## 3 Optimization
### Optimization of the Soft Cascaded Classifier  
A considerably high precision of the detector is desirable in order to satisfactorily initialize the trackers by only actual construction workers [8]. This prevents the initialization of false positive tracks as well as tracker updates based on false detections. However, to be suitable for a monitoring application, the detector must be able to identify workers in real-time in the first instance. To obtain a satisfying classifier in terms of detection speed with a preferably high precision at an acceptable recall, we conduct a grid search by varying different training parameters. In preliminary experiments, we already found that subdividing the color histograms into five bins is sufficient for the classifier to properly recognize the characteristics of a construction worker's helmet and safety vest. Other parameters to be investigated include the minimal size of the feature descriptorsprovided by the feature pool. Too small feature descriptors may affect the classification. The feature descriptors' sensitivity to noise increases with decreasing size which may impair the classification. Similar results hold for slight translations, rotations and scalings of the object to be detected within the RoI provided by the background subtraction. By this, too small feature descriptors may easily be positioned off the corresponding feature. On the other hand, large feature descriptors may miss small features. For these reasons, we investigate the effect on the feature descriptors' sizes to the detection quality. We vary the minimal feature size of the feature descriptors provided in the feature pool for training between 10% and 30% of the given image patch size. Additionally, we vary the quantity of training samples from 200 to 2000 to find the optimal generalization behavior. Finally, to speed up the recognition process, we determine the minimum number of weak classifiers required for a reliable classification. For that, we vary the number of weak classifiers constituting our cascade from 50 to 350. To compare the detection results while varying a parameter, we juxtapose the classifiers' receiver operating characteristic (ROC) curves. For this, we apply the trained classifiers to the validation dataset and plot their true positive rate (TPR) against their false positive rate (FPR) with respect to the particular classifier's confidence. Figure 6 illustrates the ROC curves for all three parameters. In addition, we calculate the accuracy of the classifier when the number of weak classifiers is varied. During the variation, we apply the classifier to the validation dataset and to the training dataset and plot the accuracy curves. The results are shown in Figure 7.  
As can be derived from Figure 5(a), providing a feature pool in which feature descriptors have a minimal size of 10% of the image patch size for the classifier yields best classification results. The classification quality decreases with increasing minimal feature size. This shows that the classification is not impaired but even improved by rather small feature descriptors. Noise and the worker's positioning seem to have only little effect, if any. The effect of different amounts of training samples are shown in Figure 5(b). As can be seen, the classification quality increases up to a total number of 1600 training samples. From then on, the quality starts to decrease again. This shows that the classifier looses essential features that describe a construction worker in general terms if more than 800 positive and negative samples are used. As Figure 5(a) depicts, the general classification quality increases with the number of the cascaded weak classifiers. Nevertheless, the ROC curves of classifiers consisting of more than 100 weak classifiers resemble each other closely for very small FPRs. Since a classifier's FPR is inversely proportional to its precision, we focus our further evaluation on those small FPRs to ensure a preferably high precision which is mandatory for a proper functioning of our monitoring approach.