Statistics-Based Initial Contour Detection of Optic Disc on a Retinal Fundus Image Using Active Contour Model

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1 Journal of Medical and Biological Engineering, 33(4): Statistics-Based Initial Contour Detection of Optic Disc on a Retinal Fundus Image Using Active Contour Model Huang-Tsun Chen 1 Chuin-Mu Wang 2,* Yung-Kuan Chan 3 Shys-Fan Yang-Mao 3 Yung-Fu Chen 4 Sheng-Fuu Lin 1 1 Department of Electrical and Control Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, ROC 2 Department of Computer Science and Information and Engineering, National Chin-Yi University of Technology, Taichung 411, Taiwan, ROC 3 Department of Management Information Systems, National Chung Hsing University, Taichung 402, Taiwan, ROC 4 College of Management, Central Taiwan University of Science and Technology, Taichung 406, Taiwan, ROC Received 2 Aug 2012; Accepted 4 Oct 2012; doi: /jmbe.1243 Abstract The retinal optic disc is the region from where the central retinal artery and optical nerve of the retina emanate. Hence, it often serves as an important landmark and reference for other features in a retinal fundus image. The features obtained from a fundus images are often helpful in the diagnosis of various eye diseases. Locating and segmenting the optic disc are key pre-processing steps for extracting retinal features. This paper proposes a statistics-based method for locating a rectangular region of interest (ROI) containing the optic disc in a retinal fundus image. From a set of candidate rectangular regions, the method chooses the ROI using statistical features, namely the mean, standard deviation, and skewness of the pixel gray levels in the candidate regions. Since an optic disc is approximately round or slightly oval in the vertical direction, this study treats the maximal inscribed circle of the ROI as the initial contour of the optic disc and uses an active contour model (ACM) to precisely segment the optic disc further based on the initial contour. The experimental results show that the proposed statistics-based method combined with an ACM provides impressive performance in the segmentation of optic discs. Keywords: Retinal fundus image, Optic disc, Eigenface, Active contour model (ACM) 1. Introduction Retinal fundus images are widely used in the clinical diagnosis of eye diseases such as diabetic retinopathy and glaucoma. An optic disc is normally a circular structure, but is known to change shape due to nerve damage in glaucoma. Its shape can therefore be used in the diagnosis and assessment of the treatment of this disease [1]. The optic disc on the retina is the region from which the central retinal artery and the optical nerve emanate. Hence, it often serves as an important landmark and reference for other features in a retinal fundus image. For example, the blood vessels on the retina radiating from the optic disc can be used to identify the fovea [2], and the optic disc dimensions can be used for glaucoma diagnosis [3, 4]. A normal optic disc is orange to pink in color. A pale disc is an optic disc which varies in color from a pale pink or orange color to white. A pale disc is an indication of a disease condition. Locating and segmenting the optic disc are key * Corresponding author: Chuin-Mu Wang Tel: ext cmwang@ncut.edu.tw pre-processing steps for extracting retina features in many algorithms [1, 2]. Optic disc segmentation is very important for the development of an automatic self-diagnosis system for eye disease [5, 6, 7]. In a normal fundus image, the optic disc is the brightest part and has a round or slightly vertical oval shape. Li and Chutatape [2] proposed an eigenface method [8] that automatically locates the optic disc. This method first determines the candidate regions by clustering the brightest pixels in the image. The minimal distance between the original retinal image and its projection onto the disc space is considered to be the center of the optic disc. They later combined the eigenface method with a modified active shape model (ASM) [9] to detect the boundary of the optic disc in a retinal fundus image [3]. Other study proposed a method for segmenting blood vessels that complements local vessel attributes with region-based attributes of the network structure [10]. The only consistently visible property of the optic nerve is that it is the convergence point of the blood vessel network. Therefore, the researchers [11] also proposed a method of optic nerve detection that finds the convergence of blood vessels based on their earlier blood vessel segmentation [10]. In the absence of a unique and strongly identifiable convergence, the

2 389 J. Med. Biol. Eng., Vol. 33 No method uses brightness as a secondary feature for optic nerve detection. Various types of pathology can be present depending on the progress of a disease. For instance, drusen and soft and hard exudates, which appear as groups of bright dots on the retina, may appear on an abnormal retina affected by diabetic retinopathy. They are signs of current or past macular edema, a serious complication of diabetic retinopathy. Drusen and soft and hard exudates may result in the incorrect identification of the optic disc since their gray level and intensity are similar to those of the optic disc. The true optic disc has bright and even regions, whereas those of drusen and soft and hard exudates are vague and uneven, creating false optic discs. The active contour model (ACM) [12] has been applied to extract anatomical structures in medical images, including the segmentation of the optic disc [1,13]. The performance of ACM highly depends on the given initial contour. In this paper, a statistics-based method is proposed to automatically locate an approximate contour of the optic disc that is then used as the initial contour of ACM for segmenting the optic disc. The statistics-based method distinguishes the region of interest (ROI) from other candidate regions based on the mean, standard deviation, and skewness of their pixel gray levels. The ROI is a rectangular area which contains the optic disc. The mean value of the pixel gray levels in a region describes the gray-level intensity, the standard deviation represents the variation of the pixel gray levels, and the skewness indicates the direction and shift degree of the mean of the pixel gray levels in the region. The gray-level variation of the pixels in a region is also called the gray-level complexity of the region. The statistics-based method considers the maximal inscribed circle of the ROI to be the initial contour of the optic disc, and then the gradient vector flow (GVF) ACM [12] is used to draw the contour of the optic disc more precisely. The simple statistics-based method provides a good initial contour for the ACM to extract the optic disc. Experimental results show that the proposed method is able to detect the location of the optic disc more precisely than can the eigenface method [2]. However, the performance of the ACM highly depends on the given initial contour. 2. Materials and methods This study uses 46 retinal fundus images provided by the Taichung Veterans General Hospital in Taiwan, R.O.C., as the test data. Each image ( pixels) is transformed into a gray-level image. Generally, optic discs vary in size even for a given person. The size of the optic disc in the left eye is often different from that in the right eye for a person. Since most optic discs are round or slightly oval, an optic disc can be enclosed by a minimum boundary rectangle. The optic discs in the 46 retinal fundus images vary in size ranging from to pixels. 23 images were randomly selected from the 46 retinal fundus images as training images; the others were used as test images for verifying the performance of the statistics-based method. The statistics-based method has two phases: a training phase and a testing phase. In the training phase, the statistical features of the true and false optic discs are extracted from the training images and used to analyze differences in the discs. In the testing phase, the region which encloses the true optic disc is first located, and then ACM is adopted to sever the optic disc using the inscribed circle of the region as the initial contour. The two phases are described in detail below. 2.1 Training phase Since the sizes of the optic discs in all 46 retinal fundus images range from to pixels, the method divides a retinal fundus image into regions of pixels. If a region contains most of the optic disc, it is considered to be the ROI; otherwise, it is considered to be a non-roi. On an abnormal retinal fundus image, many exudates often cling to blood vessels. The gray-level intensity of the exudates is generally similar to that of an optic disc, and the blood vessels in the retinal fundus radiate outward from the optic disc. Hence, the eight adjacent regions, each containing pixels, of the ROI are selected to investigate the differences between the ROI and the non-rois based on their statistical features. Since non-rois looks more vague and uneven than the ROI, the proposed statistics-based method computes the means (MEAN), standard deviations (STD), and skewnesses (SK) of the ROI and the non-rois. All the MEANs, STDs, and SKs of the ROIs are then used to obtain the linear regression equations that respectively express the relationships between MEANs and STDs; between STDs and SKs; and between SKs and MEANs of the ROIs. Generally, there are some big blood vessels inside the optic disc. The pixels of blood vessels are usually much darker than other pixels in the optic disc. These dark pixels may cause difficulty in deriving the above three relationships. Hence, only the b% brightest pixels in a region, called bright pixels, are taken into account to compute the MEAN, STD, and SK of the region. Figure 1 shows the ROI and its eight adjacent regions in a retinal fundus image. Figure 1 states the relationship between the MEANs and STDs of the nine regions, where signifies a non-roi and stands for the ROI. The line segments L 1, L 2, and L 3 in Fig. 2 are the linear regression equations of the three relationships between MEANs and STDs, between SKs and MEANs, and between STDs and SKs of the ROIs, respectively, in the 23 training images. Let the variables Mean, Std, and Sk be the MEAN, STD, and SK of a ROI. Also, let: L 1 : Mean + a 1 Std + b 1 = 0; L 2 : Mean + a2 Sk+b2 = 0; and L 3 : Std + a3 Sk + b3 = 0. Here L 2 is the perpendicular bisector of L 2 ; a 1, a 2, a 3 are the coefficient terms; b 1, b 2, and b 3 are constant terms of equations L 1, L 2, and L 3, respectively. Figure 2 shows that most non-rois are located at the bottom-left side of L 1. Consider the MEAN value MEAN and STD value STD of a region. If the coordinates (MEAN,STD) are located on the bottom-left side of L1, and farther from L1, it is more likely that the region is a non-roi than a ROI; otherwise, the region is more likely to be a ROI than a non-roi. Therefore, the possibility of the region being a non-roi is defined as

3 Initial Contour Detection of Optic Disc 390 MEAN a1 STD b1 b 1. Similarly, from Fig. 2 and 2(c), the possibilities of the region being a ROI are MEAN a2 SK b2 b STD a3 SK b3 and, where SK is the SK value of the region. b3 Hence, the possibility P(MEAN, STD, SK) of the region being a ROI can be defined as: 2 regions. The shadow regions in Fig. 3(d) are the three selected candidate regions of the retinal fundus image in Fig. 3. L 1 P MEAN STD SK MEAN a STD MEAN a SK STD a SK b b b (,, ) L 2 L' 2 Figure 1. The ROI and its eight adjacent regions on a retinal fundus image; the relationship between their MEANs and STDs. points are from non-roi s and point from the ROI. 2.2 Testing phase L 3 For a given retinal fundus image, the image is divided into overlapping regions of pixels. Let (l, u) and (r, d) be the top-left and the bottom-right coordinates of region B, respectively. Then, the top-left and the bottom-right coordinates of the left region adjacent to B are (l + 2, u) and (r + 2, d), respectively, and those of the region below B are (l, u + 2 ) and (r, d + 2 ), respectively. Figure 3(c) shows the overlapping segmentation of the retinal fundus image in Fig. 3. The rectangles in Fig. 3(c) respectively encircle the first and second regions. The optic disc is usually the brightest part of the retinal fundus image. First, the statistics-based method only considers the regions most of whose pixels are extremely bright. The pixels of the image with the highest 1% gray-level intensity are selected. We call the selected. Figure 3 shows the white pixels of the retinal fundus image in Fig. 3. Second, three regions which do not adjoin one another and have the highest numbers of white pixels are chosen as the candidate regions. If two candidate regions are next to each other, they may be mapped to the same candidate regions in the next step. Hence, three discontinuous regions are selected to be the candidate (c) Figure 2. The relationships between: mean and STD; between mean and skewness; and (c)between STD and skewness. Next, the positions of the three selected candidate regions are fine-tuned. For each pixel p(i, j), which is located at coordinates (i, j) in the image, in one candidate region R, the method calculates the number N'(i, j) of white pixels in the region R'(i, j) whose top-left and bottom-right coordinates are respectively (i , j ) and (I + 2, j + 2 ), and substitutes R'(i, j) for R as the candidate region if N'(i, j) is greater than the number of white pixels in R. Figure 3(e) shows the three candidate regions of the retinal fundus image after fine-tuning.

4 391 J. Med. Biol. Eng., Vol. 33. No Results A retinal fundus image The 1% bright pixels This section evaluates the performance of the proposed statistics-based method via experiments. Two paradigms of the test data are adopted in this study. The first paradigm consists of 23 retinal fundus images, randomly chosen from the 46 retinal fundus images as the training images, with the other images used as the test images. The second paradigm uses the test and training images in the first paradigm as the training and test images, respectively. (c) A little overlapping (d) Three candidate regions Figure 4. The detected ROI and its maximal inscribed circle used as the initial contour and the final contour of the optic disc obtained by the GVF ACM. (e) Three candidate after fine-tuning (f) ROI Figure 3. The 1% of the brightest pixels and three candidate regions. The MEANs, STDs, and SKs of the three candidate regions are then calculated. Only the b% brightest pixels in each region are used to calculate the region s MEAN, STD, and SK. The possibility of each candidate region is then computed using Eq. (7) based on its MEAN, STD, and SK. The candidate region with the highest possibility to be the ROI is determined. Figure 3(f) shows the ROI selected from the three candidate regions in Fig. 3(e). Finally, the maximal inscribed circle of the ROI is considered as the initial contour of the optic disc, and then the optic disc is segmented using the GVF ACM based on this initial contour. The green rectangle in Fig. 4 shows the ROI of the retinal fundus image in Fig. 3(f), where the circle is the maximal inscribed circle of the ROI. Figure 4 shows the contour of the optic disc obtained using the GVF ACM. In these experiments, the minimal region R surrounding the whole optic disc on each retinal fundus image was manually drawn by an experienced doctor. The distance between the central pixels of R and R (called location error) was utilized to measure the location accuracy of the initial contour obtained by the proposed statistics-based method, where R is the minimal rectangle which encloses the whole optic disc obtained by the segmentation method. The edge mismatch (EMM) [14], modified Hausdorff distance (MHD) [14], and relative error (RE) [15] are often used to measure segmentation errors. These measures are thus used here to evaluate the segmentation errors. In these experiments, the target optic disc contour on each retinal fundus image was manually drawn by an experienced doctor. The segmentation error of a segmentation method is the difference between the target contour and that segmented by the segmentation method. In the first experiment, the images in the two paradigms were respectively used to probe the influence of the b% brightest pixels on the performance of the proposed method. The experimental results listed in Table 1 illustrate that the Table 1. Results of first experiment. b(%) Paradigm a 1 a 2 a 3 b 1 b 2 b 3 Average location error

5 Initial Contour Detection of Optic Disc 392 Figure 5. Six test retinal fundus images and the central points specified by three different segmentation methods. The symbol indicates the central pixel and + points out the central pixel of the initial contour of the optic disc demarcated by the statistics-based method. marks the central pixel of the optic disc specified by the eigenface method, marks the central pixel of the optic disc specified by the fuzzy convergence method and indicates the central pixel of an optic disc cut by the GVF ACM. Table 2. Comparison of average location errors and execution times. Method Average location error (pixels) Execution time (seconds) Eigenface method Fuzzy convergence (*6.22) Statistics-based (paradigm 1) Statistics-based (paradigm 2) GVF ACM (paradigm 1) GVF ACM (paradigm 2) * Not including the time required for vessel segmentation Eigenface Method fuzzy convergence Statistics-based (paradigm 1) Statistics-based (paradigm 2) GVF ACM (paradigm 1) GVF ACM (paradigm 2) Figure 6. The location errors of the 46 retinal fundus images obtained by the eigenface method, fuzzy convergence, the statistics-based method, and the GVF ACM. proposed method performs best when b% is set to 85%. In this case, the parameters of Eq. (7) obtained from the first paradigm are a 1 = 3.200, a 2 = , a 3 = , b 1 = , b 2 = , and b 3 = The parameters obtained from the second paradigm are a 1 = 3.398, a 2 = , a 3 = , b 1 = , b 2 = , and b 3 = Figure 5 shows six test images. The symbol indicates the central pixel of R and + indicates the central pixel of the initial contour of the optic disc demarcated by the proposed method. The optic discs were also segmented using the eigenface method and fuzzy convergence method. In Fig. 5, and mark the central pixels of the optic disc specified by the eigenface method and the fuzzy convergence method, respectively. Table 2 shows the average location errors of the central pixels of the ROIs obtained using the proposed (b% = 85%), eigenface, and fuzzy convergence methods. The execution times listed in Table 2 are the total times required to segment the ROIs from the 23 test images. Figure 6 shows all the location errors of the 46 retinal fundus images acquired by the proposed and eigenface methods. From Table 2 and Fig. 6, the proposed method outperforms the eigenface and fuzzy convergence methods in terms of overall segmentation. In experiment 3, the GVF ACM was used to segment the optic discs from the ROIs obtained by the proposed method. The parameters α and β were set to 1 and 0.1, respectively. The symbol in Fig. 5 indicates the central pixel of an optic disc

6 393 J. Med. Biol. Eng., Vol. 33 No cut by the GVF ACM. Table 2 lists the average location errors obtained by the GVF ACM and the execution times required to locate the initial contour by the proposed method and segment the optic discs of the 46 retinal fundus images by GVF ACM. Figure 6 shows all the location errors obtained by the GVF ACM. Table 3 shows the average segmentation errors for the eigenface, fuzzy convergence, and proposed methods and then segmented by GVF ACM. Table 3. Comparison of average segmentation errors. Error Eigenface Fuzzy Convergence Paradigm 1 Paradigm 2 EMM RE MHD Discussion and conclusions Optic disc segmentation is very important for the development of an automatic eye disease self-diagnosis system. This paper proposed a statistics-based method that first selects the ROI in a retinal image from candidate regions based on the means, standard deviations, and skewnesses of their pixel gray levels. The maximal inscribed circle of the ROI is then ascribed as the initial contour, which is then used by the GVF ACM to slice the optic disc. The proposed method combined with GVF ACM provides an automated method for segmenting the optic disc. The statistics-based method is simple and can provide a good initial contour for ACM to make optic disc extraction faster and more precise. The experimental results show that the proposed method segments the optic disc more precisely than can the eigenface and fuzzy convergence methods and with less computation time. Acknowledgments The authors would like to thank Dr. Cheung of Taichung Veteran General Hospital for his kindness in supplying the fundus images for this study. In addition, the authors also thank the National Scientific Council (NSC) of the Republic of China (R.O.C.) for supporting this work under grant NSC E References [1] D. T. Morris and C. Donnison, Identifying the neuroretinal rim boundary using dynamic contour, Image Vis. Comput., 17: , [2] H. Li and O. Chutatape, Automatic location of optic disk in retinal images, IEEE Int. Conf. on Image Proc., 2: , [3] H. Li and O. Chutatape, [3] H. Li and O. Chutatape, Automatic location of optic disk in retinal images, IEEE Int. Conf. on Image Proc., 2: , 2001.Boundary detection of optic disc by a modified ASM method, Pattern Recognit., 36: , [4] C. Sinthanayothin, J. F. Boyce, H. L. Cook and T. H. Williamson, Automated location of the optic disc, fovea, and retinal blood vessels from digital gray-level fundus Images, Br. J. Ophthalmol., 83: , [5] S. A. Salem, N. M. Salem and A. K. Nandi, Segmentation of retinal blood vessels using a novel clustering algorithm (RACAL) with a partial supervision strategy, Med. Biol. Eng. Comput., 45: , [6] S. Li and J. Chen, Detection of the optic disc on retinal fluorescein angiograms, J. Med. Biol. Eng., 31: , [7] C. Köse and C.İkibaş, Statistical techniques for detection of optic disc and macula and parameters measurement in retinal fundus images, J. Med. Biol. Eng., 31: , [8] M. Turk and A. P. Pentland, Eigenfaces for recognition, J. Cogn. Neurosci., 3: 71-86, [9] T. F. Cootes, C. J. Taylor, D. H. Cooper and J. Graham, Active shape model-their training and application, Comput. Vis. Image Underst., 61: 38-59, [10] A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Trans. Med. Imaging, 19: , [11] A. Hoover and Goldbaum, M.: Locating the optic nerve in retinal image using the fuzzy convergence of the blood vessels, IEEE Trans. Med. Imaging, 22: , [12] C. Y. Xu and J. L. Prince, Snakes, shapes, and gradient vector flow, IEEE Trans. Image Process., 7: , [13] A. Osareh, M. Mirmehdi, B. Thomas and R. Markham, Gray-level morphology and snakes for optic disc location, Proc. 6th Med. Imag. Und. Anal. Conf., 21-24, [14] M. Sezgin and B. Sankur, Survey over image thresholding techniques and quantitative performance evaluation, J. Electron. Imaging, 13: , [15] S. F. Yang-Mao, Y. K. Chan and Y. P. Chu, Edge enhancement nucleus and cytoplast contour detector of cervical smear images, IEEE Trans. Syst. Man Cybern. Part B-Cybern., 38: , 2008.