# Bisector-Based Tracking of In Plane Subpixel Translations and Rotations
## 4 Results
### Experimental Results
#### 4.2.2 Video Processing and Object Tracking Calculation
\begin{table}
\begin{tabular}{c c c c} \hline  & **Minim. Method** & **Solving (5)** & **Theoretical** \\ \hline \(\Delta x(x_{A},y_{A})\) & \(-0.47\pm 0.01\) & \(-0.25\pm 0.06\) & \(-0.5698\) \\ \(\Delta y(x_{A},y_{A})\) & \(0.033\pm 0.007\) & \(0.049\pm 0.006\) & \(0.0591\) \\ \(\phi\) & \(-0.0187\pm 0.0004\) & \(-0.005\pm 0.004\) & \(-0.0228\)[1] \\ \hline \end{tabular} \({}^{1}\) Distances in millimeters and angles in radians.  
\end{table} 
Table 1: Horizontal and vertical distances and torsional angle obtained from the location vector components computed using different methods for the experiment in Figure 9, and the theoretical values. Errors are obtained as standard deviation of the computed component of the last 50 frames of the sequence, when the system is static. Figure 9: Frame of the recorded video (see Visualization 3) of the U-shaped beam during the experiment with the selected segments in blue, the intersection (red square), and the computed bisector (pink). Besides the rotation and the total displacement of points once the applied load has stabilized, the proposed method allows for the instantaneous measurement of these quantities in time, while the load is being transferred from the operator's hand to the structure and the structure distributes the stresses and suffers strains though the whole structure. The load was applied slowly enough to avoid an additional impact factor in the structure, but fast enough to minimize transference time from the operator's hand to the structure. Despite this, some small time was spent during this transference and hence both effects (transference load and strain-stresses redistribution) are mixed in the results in time. In Figure 10, we represent the relative displacement of the point A in (a) the \(x\)-direction, (b) the \(y\)-direction, and (c) the torsional angle computed both separately solving (5) and with the proposed minimization method for the video of Figure 9. Separately solving Equation (5) seems to work well; however, it suddenly provides an inaccurate solution from around 0.8 s. This might be because the errors of both fittings accumulate. The results provided by the minimization method show a smooth behaviour, which allows us to assess the dynamic process. Note that the accuracy of the method (0.01 mm, equivalent to 0.1 px) and the theoretical total displacement in the \(y\)-direction (0.07 mm) are of the same order, so the graph in Figure 10b seems wrinklier, and thus the results obtained for this displacement are not reliable. On the other hand, we have processed the video from the camera recording the contact distance measurer (Figure 11a) in order to obtain the vertical displacement of the beam in time. This measurement can be used to evaluate the results provided by the minimization method in the dynamic process of the deflection. Therefore, we compare it with the results of the proposed technique. Each frame was cropped, binarized, and transformed to polar coordinates around the centre of the clock (Figure 11b). This point was manually selected in the first frame of the sequence. The sum of the intensity values of the columns of that image in polar coordinates is at a minimum where the needle is, so we computed the column of minimum sum and we quantized the number of columns to one hundred discrete levels between 0 and 1, which corresponds to the hundredths of a millimetre (Figure 11c) of the accuracy of the device. Each time a whole lap was performed, we added 1 mm. Figure 10: (**a**) \(x\)-displacements at A, (**b**) \(y\)-displacements at A, and (**c**) torsional angle computed using the proposed minimization method (red) and separately solving Equation (5) (blue). In Figure 12, we have represented the displacement measured with the contact measurer at the point D, \(\left[\mathrm{Y}\left(x_{D},y_{D}\right)\right]_{t}\), versus the torsional angle computed from the orientation of the bisector obtained with the proposed method at the point A, \(\left[\theta\right]_{t}=\left[\beta\right]_{t}-\left[\beta\right]_{0}\).