# Automatic Detection of Ballast Unevenness Using Deep Neural Network
## 3 Experimental Results
### Training and Testing the YOLACT Network
The first column represents the image of the track, the second the image with the predicted bounding box and mask overlaid on it, the third the predicted bounding box and mask and the fourth the target (truth) bounding box and mask. According to [39], [PERSON]'s test satisfies all the aforementioned criteria. This test uses the contingency table to calculate the [PERSON]'s test statistic [39]:  
\[statistic=\frac{(a-b)^{2}}{a+b} \tag{10}\]  
Let _model_1_ denote the first model and _model_2_ denote the second model. Then, \(a\) denotes the number of samples correctly classified by _model_1_ and simultaneously misclassified by _model_2_; \(b\) denotes the number of samples misclassified by _model_1_ and simultaneously correctly classified by _model_2_; \(a\) and \(b\) are obtained from the contingency table. If \(a\) and \(b\) are similar, both models make errors in much the same proportion, just on different instances of the test set. In this case, the result of the test would not be significant and the null hypothesis would not be rejected. On the other hand, if \(a\) and \(b\) are not similar, not only do both models make different errors, but in fact have a different relative proportion of errors on the test set. In this case, the result of the test would be significant and we would reject the null hypothesis. Therefore, the rejection of the null hypothesis means that the two models have different performances when trained on the particular training. The null hypothesis is rejected when \(p\) value \(\leq\) alpha and is not rejected when \(p\) value > alpha. Alpha denotes a significance level and \(p\) value is probability and measures how likely it is that any observed difference between the models is due to chance. A \(p\) value close to 0 indicates that the observed difference is unlikely to be due to chance. [PERSON]'s test was performed separately for the object classification part and the pixel classification part of the Mask R-CNN and YOLACT models. The test was conducted on 320 images (_test_data_ set) that contained 1287 sleepers and 10,194,844, pixels belonging to sleepers. During testing, the significance level alpha was set to 0.05. In the test of the null hypothesis, \"the object classification part of Mask R-CNN with Resnet101 and the object classification part of YOLACT with Resnet101 are the same model\", the [PERSON]'s test generated \(p\) value = 0.00464. Therefore, this hypothesis can be rejected and it means that these two models are different for the object classification parts. In the testing of the pixel classification part, the null hypothesis was formulated as \"the pixel classification part of Mask R-CNN with Resnet101 and the pixel classification part of YOLACT with Resnet101 are the same model\". The [PERSON]'s test generated a \(p\) value = 0.00138. Therefore, this hypothesis can be rejected as well and it means that these two models are different for the pixel classification parts. Based on Tables 1 and 2 and [PERSON]'s tests, the authors decided to choose the Mask R-CNN network with Resnet101 for the detection and segmentation of the sleepers. We emphasized the accuracy of the detection and segmentation of the sleepers at the expense of an increased processing time.