# Recognizing and Recovering Ball Motion Based on Low-Frame-Rate Monocular Camera
## 4 Experimental Results
### Streak Detection Results  
We evaluated the contour acquiring method of Section 3.2. This method eliminates noise from the image to extract streaks. Thus, we tested our method with images containing both noises and streaks and observed whether streaks were detected and how complete they were. Streak detection can be considered a binary classification problem where an image is either classified as containing a streak or not containing a streak. The confusion matrix is a means to evaluate the performance of the algorithms involved in such classifications [20; 21; 22]. The confusion matrix elements encapsulate the following information. 1. True Positive (TP): The TP defines those images which are verified as containing a streak and also identified by the method as containing a streak. 2. True Negative (TN): The TN defines those images which are verified as not containing a streak and also identified by the method as not containing a streak. 3. False Positive (FP): The FP defines those images which are verified as not containing a streak and also identified by the method as containing a streak. 4. False Negative (FN): The FP defines those images which are verified as containing a streak and also identified by the method as not containing a streak. Then, the precision, recall, and F1-score are further utilized to compute performance metrics for our method. The precision gives us the percentage of the correct prediction from our method's total prediction. Recall gives us the percentage of how many total positive cases are predicted correctly with our method. Finally, F1-score gives the combined result of precision and recall. It is a harmonic mean of precision and recall. These metrics are calculated as:  
\[\text{precision}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{19}\]  
\[\text{recall}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{20}\]  
\[\text{F1\_score}=\frac{2*\text{precision}*\text{recall}}{\text{precision}+ \text{recall}} \tag{21}\]  
To measure the streak integrity of detected streaks, we defined the length of a concatenated streak block (as introduced in Section 3.2.3) as its predicted length (PL) and the length manually marked as true length (TL). Then, the streak integrity for each streak could be calculated as PL/TL. We recorded 22 shots in 5 scenes with different backgrounds and light intensities. The recorded video consisted of 82 frames containing the streaks and 90 frames without the streaks. Table 2 shows the confusion matrix of the result of distinguishing streaks. The precision was 0.987, the recall was 0.951, and the F1-score was 0.969. In the results, four streaks were not detected. The reason was that the background was too dark, or the background color was similar to the sphere. In these cases, the sphere would blend completely into the background. Another reason was that the color variation of the background was too rich (the background was full of characters), resulting in failures in streak profile fitting (as introduced in Section 3.1). \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Value** \\ \hline \(T\) & 3 \\ \(T_{max\_area}\) & 15000 \\ \(T_{min\_area}\) & 150 \\ \(T_{min\_area}\) & 0.33 \\ \(T_{peri}\) & 3.1 \\ \(\beta\) & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The thresholds and weights in our experiment. Meanwhile, in Table 2, there is a case of FP. When marking the sample manually, we excluded streaks that intersect the image border. However, during detection, the trajectory may be intermittent. The streak blocks that did not intersect the border were identified as valid streaks by our method. The extra streak was a block of an intermittent streak, and thus, the error could be neglected. Figure 13 shows an example of the candidate block detection process. These figures contain a blur streak. Figure 13a is cropped from an original image, which contains a gray streak. Figure 13b is the output of the interframe difference method and contains a lot of noise. In Figure 13c, they are presented in the form of blocks.