44 5. DETECTION OF THE ONH USING THE HOUGH TRANSFORM

Figure 5.1: Flowchart of the procedure developed to detect the ONH using the Hough transform. The sections of the book that provide descriptions of the various steps are labeled. The step of selection the best-fitting circular approximation of the ONH using the reference intensity is described in the present chapter.

boundary of the ONH with both the Canny and Sobel methods.The Canny method gives connected edges whereas the Sobel operators give disconnected edges. The edge map resulting from the Canny method is much cleaner than that from the Sobel operators, without a large number of isolated points related to the small vessels present in the image. However, the Canny method is computationally more complex than the Sobel operators because of its optimization procedures. In the case of the STARE image in Figure 5.3, we can hardly find edges around the boundary of the ONH because the ONH is obscured by the effects of pathology.

5.2ANALYSIS OF THE HOUGH SPACE

5.2.1PROCEDURE FOR THE DETECTION OF THE ONH

After obtaining the edge map, the Hough transform was used to detect the circles existing in the image (see Section 3.4.1). The Hough accumulator is a 3D array, each cell of which is incremented for each nonzero pixel of the edge map that meets the stated condition. For example, the value for

46 5. DETECTION OF THE ONH USING THE HOUGH TRANSFORM

Figure 5.2: (a) Image 01 of the DRIVE dataset. (b) Preprocessed luminance image. (c) Binary edge image obtained using the output of the MATLAB version of the Sobel operators thresholded at 0.02 of the normalized intensity. (d) Part (c) magnified in the ONH area. (e) Binary edge image using the output of the MATLAB version of the Canny method thresholded at 0.17 of the normalized intensity. (f ) Part

(e) magnified in the ONH area.

the cell (a, b, c) in the Hough accumulator is equal to the number of edge map pixels of a potential circle in the image with the center at (a, b) and radius c. In the case of the images in the DRIVE dataset, the size of each image is 584 × 565 pixels (see Section 4.1). The spatial resolution of the images in the DRIVE dataset is about 20 μm per pixel. The physical diameter of the ONH is about 1.5 mm, on the average [32]. Assuming the range of the radius of a circular approximation to the ONH to be 600 to 1000 μm, the range for the radius c was determined to be 31 to 50 pixels. Hence, the size of the Hough accumulator was set to be 584 × 565 × 20.

For the STARE images, the size of the images is 700 × 605 pixels (see Section 4.2). The approximate spatial resolution is 15 μm per pixel, obtained by converting that of the DRIVE images with the scale factor derived by ter Haar [27] (see Section 4.3). Hence, the range for c was determined to be 46 to 65 pixels (limited to 20 pixels) for images from the STARE dataset.

The potential circles indicated by the Hough accumulator were ranked in terms of the corresponding value of the accumulator cell, and the top 30 were selected for further analysis. The top three circles in the Hough space for the test image 02 in the DRIVE dataset are shown in Figure 5.4. We can observe that the first circle in the Hough space fits the actual ONH well, whereas the second and third circles match arches of the blood vessels.

5.2.2SELECTION OF THE CIRCLE USING THE REFERENCE INTENSITY

The first circle indicated by the Hough accumulator may not always correspond to the best circular approximation of the ONH. To address this limitation, a criterion was included to select the most appropriate circle by using the intensity information, shown as the last step in the flowchart in Figure 5.1.

After preprocessing (see Section 3.1), a 5 × 5 median filter was applied to the luminance image, to remove outliers (noisy pixels) in the image. Then, the maximum intensity in each image was calculated to serve as a reference intensity for the selection of circles.

Because we expect the ONH to be one of the bright areas in the fundus image, a threshold equal to 0.9 times the reference intensity was used to check the maximum intensity within a circular area with half of the radius of each potential circle. If the test failed, the circle was rejected, and the next circle was tested.

Figure 5.5 shows two examples from the DRIVE dataset. In each case, the blue dash-dot circle corresponds to the global maximum in the Hough parameter space; the black dashed circle corresponds to the highest local maximum in the Hough space that also meets the condition based

48 5. DETECTION OF THE ONH USING THE HOUGH TRANSFORM

Figure 5.3: (a) Image im0001 of the STARE dataset. (b) Preprocessed luminance image. (c) Binary edge image obtained using the output of the MATLAB version of the Sobel operators with an automatically chosen threshold. (d) Part (c) magnified in the ONH area. (e) Binary edge image obtained using the output of the MATLAB version of the Canny method thresholded at 0.17 of the normalized intensity. (f ) Part (e) magnified in the ONH area.

Figure 5.4: (a) Image 02 of the DRIVE dataset. (b) Preprocessed luminance image. (c) Binary edge image obtained using the MATLAB version of the Sobel operators thresholded at 0.02 of the normalized intensity. (d) The top three circles in the Hough space superimposed on the original color image. The black contour in solid line corresponds to the first circle.The cyan dashed circle corresponds to the second circle. The blue dash-dot circle corresponds to the third circle.

5.2. ANALYSIS OF THE HOUGH SPACE 49

Figure 5.5: (a) Test image 03 of the DRIVE dataset. (b) The result of detection of the ONH for image 03.The blue dash-dot circle corresponds to the global maximum in the Hough parameter space.The black dashed circle corresponds to the highest local maximum in the Hough space that also meets the condition based on 90% of the reference intensity.The cyan contour in solid line is the contour of the ONH marked by the ophthalmologist. Distance = 1.15 mm, overlap = 0.12 after using the intensity condition. (c) Test image 10 of the DRIVE dataset. (d) Result for image 10 with distance = 0.04 mm, overlap = 0.90 after using the intensity condition. Reproduced with permission from X. Zhu, R.M. Rangayyan, and A.L. Ells “Detection of the optic disc in fundus images of the retina using the Hough transform for circles”, Journal of Digital Imaging, 23(3): 332-341, June 2010. © Springer.