Prerna Sethi and Hilary W. Thompson
as vessel segments. However, circular Hough transform proved to be a computationally intensive procedure, almost making the procedure impractical to use.
9.1.1.3. Top-hat transform
Top-hat transform is a composite operation that extracts the bright objects from an uneven background by using morphological opening or closing operations. The mathematical formulation for a top-hat transform based on Refs. [19, 20] is described below.
Consider the gray-tone mathematical morphology operations. Let f(x) be the values in the gray pixel levels in (x, u). The transformed image is defined by f(x), where x is the set of pixels corresponding to the image. With the structuring element centered on x, the following transformation is defined as:
Opening: Oλ(X) = Dλ(Eλf(X)) and |
(9.5) |
Closing: Cλ(X) = Eλ(Dλf(X)), |
(9.6) |
where Eλf(X) is defined as an erosion operation such that, Eλf(X) = inf{ f(u):u λx} and Dλf(X) is defined as a dilation operation, in which Dλf(X) = sup{f(u):u λx}. The opening and closing functions form the basis of top-hat transform. The opening function is usually used to separate distinct areas, and the closing operation is used to join them. The peaks and valleys can be extracted based on the size of the structuring element.21
Spencer et al.13 used a bilinear top-hat transformation based on the linear structuring element to segment MAs from the arterioles and venules providing a robust discrimination between the linear and circular features. Mendonca et al.22 applied the bilinear top-hat transform to reduce the detection of linear structures, such as retinal vessels.
9.1.2. Image Segmentation
Image segmentation is defined as a process that divides a digital image into nonoverlapping, disjoint regions by assigning labels to each pixel so that the pixels with the same label display certain common visual characteristics.23 The process of image segmentation can be categorized
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Automated Microaneurysm Detection in Fluorescein Angiograms for Diabetic Retinopathy
into three approaches: the region approach, the boundary approach, and the edge approach.24 We will briefly discuss each of these three approaches.
9.1.2.1. The region approach
Thresholding is one of the popular region approach techniques, in which all the pixels at or above the threshold gray level are assigned to an object while the pixels below the gray-level threshold fall on the other side of the object. Thresholding is computationally simple and easy to implement. Thresholding provides good results with the images where the objects have a uniform gray-level interior and the background is a contrasting but uniform gray level as well. Thresholding is further categorized into adaptive thresholding, global thresholding, and optimal threshold selection.
Particularly, in detecting MAs from the fluorescein angiographic images, Spencer et al.13 performed an initial segmentation on the images by applying a bilinear top-hat transformation and matched filtering. They further applied thresholding to the processed image to convert the image into a binary image, which contained the candidate MAs. Mendonca et al.22 applied thresholding by detecting the local maxima and considering those points as “seeds” that have an intensity value higher than a certain threshold value. A region growing procedure was then applied to limit the segments, which will be classified as MAs.
9.1.2.2. The gradient-based method
The boundary approach is a gradient-based segmentation method that attempts to segment the image into its interior and exterior points by initiating the process with a gradient magnitude image, which contains a single object on a contrasting background. The pixel with the highest gray level is identified as a boundary point. The three-by-three neighborhood centered around the first boundary point is searched, and the point with the highest gray level is chosen. This process is iterative and traces the maximum gradient boundary.
In gradient image thresholding, the image is thresholded at a low level to identify the object and the background below the threshold and the edge points above it. Increasing the threshold gradually causes the objects and the
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