a few edges left unobvious, which make the cell contour discontinuous. When our searching algorithm is running, there may be some angles at which the algorithm cannot find proper contour points. To solve this problem, we introduce a parameter j , which controls how many steps the algorithm will continue to search for. In addition, we use another parameter d to control the searching zone along the radial line at the corresponding angle. When the algorithm fails to find the proper contour point at a certain angle, both j and d control the region size where it continues the searching process. To some extent, j and d are related to the spatial relationship between those contour points in a small region, and their values should be carefully designed based on statistical analysis.
7
t d d = d ´ round [ ] (18) 2 where round [ ] is an operator that rounds the element in [ ] to the nearest integer. Then, the searching zone is [ r e - d d , re + d d ] , which is dynamically varying with respect to t . That is, we use a large dynamic searching zone in Stage 2 to search for the contour points that are a little far away from the basic contour points (or the located points in Stage 1). Algorithm 1 Initializing: Set the initial angle q 0 , which is selected according to the basic contour points; Set a counter t = 0 ; Angle scanning (contour searching): The angle scanning process starts from q 0 , steps by increments of Dq each time, and ends until the whole circle (2p ) has been covered. The algorithm repeatedly executes the following statements in each loop (each qi ): if (the contour point at qi has been fixed) clear the counter ( t = 0 ); continue to scan the next angle qi +1 ; else if ( t < j small ) estimate the position re of the contour point at the current angle qi by the least squares estimation; set the searching zone to [ r e - d , r e + d ] along the radial line; if (there are no intensity peaks in the searching zone) update t = t + 1 and continue to scan the next angle; else find the intensity peak (nearest to re ) of the radial edge in the searching zone and set it as the exact position of the current contour point; clear the counter ( t = 0 ); end else // t reaches its maximum, t = j small ;
Fig. 9. A brief illustration of the contour searching process based on the dynamic searching principle (the original cell image is in Fig. 8 and the dashed radial line is to be scanned).
The dynamic searching principle is described as follows. The whole searching process can be divided into two stages. In Stage 1, we set j to a small value j small and set d to a fixed value. That is, we use a small fixed searching zone to search for the contour points that are close to the basic contour points. The execution steps of Stage 1 are briefly summarized in Algorithm 1. In Stage 2, the execution steps are similar to those steps in Stage 1 except that we set j to a large value jlarge and set d to a dynamically varying value d d :
continue to scan the next angle qi +1 ; end end In each stage, the searching algorithm involves two circular scanning processes: first, it scans around the nucleus counter-clockwise; second, it scans clockwise. Afterwards, if the located contour points corresponding to the same radial line are different, we average their positions to obtain the final contour point on this radial line. The whole searching process is briefly shown in Fig. 9. In our searching algorithm, the angle scanning is performed step by step, which results in a set of sparse contour points. Moreover, a dynamic searching principle is introduced into this algorithm. Therefore, this algorithm is called a dynamic sparse contour searching (DSCS) algorithm. Fig. 10(c) shows some results of this algorithm. We can find that the contour points
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PAPER IDENTIFICATION NUMBER < method. This initial contour is actually the rough boundary of the whole cell region containing both the center cell and parts of its neighboring cells. Consequently, the Snake can hardly converge to the true cell boundary because of the interferential edges in the cell overlapping regions. On the contrary, the proposed DSCS algorithm provides the GVF Snake with a better initial contour that is very close to the true cell boundary (see Fig. 10(c)), and with this initial contour, the GVF Snake is prone to converge to the true cell boundary. More cell contour extraction results obtained by our method are provided in Fig. 12. We can see that the proposed method still works well and successfully extracts the cell contours, while the RGVF Snake is not able to extract the cell contours in overlapping cells images. The experimental results shown in Table II, Table III, Fig. 11 and Fig. 12 indicate that the proposed method is effective for segmentation of both single cell and partially overlapping cells in cervical smear images. C. Discussions The five key parameters of the proposed method are: e , m ,
d , j small , and jlarge , respectively, as described in TABLE I. These parameters were obtained after experiments in 50 randomly selected images from Dataset 1 and Dataset 2, and the numerical evaluation of our method was based on these parameters setting (in TABLE I). Actually, we randomly selected 25 cell images (including 5 single cells and 20 overlapping cells) from each dataset, and then we took these images as a training set to obtain a proper value for each parameter. We found that based on the parameters setting in TABLE I, 48 images of the training set can be well segmented, while the results of the rest 2 images are not so good. These 2 images contain either too obscure boundaries or high degrees of cell overlapping (more than a half of the cell contour is overlapped). In order to evaluate the computational efficiency of the proposed method, we used Dataset 1 to test the processing time of the individual steps (in Table IV) of our method. The average image size of Dataset 1-A is 270 ´ 296 pixels, and the average size of Dataset 1-B is 280 ´ 302 pixels. From Table IV, we can see that the edge enhancement and the DSCS steps cost the majority of the processing time. These steps are especially designed to cope with the segmentation of overlapping cells. If the proposed method is optimized in C code, the processing time would be significantly reduced. The proposed method is able to cope with the case that half (or less than a half) of the cell contour is overlapped by other cells. For the case that more than a half of the cell contour is overlapped, our method might still work well to obtain a reasonable cell contour. However, our method is not suitable for the case that the whole cell is entirely embedded in the cell clusters, e.g., the last cell in Fig. 1, where no strong contour points can be found. In addition, our method bears little relation to how many cells that the center cell is overlapped by. This can be illustrated by the second row of Fig. 11. The main concern is that the cell should contain a few strong contour parts.
10 TABLE IV AVERAGE EXECUTION TIME (IN SECONDS) OF THE PROPOSED METHOD FOR DATASET 1 Step
Dataset 1-A
Preprocessing + MF K-means Edge enhancement + DSCS Evolution of GVF Snake
Dataset 1-B
21.06
21.35
130.76
143.16
5.94
6.23
Also, the proposed method is extendable to cope with two or more overlapping cells segmentation. To address this topic, we should first extract each cell nucleus in the image; Second, set each nucleus as a center and adaptively crop the original image to a small image that just contains the whole cell belonging to this nucleus; Then, the proposed method can be applied to this small image containing one whole cell; Finally, all the extracted cell contours are combined to obtain the final results. However, in the second step, how to adaptively crop the original image according to the center nucleus is to be solved. The prior knowledge of the cell shape and some image-dependent information may be useful. In our future work, we will investigate this topic to make our method more reliable for multi-cell segmentation. VI. CONCLUSIONS AND FUTURE WORK This paper proposes an effective framework for segmentation of overlapping cells in cervical smear images. After carefully investigating the geometric structure of a cell contour, we propose to use a set of sparse contour points to approximately represent the cell contour and consider the cell contour extraction as a contour points locating problem. We first adopt a MF K-means method to eliminate the small contaminations and extract the cell nucleus and the background. Then, we propose a gradient decomposition-based edge enhancement method to enhance the edges of the center cell. Based on the cell nucleus, the background and the enhanced edge map, we propose a DSCS algorithm to locate the sparse contour points of the cell. Finally, we combine the DSCS algorithm with the GVF Snake model to extract the accurate cell contour. In the experiments, we use the ZSI and the MHD criteria to evaluate the performance of the proposed method. Experimental results show that the proposed method is more accurate and robust than the recently proposed RGVF Snake [2] for segmentation of partially overlapping cells in cervical smear images. The whole process of the proposed method is fully automatic. The proposed techniques may be also applicable to object contour extraction in other kinds of images. Our future work will focus on integrating the proposed segmentation method with the cell ROI (region of interest) locating method, which aims at extracting the cell nuclei and the whole cell regions in low resolution cervical smear images, to make complete segmentation of cervical cells in practical cervical smear images. Once the nucleus and cytoplasm of each cell in the cervical smear images are accurately extracted, we could use their morphologic and architectural properties to screen out the abnormal cervical cells and help the cytotechnologists to make
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> PAPER IDENTIFICATION NUMBER < reliable diagnosis of the disease. Our ultimate goal is to develop a computer-assisted cervical cancer diagnostic system. ACKNOWLEDGEMENTS The authors would like to thank Mr. K. Li and Mr. W. Liu for their open RGVF snake demo. REFERENCES [1] T. Kuie, Cervical Cancer: Its Causes and Prevention, Singapura: Times Book Int, 1996. [2] K. Li, Z. Lu, W. Liu, and J. Yin, “Cytoplasm and nucleus segmentation in cervical smear images using Radiating GVF snake,” Pattern Recognition, vol. 45, no. 4, pp. 1255-1264, 2012. [3] M. E. Plissiti, C. Nikou, and A. Charchanti, “Automated detection of cell nuclei in Pap smear images using morphological reconstruction and clustering,” IEEE Transactions on Information Technology in Biomedicine, vol. 15, no. 2, pp. 233-241, 2011. [4] S.-F. Yang-Mao, Y.-K. Chan, and Y.-P. Chu, “Edge enhancement nucleus and cytoplast contour detector of cervical smear Images,” IEEE Transactions on Systems, Man, and Cybernetics-Part B, vol. 38, no. 2, pp. 353-366, 2008. [5] N. A. Mat-Isa, M. Y. Mashor, and N. H. Othman, “An automated cervical pre-cancerous diagnostic system,” Artificial Intelligence in Medicine, vol. 42, no. 1, pp. 1-11, 2008. [6] WHO, Comprehensive Cervical Cancer Control: A Guide to Essential Practice: WHO Press, 2006. [7] A. Genctav, S. Aksoy, and S. Onder, “Unsupervised segmentation and classification of cervical cell images,” Pattern Recognition, vol. 45, no. 12, pp. 4151-4168, 2012. [8] P. Bamford, and B. Lovell, “Unsupervised cell nucleus segmentation with active contours,” Signal Processing, vol. 71, no. 2, pp. 203-213, 1998. [9] C. Bergmeir, M. G. Silvente, and J. M. Benitez, “Segmentation of cervical cell nuclei in high-resolution microscopic images: A new algorithm and a web-based software framework,” Computer methods and programs in biomedicine, vol. 107, no. 3, pp. 497-512, 2012. [10] N. M. Harandi, S. Sadri, N. A. Moghaddam, and R. Amirfattahi, “An automated method for segmentation of epithelial cervical cells in images of ThinPrep,” Journal of Medical Systems, vol. 34, no. 6, pp. 1043-1058, 2010. [11] C.-H. Lin, Y.-K. Chan, and C.-C. Chen, “Detection and segmentation of cervical cell cytoplast and nucleus,” International Journal of Imaging Systems and Technology, vol. 19, no. 3, pp. 260-270, 2009. [12] P.-Y. Pai, C.-C. Chang, and Y.-K. Chan, “Nucleus and cytoplast contour detector from a cervical smear image,” Expert Systems with Applications, vol. 39, no. 1, pp. 154-161, 2012. [13] M. E. Plissiti, C. Nikou, and A. Charchanti, “Combining shape, texture and intensity features for cell nuclei extraction in Pap smear images,” Pattern Recognition Letters, vol. 32, no. 6, pp. 838-853, 2011. [14] M.-H. Tsai, Y.-K. Chan, Z.-Z. Lin, S.-F. Yang-Mao, and P.-C. Huang, “Nucleus and cytoplast contour detector of cervical smear image,” Pattern Recognition Letters, vol. 29, no. 9, pp. 1441-1453, 2008. [15] H. S. Wu, J. Gil, and J. Barba, “Optimal segmentation of cell images,” in IEE Proceedings of Vision, Image and Signal Processing, 1998, pp. 50-56. [16] P. Bamford, and B. C. Lovell, “A water immersion algorithm for cytological image segmentation,” in Proceedings of the APRS Image Segmentation Workshop, Sydney, Australia, 1996, pp. 75-79. [17] C. Park, J. Z. Huang, J. X. Ji, and Y. Ding, “Segmentation, inference, and classification of partially overlapping nanoparticles,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 3, pp. 669-681, 2013. [18] K. Peng, X. Chen, D. Zhou, Y. Liu and Y. Zhai, “3-D reconstruction using image sequences based on projective depth and simplified iterative closest point,” Optical Engineering, vol. 51, no. 2, pp. 021110-1, 2012. [19] J. Jantzen, and G. Dounias, “Analysis of Pap-smear image data,” in Proceedings of the Nature-Inspired Smart Information Systems 2nd Annual Symposium, 2006.
11 [20] L. Zhang, S. Chen, T. Wang, Y. Chen, S. Liu, and M. Li, “A practical segmentation method for automated screening of cervical cytology,” in 2011 International Conference on Intelligent Computation and Bio-Medical Instrumentation, 2011, pp. 140-143. [21] C. Xu, and J. L. Prince, “Snakes, shapes, and Gradient Vector Flow,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 359-369, 1998. [22] N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 9, no. 1, pp. 62-66, 1979. [23] M. E. Plissiti, C. Nikou, and A. Charchanti, “Accurate localization of cell nuclei in Pap smear images using Gradient Vector Flow deformable models,” in Proceedings of 3rd International Conference on Bio-inspired Signals and Systems (BIOSIGNALS 2010), Valencia, Spain, 2010, pp. 284-289. [24] J. Canny, “A computational approach to edge detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, 1986. [25] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active contour models,” International Journal of Computer Vision, vol. 1, no. 4, pp. 321-331, 1988. [26] A. Buades, B. Coll, and J. M. Morel, “Self-similarity-based image denoising,” Communications of the ACM, vol. 54, no. 5, pp. 109-117, 2011. [27] R. C. Gonzalez, and R. E. Woods, Digital Image Processing, Second ed. ed., New York: Prentice Hall, 2002. [28] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, New Jersey, USA: Prentice Hall PTR, 1993. [29] A. Zijdenbos, B. Dawant, R. Margolin, and A. Palmer, “Morphometric analysis of white matter lesions in MR images: method and validation,” IEEE Transactions on Medical Imaging, vol. 13, no. 4, pp. 716-724, 1994. [30] M. Sezgin, and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” Journal of Electronic Imaging, vol. 13, no. 1, pp. 146-165, 2004. [31] L. R. Dice, “Measures of the amount of ecologic association between species,” Ecology, vol. 26, no. 3, pp. 297-302, 1945.
Tao Guan is a Ph.D. student at National University of Defense Technology, China. He received his Master degree in information and communication engineering from National University of Defense Technology in 2009. His research interests include medical image processing, computer vision.
Dongxiang Zhou received the Ph.D. degree in information and communication engineering from National University of Defense Technology, China, in 2000. He is currently an assistant professor at National University of Defense Technology. His major research interests concern computer vision, image processing.
Yunhui Liu received his Ph.D. degree in mathematical engineering and information physics from the University of Tokyo, Japan, in 1992. He is currently a professor at The Chinese University of Hong Kong, China. His research interests include visual servoing, robotics and automatic control. He is a fellow of IEEE.
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PAPER IDENTIFICATION NUMBER < Since the Herlev dataset [19] is publicly available, the second topic has also attracted much attention. Mao-Yang et al. [4] proposed an edge-based method to extract cell contours in single-cell cervical smear images. They employed a trim-meaning filter and a bi-group enhancer to remove noise and enhance the obscure edges in cell images, respectively. Then, they proposed a mean vector difference enhancer using the GVF vectors [21] to further brighten the obscure edges. The cell contours are finally obtained by automatic thresholding [22] and morphological operations. Li et al. [2] proposed to extract cell contours using the Radiating GVF (RGVF) Snake model. The edge and region information are combined to solve the cell segmentation problem. A spatial K-means clustering algorithm is used for rough extraction of the cell nucleus and cytoplasm. Then, a stack-based refinement method is proposed to compute the radiating edge map. The GVF Snake model [21] is finally employed to extract the cell contour. High accuracy of the segmentation result has been shown in their work. However, their approach may be only suitable for the segmentation of single-nonoverlapping cells. Due to the challenge of cell overlapping, most of the recent studies [2, 4, 11, 12] only dealt with images with single-nonoverlapping cells. To the best of our knowledge, accurate segmentation of overlapping cervical cells has not been sufficiently addressed. The aim of this paper is to address the problem of partially overlapping cells segmentation in high resolution cervical smear images (e.g., the Herlev dataset [19]). Since the cervical cell generally has an irregular shape, the active contour model (Snake model) is a suitable tool for cervical cell image segmentation [2, 8, 23]. The dual active contour model [8] and the RGVF Snake model [2] have been proposed for segmentation of cervical cell images. The common idea of these two models lies in the fact that the nucleus is in the center of the whole cell and surrounded by the cytoplasm, and they both analyze the cell structure from a center-radial direction, which is an effective way to solve the problem of cell image segmentation. The work presented in this paper is inspired by these two models as well as the hysteresis thresholding method in the Canny [24] edge detector. Based on carefully investigating the cell contour structure from a center-radial direction, we summarize the characteristics of the cell contour points and propose a novel cell segmentation method in this paper. We first approximately represent the cell contour as a set of sparse contour points. Inspired by the hysteresis thresholding method [24], we further divide these contour points into two categories: the strong contour points (between the cytoplasm and the background) and the weak contour points (in the cell overlapping regions). Then, we consider the cell segmentation as a contour points locating problem and propose a dynamic sparse contour searching (DSCS) algorithm to search for the weak contour points based on the strong contour points. Finally, we combine the DSCS algorithm with the GVF Snake model [21] to obtain accurate cell segmentation results. In the rest of this paper, Section II summarizes the characteristics of cell contours in detail and presents the main idea as well as the framework of our method. Section III and Section IV describe the details of the individual
2 steps of the proposed segmentation method. Section V analyzes the performance of the proposed method on two cervical smear image datasets. Conclusions and future work of this paper are presented in Section VI. Due to the fact that recent studies [2, 3, 7] have already obtained high accuracy of nuclei segmentation results and the main challenge in our work is the segmentation of the whole cell in overlapping cells images, we do not show the nuclei segmentation results in this paper. II. OVERVIEW OF THE PROPOSED SEGMENTATION FRAMEWORK In cervical smear images, there are a large number of overlapping cells that make the cervical cell segmentation a challenging problem. Fig. 1 shows some cell images with overlapping cells from the Herlev dataset [19]. The difficulties for segmentation of such kind of images are mainly caused by three aspects: 1) There are plenty of small artifacts dispersedly distributed in the whole image; 2) The color (or intensity) in the cell region is not uniformly distributed due to cell overlapping and uneven illumination; and 3) Cell contours belonging to different cells in the overlapping regions intersect with each other and it is even a time-consuming task for human to distinguish the true cell boundaries.
Fig. 1. Cervical smear images containing overlapping cells.
To address the aforementioned difficulties and extract accurate cell contours, we investigated the GVF Snake [21] model for cervical cell segmentation. Because the Snake [25] is an elastic shape model, which is suitable for the description of cell contours, we use the GVF Snake as the final step of our segmentation method. However, there are two problems to be solved when applying the GVF Snake to segmentation of overlapping cells: one is how to automatically estimate the initial contour; the other is how to enhance the true edges of the cell and suppress the false edges caused by other unconcerned overlapping cells and artifacts. The aim of solving these two problems is to make the Snake converge to the true cell boundary. In this paper, we solve these two problems and propose an initial contour estimation method based on a DSCS algorithm. The main idea of our segmentation framework is briefly summarized as follows. After investigating the geometric structure of cell contours, we summarize their characteristics and make three assumptions to approximately describe a cell contour below: Assumption 1: A cell contour is composed of a set of contour points, and the nucleus is surrounded by these points. If we draw a radial line starting from the nucleus center, there would be one contour point on this line. We use the polar coordinates ( r , q ) as the representation of cell contour points and set the nucleus center as the origin. For a contour point pi , qi represents the angle between its corresponding radial line and a reference radial axis,
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> PAPER IDENTIFICATION NUMBER
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m max{ f gde } f gde (i, j ) = í (8) others ïî0 , where m is a weight, and max{ f gde } is the maximum of f gde .
a2 Fig. 7. Illustration of the difference between the gradient vectors at different cell contour points.
In our method, the Sobel operator [27] is first employed to calculate the gradient edge map of the cell image denoised by the non-local means filter in Section III-A. Let W (i, j ) be the corresponding window of pixel (i, j ) with 3 ´ 3 pixels, then r the gradient g (i, j ) at pixel (i, j ) is r g (i, j ) = ( M x * W (i, j ), M y *W (i, j ) ) (5) r 2 2 g (i, j ) = ( M x * W (i, j )) + ( M y * W (i, j )) (6) where * is the operator of convolution, M x and M y are two
3 ´ 3 Sobel convolution masks.
(a)
(b)
(c)
effectively enhanced, whereas the false edges belonging to other unconcerned overlapping cells and artifacts are mostly suppressed. It should be noted that there may be a few parts of the cell contour that are not convex, and these parts are not enhanced. However, the main aim of our edge enhancement method is to suppress the false edges belonging to other unconcerned cells, and the loss of a few true cell edges may not significantly influence our method, because in the final step, we use the original edge map as well as the enhanced edge map for the final contour extraction, as described in eq. (19). In order to further suppress the false edges, we redefine f gde
(d)
Fig. 8. (a) Original cell images. (b) Sobel edge map. (c) Enhanced edge map by our method. (d) Extracted basic contours.
Then, the enhanced edge map is defined as: cos a + cos a r f gde (i, j ) = g (i, j ) × (7) 2 r where a is the angle between the gradient g (i, j ) and the corresponding radial line (as Fig. 7 shows). Fig. 8(c) shows some edge enhancement results of our method. We can find that most of the true edges belonging to the center cell are
m is used to suppress the false weak edges and make the rest steps more robust. Since a large value may result in the loss of many true cell edges, m is supposed to be a small value. IV. ACCURATE CELL CONTOUR EXTRACTION The major difficulty in overlapping cells segmentation is the correct segmentation of the cell overlapping regions. Our edge enhancement method described in the previous section can make the true cell contour more distinct, but it is still a difficult problem to effectively extract the whole cell contour. Recent studies [2, 10] have attempted to use the rough boundary of the whole cell region (including all other overlapping cells) or a circle that encloses the cell as the initial contour of the GVF Snake model. However, such initial contours obtained by these methods are far away from the true cell boundaries. Therefore, the GVF Snake is prone to be disturbed by the interferential edges in the cell overlapping regions and can hardly converge to the true cell boundary. In order to estimate the initial contour as close as possible to the true cell boundary, we propose a DSCS algorithm to achieve this objective in this section. A. Basic contour extraction In Section II, we have made three assumptions to describe a cell contour. According to Assumption 3, the cell contour can be divided into two parts: the strong contour and the weak contour. The strong contour is more obvious than the weak contour. Although the weak contour is unobvious, it is, to some extent, connected with the strong contour in the enhanced edge map (see Fig. 8). Based on this fact, the main idea of our contour extraction is that we first extract the strong contour and set it as the basic contour, and then the proposed DSCS algorithm is performed to gradually locate the weak contour points starting from the basic contour points. The basic contour belongs to the strong contour that lies between the cell cytoplasm and the background. Therefore, we first extract the background in the pre-segmentation result and further extract its rough boundary using morphological operators. Let f bkg be the background and Ñf bkg be the rough boundary of the background, then
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PAPER IDENTIFICATION NUMBER < boundaries. From Fig. 8(c), we can find that most of the true edges of the cell contour are enhanced by our edge enhancement method in Section III-C, but there are still a few edges left unobvious, which make the cell contour discontinuous. When our searching algorithm is running, there may be some angles at which the algorithm cannot find proper contour points. To solve this problem, we introduce a parameter j , which controls how many steps the algorithm will continue to search for. In addition, we use another parameter d to control the searching zone along the radial line at the corresponding angle. When the algorithm fails to find the proper contour point at a certain angle, both j and d control the region size where it continues the searching process. To some extent, j and d are related to the spatial relationship between those contour points in a small region, and their values should be carefully designed based on statistical analysis.
7
t d d = d ´ round [ ] (18) 2 where round [ ] is an operator that rounds the element in [ ] to the nearest integer. Then, the searching zone is [ r e - d d , re + d d ] , which is dynamically varying with respect to t . That is, we use a large dynamic searching zone in Stage 2 to search for the contour points that are a little far away from the basic contour points (or the located points in Stage 1). Algorithm 1 Initializing: Set the initial angle q 0 , which is selected according to the basic contour points; Set a counter t = 0 ; Angle scanning (contour searching): The angle scanning process starts from q 0 , steps by increments of Dq each time, and ends until the whole circle (2p ) has been covered. The algorithm repeatedly executes the following statements in each loop (each qi ): if (the contour point at qi has been fixed) clear the counter ( t = 0 ); continue to scan the next angle qi +1 ; else if ( t < j small ) estimate the position re of the contour point at the current angle qi by the least squares estimation; set the searching zone to [ r e - d , r e + d ] along the radial line; if (there are no intensity peaks in the searching zone) update t = t + 1 and continue to scan the next angle; else find the intensity peak (nearest to re ) of the radial edge in the searching zone and set it as the exact position of the current contour point; clear the counter ( t = 0 ); end else // t reaches its maximum, t = j small ;
Fig. 9. A brief illustration of the contour searching process based on the dynamic searching principle (the original cell image is in Fig. 8 and the dashed radial line is to be scanned).
The dynamic searching principle is described as follows. The whole searching process can be divided into two stages. In Stage 1, we set j to a small value j small and set d to a fixed value. That is, we use a small fixed searching zone to search for the contour points that are close to the basic contour points. The execution steps of Stage 1 are briefly summarized in Algorithm 1. In Stage 2, the execution steps are similar to those steps in Stage 1 except that we set j to a large value jlarge and set d to a dynamically varying value d d :
continue to scan the next angle qi +1 ; end end In each stage, the searching algorithm involves two circular scanning processes: first, it scans around the nucleus counter-clockwise; second, it scans clockwise. Afterwards, if the located contour points corresponding to the same radial line are different, we average their positions to obtain the final contour point on this radial line. The whole searching process is briefly shown in Fig. 9. In our searching algorithm, the angle scanning is performed step by step, which results in a set of sparse contour points. Moreover, a dynamic searching principle is introduced into this algorithm. Therefore, this algorithm is called a dynamic sparse contour searching (DSCS) algorithm. Fig. 10(c) shows some results of this algorithm. We can find that the contour points
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PAPER IDENTIFICATION NUMBER < method. This initial contour is actually the rough boundary of the whole cell region containing both the center cell and parts of its neighboring cells. Consequently, the Snake can hardly converge to the true cell boundary because of the interferential edges in the cell overlapping regions. On the contrary, the proposed DSCS algorithm provides the GVF Snake with a better initial contour that is very close to the true cell boundary (see Fig. 10(c)), and with this initial contour, the GVF Snake is prone to converge to the true cell boundary. More cell contour extraction results obtained by our method are provided in Fig. 12. We can see that the proposed method still works well and successfully extracts the cell contours, while the RGVF Snake is not able to extract the cell contours in overlapping cells images. The experimental results shown in Table II, Table III, Fig. 11 and Fig. 12 indicate that the proposed method is effective for segmentation of both single cell and partially overlapping cells in cervical smear images. C. Discussions The five key parameters of the proposed method are: e , m ,
d , j small , and jlarge , respectively, as described in TABLE I. These parameters were obtained after experiments in 50 randomly selected images from Dataset 1 and Dataset 2, and the numerical evaluation of our method was based on these parameters setting (in TABLE I). Actually, we randomly selected 25 cell images (including 5 single cells and 20 overlapping cells) from each dataset, and then we took these images as a training set to obtain a proper value for each parameter. We found that based on the parameters setting in TABLE I, 48 images of the training set can be well segmented, while the results of the rest 2 images are not so good. These 2 images contain either too obscure boundaries or high degrees of cell overlapping (more than a half of the cell contour is overlapped). In order to evaluate the computational efficiency of the proposed method, we used Dataset 1 to test the processing time of the individual steps (in Table IV) of our method. The average image size of Dataset 1-A is 270 ´ 296 pixels, and the average size of Dataset 1-B is 280 ´ 302 pixels. From Table IV, we can see that the edge enhancement and the DSCS steps cost the majority of the processing time. These steps are especially designed to cope with the segmentation of overlapping cells. If the proposed method is optimized in C code, the processing time would be significantly reduced. The proposed method is able to cope with the case that half (or less than a half) of the cell contour is overlapped by other cells. For the case that more than a half of the cell contour is overlapped, our method might still work well to obtain a reasonable cell contour. However, our method is not suitable for the case that the whole cell is entirely embedded in the cell clusters, e.g., the last cell in Fig. 1, where no strong contour points can be found. In addition, our method bears little relation to how many cells that the center cell is overlapped by. This can be illustrated by the second row of Fig. 11. The main concern is that the cell should contain a few strong contour parts.
10 TABLE IV AVERAGE EXECUTION TIME (IN SECONDS) OF THE PROPOSED METHOD FOR DATASET 1 Step
Dataset 1-A
Preprocessing + MF K-means Edge enhancement + DSCS Evolution of GVF Snake
Dataset 1-B
21.06
21.35
130.76
143.16
5.94
6.23
Also, the proposed method is extendable to cope with two or more overlapping cells segmentation. To address this topic, we should first extract each cell nucleus in the image; Second, set each nucleus as a center and adaptively crop the original image to a small image that just contains the whole cell belonging to this nucleus; Then, the proposed method can be applied to this small image containing one whole cell; Finally, all the extracted cell contours are combined to obtain the final results. However, in the second step, how to adaptively crop the original image according to the center nucleus is to be solved. The prior knowledge of the cell shape and some image-dependent information may be useful. In our future work, we will investigate this topic to make our method more reliable for multi-cell segmentation. VI. CONCLUSIONS AND FUTURE WORK This paper proposes an effective framework for segmentation of overlapping cells in cervical smear images. After carefully investigating the geometric structure of a cell contour, we propose to use a set of sparse contour points to approximately represent the cell contour and consider the cell contour extraction as a contour points locating problem. We first adopt a MF K-means method to eliminate the small contaminations and extract the cell nucleus and the background. Then, we propose a gradient decomposition-based edge enhancement method to enhance the edges of the center cell. Based on the cell nucleus, the background and the enhanced edge map, we propose a DSCS algorithm to locate the sparse contour points of the cell. Finally, we combine the DSCS algorithm with the GVF Snake model to extract the accurate cell contour. In the experiments, we use the ZSI and the MHD criteria to evaluate the performance of the proposed method. Experimental results show that the proposed method is more accurate and robust than the recently proposed RGVF Snake [2] for segmentation of partially overlapping cells in cervical smear images. The whole process of the proposed method is fully automatic. The proposed techniques may be also applicable to object contour extraction in other kinds of images. Our future work will focus on integrating the proposed segmentation method with the cell ROI (region of interest) locating method, which aims at extracting the cell nuclei and the whole cell regions in low resolution cervical smear images, to make complete segmentation of cervical cells in practical cervical smear images. Once the nucleus and cytoplasm of each cell in the cervical smear images are accurately extracted, we could use their morphologic and architectural properties to screen out the abnormal cervical cells and help the cytotechnologists to make
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> PAPER IDENTIFICATION NUMBER < reliable diagnosis of the disease. Our ultimate goal is to develop a computer-assisted cervical cancer diagnostic system. ACKNOWLEDGEMENTS The authors would like to thank Mr. K. Li and Mr. W. Liu for their open RGVF snake demo. REFERENCES [1] T. Kuie, Cervical Cancer: Its Causes and Prevention, Singapura: Times Book Int, 1996. [2] K. Li, Z. Lu, W. Liu, and J. Yin, “Cytoplasm and nucleus segmentation in cervical smear images using Radiating GVF snake,” Pattern Recognition, vol. 45, no. 4, pp. 1255-1264, 2012. [3] M. E. Plissiti, C. Nikou, and A. Charchanti, “Automated detection of cell nuclei in Pap smear images using morphological reconstruction and clustering,” IEEE Transactions on Information Technology in Biomedicine, vol. 15, no. 2, pp. 233-241, 2011. [4] S.-F. Yang-Mao, Y.-K. Chan, and Y.-P. Chu, “Edge enhancement nucleus and cytoplast contour detector of cervical smear Images,” IEEE Transactions on Systems, Man, and Cybernetics-Part B, vol. 38, no. 2, pp. 353-366, 2008. [5] N. A. Mat-Isa, M. Y. Mashor, and N. H. Othman, “An automated cervical pre-cancerous diagnostic system,” Artificial Intelligence in Medicine, vol. 42, no. 1, pp. 1-11, 2008. [6] WHO, Comprehensive Cervical Cancer Control: A Guide to Essential Practice: WHO Press, 2006. [7] A. Genctav, S. Aksoy, and S. Onder, “Unsupervised segmentation and classification of cervical cell images,” Pattern Recognition, vol. 45, no. 12, pp. 4151-4168, 2012. [8] P. Bamford, and B. Lovell, “Unsupervised cell nucleus segmentation with active contours,” Signal Processing, vol. 71, no. 2, pp. 203-213, 1998. [9] C. Bergmeir, M. G. Silvente, and J. M. Benitez, “Segmentation of cervical cell nuclei in high-resolution microscopic images: A new algorithm and a web-based software framework,” Computer methods and programs in biomedicine, vol. 107, no. 3, pp. 497-512, 2012. [10] N. M. Harandi, S. Sadri, N. A. Moghaddam, and R. Amirfattahi, “An automated method for segmentation of epithelial cervical cells in images of ThinPrep,” Journal of Medical Systems, vol. 34, no. 6, pp. 1043-1058, 2010. [11] C.-H. Lin, Y.-K. Chan, and C.-C. Chen, “Detection and segmentation of cervical cell cytoplast and nucleus,” International Journal of Imaging Systems and Technology, vol. 19, no. 3, pp. 260-270, 2009. [12] P.-Y. Pai, C.-C. Chang, and Y.-K. Chan, “Nucleus and cytoplast contour detector from a cervical smear image,” Expert Systems with Applications, vol. 39, no. 1, pp. 154-161, 2012. [13] M. E. Plissiti, C. Nikou, and A. Charchanti, “Combining shape, texture and intensity features for cell nuclei extraction in Pap smear images,” Pattern Recognition Letters, vol. 32, no. 6, pp. 838-853, 2011. [14] M.-H. Tsai, Y.-K. Chan, Z.-Z. Lin, S.-F. Yang-Mao, and P.-C. Huang, “Nucleus and cytoplast contour detector of cervical smear image,” Pattern Recognition Letters, vol. 29, no. 9, pp. 1441-1453, 2008. [15] H. S. Wu, J. Gil, and J. Barba, “Optimal segmentation of cell images,” in IEE Proceedings of Vision, Image and Signal Processing, 1998, pp. 50-56. [16] P. Bamford, and B. C. Lovell, “A water immersion algorithm for cytological image segmentation,” in Proceedings of the APRS Image Segmentation Workshop, Sydney, Australia, 1996, pp. 75-79. [17] C. Park, J. Z. Huang, J. X. Ji, and Y. Ding, “Segmentation, inference, and classification of partially overlapping nanoparticles,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 3, pp. 669-681, 2013. [18] K. Peng, X. Chen, D. Zhou, Y. Liu and Y. Zhai, “3-D reconstruction using image sequences based on projective depth and simplified iterative closest point,” Optical Engineering, vol. 51, no. 2, pp. 021110-1, 2012. [19] J. Jantzen, and G. Dounias, “Analysis of Pap-smear image data,” in Proceedings of the Nature-Inspired Smart Information Systems 2nd Annual Symposium, 2006.
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Tao Guan is a Ph.D. student at National University of Defense Technology, China. He received his Master degree in information and communication engineering from National University of Defense Technology in 2009. His research interests include medical image processing, computer vision.
Dongxiang Zhou received the Ph.D. degree in information and communication engineering from National University of Defense Technology, China, in 2000. He is currently an assistant professor at National University of Defense Technology. His major research interests concern computer vision, image processing.
Yunhui Liu received his Ph.D. degree in mathematical engineering and information physics from the University of Tokyo, Japan, in 1992. He is currently a professor at The Chinese University of Hong Kong, China. His research interests include visual servoing, robotics and automatic control. He is a fellow of IEEE.
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