Chapter Four 36 We perform 24 iterations. The accuracy and loss can be seen in Figure 4.14. The graph of accuracy increases and the loss decreases, but after 3 epochs, both graphics change slowly. The trend of the graph of validation follows the training.
The training accuracy trend of the last six iterations seems flat at around 70%. There is also a decreasing trend of the validation accuracy from the nineteenth to twenty-first iteration. Therefore, the training is stopped after 24 iterations.
The highest training accuracy is 70.8% at the nineteenth, first, and twenty-third iterations. Among these iterations, the highest validation accuracy occurs at the nineteenth iteration. Hence, we choose the result of the nineteenth iteration as the optimum parameters.
The test data contains 9×750 = 6,750 images. The accuracy when we applied the model to the test data is 63.98%. Table 4.1 shows the details of the accuracy and loss of each category in the second CNN model. The accuracy of the four categories is more than 87%, but the other four categories have an accuracy of less than 50%. The lowest accuracy is the category of wiggly jump, that is 18.93%.
Figure 4.14: The result of the process of the updating parameters of the model.
Figure 4.15 shows the results when the second CNN model is applied to the image of real capillaries. The horizontal bars in the second column show the score of each category.
The right vertical axis shows the precise number of each bar. The left vertical axis shows the category number related to Table 4.1.
Chapter Four 37 Table 4.1: The accuracy and loss of each category from the second CNN model.
No. Category Accuracy Loss
1 Straight fine 38.13 1.040 2 Straight 1 Branch 95.87 0.161 3 Straight 2 Branches 87.73 0.284 4 Straight Jump 96.53 0.130 5 Straight Sharp 99.87 0.003
6 Wiggly fine 65.47 1.097
7 Wiggly 1 Branch 27.33 1.415 8 Wiggly 2 Branches 46.00 1.215
9 Wiggly Jump 18.93 1.483
Average 63.98 0.759
For the first approach, the results show that it works quite well to classify the capillaries1 into straight or wiggly. First, detecting the outer edge is done by the active contour method. This method works well, even for the noisy image. From the outer edge, the curvature is approximated. It then transformed by Fourier.
The advantage of this approach is that it can be implemented directly to the image independently. If the image is a little noisy, it still works. How much the curvature bend might be detected by this method. From this result, we have a hypothesis which is not proven yet that the frequency at which the peak magnitude occurs is related to the number of significant wiggles on the outer edge of the capillary.
The disadvantage of this approach is that it cannot give more details explanation about the abnormal patterns of the capillaries. Another lack is that it is relatively not easy to determine the appropriate distance between three points which are used to calculate the curvature. If this distance is too close, the noise effect can affect the curvature quite high. If the distance is too far, we lose the important information on the curvature.
The second approach is the convolutional neural network. It is applied generally on image classification. Now, it is specifically applied to classify the capillaries into two categories, straight and wiggly. The model is combined by VGG16 such that it still works even for the limited number of training data. The output is then the score of each category.
The parameters are updated iteratively by minimizing the loss function, that is the Average Negative Log Likelihood. From the result of the training, it can be seen how the accuracy and how close the output’s result of the model to the targeted output.
Chapter Four 38
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.001 0.000 0.002 0.006 0.127 0.001 0.244 0.399 0.221
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.006 0.006 0.027 0.024 0.177 0.002 0.212 0.468 0.078
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.003 0.001 0.005 0.063 0.022 0.001 0.377 0.490 0.038
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.010 0.028 0.069 0.055 0.142 0.005 0.304 0.255 0.132
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.015 0.025 0.043 0.701 0.001 0.000 0.190 0.021 0.003
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.017 0.022 0.039 0.289 0.005 0.003 0.486 0.127 0.013
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.018 0.075 0.118 0.281 0.012 0.008 0.388 0.065 0.036
0.0 0.2 0.4 0.6 0.8 1.0
98 76 54 32 1
0.024 0.068 0.106 0.030 0.076 0.001 0.462 0.209 0.024
Figure 4.15: The results of the second CNN model applied to the images of capillary taken by a microscope. The score in each category is presented by the horizontal bar
next to each image.
Chapter Four 39 The disadvantage of this approach is that it needs a huge amount of dataset on the training. The computational cost to obtain the optimum parameters is high. The more images used in the training dataset, the better the performance of the model and the more time is needed to train. The other lack is that the size of the image, the mean of the pixel, and the deviation of the pixel needs to be adjusted such that it is compatible with the model. Next, this model does not work well on the image of a straight capillary which has a jump, cross-section, or changed curvature often. However, this last lack occurs because there is no image similar to these case in the training dataset.
The advantage of this approach is that once the optimum parameters are obtained, the computational cost in the test dataset is quite fast. We can divide the abnormal patterns into several categories.
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