CHAPTER-4 LOCALIZATION AND CONTOUR DETECTION OF OPTIC DISK

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1 CHAPTER-4 LOCALIZATION AND CONTOUR DETECTION OF OPTIC DISK Ocular fundus images can provide information about ophthalmic, retinal and even systemic diseases such as hypertension, diabetes, macular degeneration and arteriosclerosis. Detection of normal and abnormal features in retinal images is fundamental and helpful for automatic understanding of these images. The normal features are the anatomical structures of fundus images that include optic disk, macula, fovea and blood vessels. Hard Exudates and hemorrhages are the major abnormal features for diabetic retinopathy, which is the foremost cause of blindness. Optic disk is a bright yellowish disk where the blood vessels and the optic nerves emerge. It is a major landmark for the detection of other anatomic features. The dimensions of the optic disk are often studied for clues of some diseases as well. In this thesis, principal component analysis (pca) and a method based on finding the vessel branch with highest number of vessel connections are investigated to locate the optic disk. To identify the contour of the optic disk a method based on geometric active contours with new variational formulation is proposed. This chapter is organized as follows. In Section 4.1, methods used to localize the optic disk are presented. Contour detection of optic disk

2 based on geometric active contour model with new variational formulation is described in Section 4.2. In Section 4.3, experimental results of the proposed methods are presented and compared with existing methods. Conclusions are given in Section LOCALIZATION OF OPTIC DISK For localizing optic disk two methods are investigated. The implementation details of these methods are explained in this section Principal Component Analysis (PCA) PCA is a powerful tool in the recognition of an identical shape to the trained shapes. The PCA based method has been widely explored in the application of face recognition [98]. The PCA based approach includes three steps. Firstly, the Eigen vectors are calculated from the training images. Then, a new fundus image is projected to the space specified by the Eigen vectors. Finally, the distance between the fundus image and its projection is calculated. The training set consists of thirty optic disk images. The training data is acquired by manually cropping a square sub-image around the optic disk from each fundus image. The intensities of the sub-images are normalized to the same range to eliminate the illumination difference between each sub-image. All the sub-images are resized to L x L pixels. Each training image is considered as a vector of dimension L 2 and L is set to 90 because most of the optic disk diameters fit well into this square.

3 In order to get the modes of variation with respect to the average image, the PCA method is applied to the training set. The subspace defined by Eigen vectors is termed as disk space. The optic disk images of the training set are denoted as vector 1, 2, 3,., M, where M defines the number of training images and is 30 for the proposed case. The training set of images is as shown in Fig.4.1. The images are average centered by subtracting the average image from each image vector. The average vector of the training set is computed using the equation 1 M i M i 1 (4.1) The average vector of the training set is shown in Fig.4.2. Let i be defined as mean centered image, i = i -. Let vector ui and λi are the Eigen vector and corresponding Eigen value of the covariance L 2 L 2 matrix C: C 1 M T T ii WW M i 1 (4.2) where W is a matrix comprised of the column vectors i placed side by side. The vector uk, is an Eigen vector with corresponding Eigen value k and was calculated using equation,

4 Fig.4.1 Training Images for Localization of Optic Disk C.uk = k.uk (4.3) The L x L sub-image Γnew is obtained by cropping an L x L square with the center pixel (x, y). To project the sub-image Γnew to disk space, the mean image Ψ should be subtracted: Φnew= Γnew -Ψ.

5 Fig.4.2. Average Vector of the Training Set The sub-image Γnew is projected against the disk space by the following transformation: u. k=1, 2,, M. (4.4) T k k new where 1, 2,..., n are n new disk spaces and n is a number of selected dominant Eigen vectors. A pre-processed image is reconstructed by using its disk spaces and Eigen disks of the training set using equation n u, r k k k1 where Φr is a reconstructed image and n is the number of dominant Eigen disks. The sub-image will be classified as optic disk if the Euclidean distance between Φr and Φnew is below a threshold

6 Fig.4.3 Examples of Eigen Disk Images value new 2. The Euclidean distance can be calculated as new new r.

7 Localization of Optic Disk Based on Finding the Branch with the Most Vessels The vasculature in the retinal image consists of many vessels of various lengths and various widths. The proposed method turns the vessel probability map into a network of vessels and branches. In this method, network information is stored about the connections between vessels and branches. By means of this network, the branch with most vessels connected to it can be selected. The selected branch is used to determine the optic disk. The binary blood vessel skeleton map is obtained using the vessel segmentation method described in chapter 3. For each skeleton pixel the amount of neighbour skeleton pixels is determined. If the amount of neighbours is smaller than three, then the pixel is added to the vessel image. Otherwise the pixel is added to the branch image. The starting and ending points of a blood vessel can be found by identifying the pixels having only one neighbour in all vessel pixels. The branches are detected by applying eight connected component analysis on the branch image. The procedure to detect vessels is: 1) when the starting point of a vessel is detected within the vessel image, the vessel is traced towards its end point. 2) the starting and ending points are marked to avoid tracing a vessel twice. The constructed vessel-branch network can be used to find the optic disk in many ways. A very simple algorithm to localize optic disk is the selection of the branch with most vessels. For each branch of the network, the number of vessels connected to it is stored. The optic

8 disk contains the optic nerve from which a few main vessels split up into many smaller vessels which spread around the retina. Vessel segments in this area of the retina are often small and are therefore often combined into one large branch of the network with many vessel objects connected to it. An increasing amount of vessel connections of a branch also increases the probability of the branch being located in the optic disk area. The algorithm is performed as follows: Select the branch with the highest number of vessel connections. If there are several branches with the highest number of vessel connections, then the branch with the highest number of branch pixels is selected. Take the bounding box of the branch with the most vessel connections. Select the bounding box center as the center of optic disk. For example, given a colour retinal image in Fig. 4.4(a), the binary vasculature and the skeleton of the vasculature overlaid on the retina image are shown in Fig. 4.4(b) and Fig. 4.4(c). The detected center of the optic disk is shown in Fig This is not the geometrical center of the optic disk and only indicates the location of the optic disk where the vessel branch with the most vessels is present. As the image contrast is very low at thin blood vessels, the binary blood vessel map shown in Fig. 4.4(b) has some broken points. But these broken points will not influence the performance of the proposed technique since the

9 (a) (b) (c) Fig.4.4. Localization of Optic Disk (a) Original Colour Retina Image (b) The Binary Vessel Map (c) Overlay of the Vessel Branch Network and the Original Image and (d) The Bounding Box of the Best Branch and the Determination of the Optic Disk Center. (d)

10 Fig.4.5. Detected Optic Disk Center brightness of the optic disk region is high compared to other regions. So the blood vessel segments near the optic disk region do not have any broken points. The detected optic disk center for the retinal image in Fig.4.4 is shown in Fig CONTOUR DETECTION OF OPTIC DISK Variation in the shape, depth or colour of the optic disk is a sign of various ophthalmic pathologies, especially for glaucoma. The accurate detection of the contour of the optic disk will be useful to study the progress of eye diseases and treatment results. The contour detection of optic disk is complicated as some parts of the optic disk contour are not well defined and some areas are partly obscured by the vessels in fundus images. A geometric active contour model is proposed to detect the contour of the optic disk in fundus images.

11 HOMOGENIZATION OF OPTIC DISK REGION As optic disk has no proper shape and its boundary is broken by outgoing blood vessels, the boundary of the optic disk appears fuzzy. Hence edge based localization methods cannot be used to detect the contour of the optic disk. Active contours are the best choice for such situation. Active contours make use of the edge information to converge on to the region having the highest edge energy. This region is to be identified as the optic disk boundary, but optic disk region is occluded by large blood vessels. In order to enable the optic disk to get lock on to the boundary, the blood vessels should be removed from the optic disk region without adding much distortion to the boundary of the optic disk. Firstly, the original colour retinal image is preprocessed using colour mathematical morphology in lab space. This helps to remove blood vessels very effectively and provides a more homogeneous optic disk region for the geometric active contour to lock onto. Dilation is performed first to remove the blood vessels in the optic disk region. Erosion is applied next to re-establish the boundaries to their former position. In the proposed method, a symmetrical disk structuring element of size 13 is used as the blood vessels are found to be not wider than 11 pixels. The morphology in lab space is performed using the method described by hanbury et al. [99]. For every arbitrary point X, dilation (Id) and erosion (Ie) by a structuring element k are defined as:

12 I I x I y Iy mini z, x I y: Iy maxi z, Z d K x e K x : Z (4.5) For the colour retinal image shown in fig. 4.6(a), the LAB morphology output is as shown in fig. 4.6(c), where the blood vessels are removed cleanly to have homogenous optic disk region Contour Detection Using Geometric Active Contour Model The optic disk contour is found by applying a Geometric active contour model with new variational formulation. In this chapter, a variational formulation that forces the snake to be close to a signed distance function which eliminates the need for re-initialization procedure is used. The variational energy functional comprises an external and an internal energy terms. The deviation of level set function from a signed distance function is penalized by the internal energy term. The motion of the zero level set towards the desired image features is driven by the external energy term. The resultant evolution of the level set function is a gradient flow that reduces the overall energy functional. During the evolution, the level set function is automatically kept as an approximate signed distance function because of the internal energy. Therefore, the re-initialization procedure is completely eliminated. For a snake, the initial contour must be close to the desired contour; otherwise the snake may

13 (a) (b) (c) (d) (e) Fig.4.6. Boundary Detection of Optic Disk (a) Colour Retina Image (b) Located Optic Disk (c) Result after Applying Colour Morphology in Lab Space (d) Initial Snake (e) Detected Optic Disk Boundary and (f) Overlay of the Groundtruth and the Result of Proposed Method. (f)

14 converge to a wrong resting place. The method described for localizing the optic disk in Section is used to automatically position the initial snake. The initial contour for the retinal image in Fig. 4.6(a) is as given in Fig. 4.6(d). In general, a snake is defined as a set of points initially positioned close to the contour of interest that are gradually brought nearer to the exact shape of the desired area in the image. For this, an iterative minimization of the variational energy functional is carried out. (4.6) P g,, v where P dxdy, is a metric to exemplify how close a function to a signed distance function in Ω R 2, and µ > 0 is a metric which controls the outcome of penalizing the deviation of function from the distance function. For the conduct of experiments, µ = 0.04 is used because for stable evolution of the level set, the product of time step and µ must be less than 0.25 [100]. ε g,λ,v() is the external energy for a function (x, y) and is defined in [100] as g,,v L va g g (4.7) Where (> 0) and v are constants and g is an edge indicator function defined as

15 g 1 1 G (4.8) * I 2 Where i is an image and gσ is the gaussian kernel having standard deviation. The terms lg() and ag() are defined as LG() = g dxdy (4.9) and AG() = gh dxdy, (4.10) Respectively, where defines the univariate dirac function, and h indicates the heaviside function. The external energy εg,λ,v drives the zero level set function towards the object boundary, while the internal energy term μ.p() penalizes the deviation of function from the signed distance function during its evolution. The gateaux derivative (first variation) of the functional in eq. (4.7) can be expressed as [ ] div div g vg (4.11) Where is the laplacian operator. Therefore, the function that minimizes this variational energy functional satisfies the euler-

16 lagrange equation 0. The steepest descent process for iterative minimization of the energy functional is the following gradient flow: div t div g vg (4.12) This gradient flow defines the evolution equation of the level set in the proposed approach. The second and third terms of right hand side of Eq. (4.12) are related to the gradient flow of the variational energy functionals Lg() and vag(), respectively, and are responsible for driving the zero level set function towards the object boundaries. The detected optic disk boundary by this method for the image in Fig. 4.6(a) is as shown in Fig. 4.6(e), and Fig. 4.6(f) shows the overlay of the result of the proposed optic disk boundary detection method on the hand-labelled groundtruth image EXPERIMENTAL RESULTS AND DISCUSSION The proposed algorithms for optic localization and contour detection are tested and evaluated on four popular research databases of colour retinal images: STARE [55], DRIVE [94], DIARETDB0 [101] and DIARETDB1[102] databases. The DIARETDB0 database consists of 130 colour retinal images of size The DIARETDB1 database consists of 89 colour retinal images of size

17 Fig.4.7. Comparison of Optic Disk Localization. + indicates the localization by the method of finding the branch with most vessels, indicates the localization of optic disk by principal components analysis method and represents the localization by the centroid of the largest cluster of the brightest pixels LOCALIZATION OF OPTIC DISK The performance of the PCA based approach and the method based on finding the vessel branch with most number of vessels are compared with the maximum local variance method [14]. An example is shown in Fig. 4.7, where + indicates the localization by the method of finding the branch with most vessels, indicates the localization of optic disk by PCA method and represents the optic disk localization by the maximum local variance method [14]. The method in [14] gives the wrong localization when processing the retinal images with large areas of lesions, while PCA based approach and algorithm of finding the branch with most vessels can obtain the

18 correct localization. The PCA based method failed in the testing images where there is a large area of abnormalities around the optic disk as there is no such case available in the training set. But the proposed algorithm based on finding the branch with most vessels works pretty well even for these images. This algorithm performed well for the input retinal images which are in a low-contrast condition. Table 4.1 shows the performance comparison with maximum local variation method in terms of success rate for the STARE, DRIVE, DIARETDB0, DIARETDB1 databases. The success rate of the method based on finding the branch with most vessels is better compared to other methods with an accuracy of 99.2% CONTOUR DETECTION OF OPTIC DISK To evaluate the performance of the proposed optic disk contour detection method, the results are compared with the state-of-the-art results obtained from GVF snake method [57], 2D Circular Hough Transform method [54] and hand labeled groundtruth segmentations. In GVF snake method, the images are preprocessed morphologically and the parameters of the energy functions are set carefully to make a balance between smoothness and accuracy on the resulted boundary. In 2D Circular Hough Transform method, the dimensions of the normal circular Hough Transform histogram are reduced from 3 to 2 dimensions by considering that the approximate optic disk radius is known. Only the first few circles are assessed by using the maximum

19 Table.4.1. Performance Comparison of Maximum Local Variation Method [14] and the Proposed Methods Database Number of Images Maximum Local Variation Method [14] Success Rate in % PCA Based Method Proposed Method STARE DRIVE DIARETDB DIARETDB point from Hough space. The optic disk contour manually marked by an experienced ophthalmologist is set to be the groundtruth. Then a simple and effective overlap measure is applied to find the accuracy of the detected contour. n( R T) M n ( R T ) (4.13) where R and T refer to the groundtruth and the detected optic disk region respectively and n(.) corresponds to the number of image pixels in a region. Specifically, the retinal images are classified into three categories, normal retinal images, abnormal retinal images with ill-defined optic disk and retinal images with fuzzy elliptic optic disk. From column by

20 Fig.4.8. First Row: Example Images with Closer View of Optic Disk; Second Row: Results from GVF Snake; Third Row: Results from Hough Transform; Last row: Results from Proposed Method. column, the first column of Fig.4.8 presents the results obtained from normal retinal images. Results of abnormal retinal images with ill-

21 defined optic disk are illustrated in the second column and the third column presents results from retinal images with fuzzy elliptic optic disk. From row by row, the first row presents original colour retinal images. The results of GVF snake method are illustrated in the second row and the last row shows simulation results of Hough transform [54]. The last row presents simulation results of the proposed method. An example of normal retinal image having elliptic optic disk is illustrated in first column of Fig.4.8, where both the proposed method and GVF snake method give the successful results; Hough transform gives the failed result. The measured accuracies for the GVF snake, Hough transform and the proposed method are 99.3%, 78% and 99.5% respectively. The example given in the second column is an optic disk having ill-defined contour and noises from the surrounding tissue. The proposed method correctly located the disk boundary, while the GVF snake and Hough transform methods failed. The accuracies for the GVF snake and Hough transform are 72% and 74% respectively. For the same image the proposed method has an accuracy of 99.1%. An example of fuzzy elliptic optic disk is shown in the third column. The accuracies for the GVF snake and Hough transform are 81% and 82% respectively. For the same image the proposed method has an accuracy of 98.2%. Table 4.2 compares the proposed approach with the GVF snake and Hough transform methods in terms of accuracy for STARE, DRIVE, DIARETDB0 and DIARETDB1 databases. It can be seen obviously that the proposed method offers better result.

22 Table.4.2. Comparison of Average Accuracy for Detecting the Boundary of Optic Disk Database Number of Images Hough Transform [54] Average Accuracy (%) GVF Snake [57] Proposed Geometric Active Contour Method STARE DRIVE DIARETDB DIARETDB CONCLUSIONS In this chapter, efficient methods for localizing the optic disk and detecting the contour of optic disk are presented. The proposed methods are implemented using MATLAB 7.4 on a core 2 Duo 1.8 GHz PC with 1GB memory. The proposed method for optic disk localization is based on finding the vessel branch with most vessels. When compared to other methods [14] [52] [53] the proposed method is fast and can locate the optic disk accurately even though the retina image contains large areas of bright lesions. The PCA based method failed to locate optic disk in retinal images that contains large area of abnormalities around the optic disk as such case is not considered in the training set. The proposed contour detection algorithm uses colour morphology and geometric active contour with new variational formulation to

23 detect the contour of optic disk. In order to have homogenous optic disk region colour mathematical morphology in Lab space is used. The contour of the optic disk is detected by employing geometric active contour with new variational formulation. The results of proposed optic disk contour detection method are compared with the results of Hough transform method, GVF snake method and validated against an experienced ophthalmologist s hand drawn groundtruth. The average accuracy obtained by the proposed method for STARE, DRIVE, DIARETDB0 and DIARETDB1 databases is better with an accuracy of 96.95% compared to the accuracy results of Hough transform method and GVF snake method which are 87.97% and 94.72% respectively. One visible advantage of the proposed optic disk contour detection method over other approaches is that the contour is detected even though the boundary of the optic disk is not continuous or blurred.