Computational Methods for Feature Detection in Optical Images

Fig. 2.15. (a) Line representation used in Hough transform and (b) accumulator cells for binning in Hough transform.8

to avoid issues of divergence. Figure 2.15 shows the parametric relationship from the transform in line space. A matrix of accumulator cells are then used to bin similar ρ and θ values discretely, with high bins corresponding to line edges in the image (Fig. 2.15).

Line detection is not overly useful in retinal image segmentation, due to the lack of straight retinal feature edges (although some blood vessels can be detected). Finding circular edges is useful for detecting the optic nerve head, and the Hough transform is a popular method because of its robust performance with broken edges (due to blood vessel occlusion).18 The equation for the circle shape space is

which produces a 3D accumulator cell matrix for the three variables. Figure 2.16 shows preliminary results and accumulator cells for both the line and circle Hough transforms.

2.3.3. Thresholding for Image Segmentation

We have discussed the use of thresholding in the previous section, providing discrimination on edge point inclusion. In cases where a specific anatomical feature has a distinct intensity range from other features and

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Fig. 2.16. (a) Accumulator cells and edge detection for line Hough transform and (b) accumulator cells and locations for circle Hough transform.

background, thresholding can provide strong segmentation results with low computation overhead. The optic disk pixels typically have high intensity, low contrast, and discontinuous edges due to blood vessel occlusion, lending itself to thresholding as a viable segmentation approach. We will discuss using intensity thresholds based on global image histograms and domain knowledge to segment a retinal image.

2.3.3.1. Segmentation with a single threshold

The simplest method for threshold segmentation is to choose, either manually or at an automatically chosen point, a threshold intensity value, t, that will include all values above (when ROI is bright) or below (when ROI is

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where g(x, y) is a binary image labeled with ones at pixels included in the segment. Setting a high threshold for optic disk segmentation and a low threshold for blood vessels, simple thresholding can provide good segmentation results, provided the retinal image has minimal illumination effects (Fig. 2.17).

Fig. 2.17. Examples of low and high simple thresholding for the segmentation of grayscale intensity image.

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Fig. 2.18. (a) Original grayscale image, (b) image histogram with two thresholds denoted, (c-top) segmentation using high and low thresholds, and (c-bottom) segmentation using only high threshold.

2.3.3.2. Multi-level thresholding

For more discrimination than a simple threshold, multi-level threshold allows intensity values to be constrained between a high and a low boundary within the image range. These boundaries can either be predefined or automatically chosen using saddle points in the histogram, which are local minimums formed in curves of the bins (Fig. 2.18). A threshold segmentation equation takes the form

where t1 and t2 are the low and high thresholds. When a large percentage of a particular anatomical feature can be contained between two value limits, segmentation specificity increases (Fig. 2.18).

2.3.3.3. Windowed thresholding

Due to the prevalence of illumination effects and difficulty of obtaining an accurate normalization solution, intra-feature intensity variance will inhibit a robust segmentation through simple and multi-thresholding methods.

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