# Camera Calibration in High-Speed Robotic Assembly Operations
## 4 Results and Discussion
In most cases, these types of applications could include parts with random positions and orientations, measurement surfaces with deviations from the planar shape, fixtures and supports with low accuracy levels (including 3D printed), and so on. The first approach showed that these variations have a higher influence on the results obtained, reflected through a higher error level. * The method using the planar interpolation was used in order to mitigate the influence of the environmental variables on the camera angle calculation. The procedure is harder to implement and uses more data, thus requiring more computational resources. The calculation is more complex, requiring the employment of the least squares method and conversions between polar coordinates and Cartesian coordinates. * The accuracy of the second approach proved to be higher. By using more measurement points, the error levels ranged from 0.25% and 2.57%, with an average of 1.02%, as shown  
* For the first approach, the average error level for the 20 pixels perimeter was 5.44%; for the 30 pixels perimeter, it was 6.59%, for the 40 pixels perimeter, it was 7.46%, and for the 50 pixels perimeter, it was 10.44%. * For the second approach, the average error level for the 20 pixels perimeter was 1.88%; for the 30 pixels perimeter, it was 0.85%, for the 40 pixels perimeter, it was 0.97%, and for the 50 pixels perimeter, it was 0.39%. * It can be observed that, as the points are measured on a wider perimeter, in the case of the planar interpolation approach, the error levels decrease. For the law of cosines approach, the error levels increase with the measurement perimeter, as the errors are cumulated due to the nature of the algorithm. * For both calibration methods, one set of points is enough to determine the position and orientation of the camera relative to the measurement plane at a certain moment. However, as this algorithm was implemented in Python, the results are updated in real-time. Whenever necessary--that is, when the measurement plane changes--the calibration subroutine--the Python program--can be accessed to perform another calibration that will determine the position and orientation of the camera relative to the new measurement plane. * The errors shown in the analysis (Tables 3 and 4) are the errors that result when comparing the real camera inclination angle to the calculated angle using the calibration algorithm. It should be noted that these are not object measurement errors. The main purpose of camera calibration is to reduce measurement errors due to image deformations induced by perspective. While it is true that a more precise calibration yields more precise results when measuring objects, any level of calibration would ultimately reduce measurement errors by some amount. Thus, it must be taken into account that, while in some cases presented above the calibration errors may reach or exceed 10%, the measurement errors induced by these offsets would be much lower. The overall assembly accuracy is determined by the 2D camera used; the calibration process itself just improves the measuring process.