# Recognizing and Recovering Ball Motion Based on Low-Frame-Rate Monocular Camera
## 5 Conclusions  
In this paper, we proposed a novel method for the recognition and recovery of sphere motions. The method filters out candidate blocks from noises and concatenates these blocks into a streak. To obtain ball position sequence in space, the method first introduced a novel coupled point pairs matching method, which exploits streak axes optimized by iteration and then presented a model to map coupled point pairs to ball 3D positions. With ball position sequences, we could finally obtain ball moving speed.  
The main contributions of this paper are as follows: (1) We proposed an improved interframe difference algorithm to automatically select the nearest optimal background frame, thus reducing the effect of noise on the results of frame difference. (2) We proposed a new coupled point pairs matching method, which iterates to eliminate the problem of streak axis fluctuation due to image blurring and to calculate the actual position of the streak axis. The method outputs an accurate coupled point pair sequence. (3) We proposed a novel sphere space mapping method that is based on coupled point pairs. The method successfully eliminates the computational error of the sphere spatial position brought by the distortion of sphere imaging, and (4) we proposed a new model for recovering the direction and velocity of sphere motion. With the pixel positions and the trajectory, the model determines the velocity of the sphere motion. This model is simple but effective and does not require complex equipment or deployment.  
We have noticed a trend to use deep learning for trajectory reconstruction. However, traditional deep learning methods could hardly form a deep understanding of the trajectory reconstruction problem. Compared to deep learning methods, an essential advantage of our approach is that we break down the trajectory reconstruction problem into three explicit sub-problems, which could help inspire new traditional and deep learning methods toward trajectory reconstruction. Meanwhile, a deep learning method will help solve our proposed sub-problems. Thus, one of our critical future works is to apply deep learning methods to the three sub-problems that we have pointed out.  
Our proposed method does not require the complex point pair matching process (as methods in [12, 19]). However, the time cost of the new method is not reduced due to the iterations used in the streak axis optimization process. Thus, another future work is to reduce the time cost brought by the optimization process to improve performance.  
Conceptualization, Y.Z. ([PERSON]) and Y.Z. ([PERSON]); methodology, W.Z. and Y.Z. ([PERSON]); software, W.Z.; validation W.Z., Y.Z. ([PERSON]), and Y.Z. ([PERSON]); formal analysis, W.Z. and Y.Z. ([PERSON]); investigation, B.Z.; resources, B.Z.; data curation, W.Z.; writing--original draft preparation, W.Z.; writing--review and editing, Y.Z. ([PERSON]); visualization, W.Z.; supervision, Y.Z. ([PERSON]) and Y.Z. ([PERSON]), project administration, B.Z.; funding acquisition Y.Z. ([PERSON]) and B.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Key Project of National Natural Science Foundation of China (U1908212), the Central government guided local science and Technology Development Fund Project (1653137155953), the Liaoning Province \"takes the lead\" science and technology research project (2021 jh1/10400006), and the Liaoning Provincial Natural Science Foundation of China (2022-MS-124).  
Not applicable.  
Data Availability Statement: Data is available on request.  
The authors declare no conflict of interest.