Rajendra Acharya, U. et al.
of 0.25, and then it was subjected to median and Wiener filtering to remove the artifacts. Finally, the optic disc was removed (explained in detection of exudates) to obtain only hemorrhages.
10.3.4. Contrast
For an image, represented by a function f(x, y) having N discrete gray levels, we defined the spatial gray level dependency matrix P(d, ) for each d and , as given by:
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where
pi, j = number of pixel pairs with intensity (i, j) . total number of pairs considered
In this equation, the term pi,j is the relative number gray of a level pair (i, j) when pixels are separated by the distance d along the angle . Finally, each element is normalized using the total number of occurrences to get co-occurrence matrix P .
Contrast is a texture parameter that indicates the amount of intensity variation in the image. This variation is given by17:
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is the elements of the co-occurrence matrix shown in Eq. (10.1). The contrast is 0 for a constant image.
10.4. Classifier Used
In this work, we have used a backpropagation algorithm (BPA) to classify images into the three main DR stages. We provide a brief description of this algorithm in the following section.
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Computer-Aided Diagnosis of Diabetic Retinopathy Stages
10.4.1. Backpropagation Algorithm
BPA is a supervised learning technique used to train ANNs18 and it is widely used to feed-forward networks. Sigmoid transfer function in theANN makes it nonlinear in nature.
The BPA algorithm is an iterative gradient algorithm used to reduce the mean square error between actual and desired outputs. This algorithm is also known as “the generalized delta rule.”18 The neurons in layers, between the input and output layers, are called hidden nodes, and they do not directly interact with the environment. Using BPA, the weights associated with the hidden layers are updated continuously so that actual output and desired output match with least error.
To address the problem stated above, we experimented between one to four hidden layers. Based on the experimental results, we chose a neural network with one hidden layer that had five neurons, because this configuration gave the best classification result. A learning constant η = 0.9 was chosen to control the step size, while the mean square error was defined as 0.001.
Figure 10.7 shows the neural network classifier configuration that was used in this work. The output layer had two neurons, implying four possible
Fig. 10.7. Three-layer feed-forward neural network.
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