## 4 Discussion  
The errors evaluated were similar to the reported in the literature for similar experimental conditions, but in 3D. With respect to the static markers, M1 presents a 12.1 mm mean error, while [PERSON] et al. [10] report values between 10 and 13 mm. For the rod protocols, M1 presents a mean error of \(-2.1\) mm, while [PERSON] et al. [19] report values between \(-1.12\) and \(6.09\) mm. The single moving camera approach was similar or better than the static camera results in both the validation protocols and also allows for a bigger area of analysis, which ensures its viability as a method to evaluate 2D underwater kinematics. The single moving camera calibrated frame by frame based on the pool markers (M1) showed the lowest errors in the static markers protocol when only the central markers were evaluated, and also showed a smaller error compared to that of the static camera in the rod protocol, even when only the central markers of the static camera were considered. In this way, the single moving camera not only allows for covering all the swimming pool, but also showed the best accuracy and precision for 2D underwater kinematic analysis. The accuracy of the single moving camera calibrated based on the principal point (M2) depends on the ability to constrain the camera movement degrees of freedom as well as of the number of reference markers in the pool. Even using a trolley car mounted on a rail and having reference points at each 190 mm, the largest errors in evaluating the positions of the markers occur for M2, which is approximately 18 mm for the static marker protocol (which could be acceptable precision for some applications) and about 58 mm for the rod position compared to that of the static position, which is possibly a more severe error. However, for the rod length, the estimated error was lower than 0.1%, which makes sense since the possible errors in the extrinsic camera parameter equally affect all the pixels in the same frame. Considering that M2 made a rough estimate of the extrinsic parameters, while M1  
Figure 4: Bland–Altman plots. Panel (**A**): comparison between static camera and M1 for the static marker protocol 95% C.I. [\(-7.7\), \(14.2\)]. Panel (**B**): comparison between static camera and M2 for the static marker protocol 95% C.I. [\(-11.5\), \(34.3\)]. Panel (**C**): comparison between static camera and M1 for the rod protocol 95% C.I. [\(-64.2\), \(34.9\)]. Panel (**D**): comparison between static camera and M2 for the rod protocol 95% C.I. [\(-62.8\), \(37.8\)]. Panel (**E**): comparison between static camera and M1 for the swimming protocol 95% C.I. [\(-0.15\), \(0.15\)]. Panel (**F**): comparison between static camera and M2 for the swimming protocol 95% C.I. [\(-0.15\), \(0.23\)]. looks for the optimal solution for each frame, M2 precision should be, at best, equal to that of M1. In fact, the difference of 1.8 mm between the methods for the rod length is lower than data sensitivity since each pixel corresponds to approximately 2.5 mm on average based on the field of view size and the camera resolution. In the static marker and rod protocols, the magnitude of the error was correlated with the marker distance from the center of the view. Moreover, the errors evaluated considering only the markers in the central positions were lower for all the conditions. These findings were expected [9; 10; 11; 12] and indicate another advantage of the use of a single moving camera: the possibility of keeping the target object always in the center of the field of view, reducing the reconstruction errors. On several kinematic applications, the relation between the markers is more important than the real position and can be used to evaluate the distances, or the markers can be used to represent a body segment for instance. Considering that M2 also seems to be a viable alternative for some underwater 2D kinematics applications, in the cases where estimating the real position of a marker is relevant, M2 is not the best option.