# Bisector-Based Tracking of In Plane Subpixel Translations and Rotations
## 4 Results
### Experimental Results
#### 4.2.2 Video Processing and Object Tracking Calculation
Therefore, the proposed method allowed us to obtain angular acceleration and velocity with accuracies of hundredths of deg/s\({}^{2}\) and thousandths of deg/s, respectively, besides tracking the position of the object (see Visualization 2). Under the assumption of being a motion consisting of a constant velocity phase between two uniformly accelerated ones, we have been able to determine the instants and angular positions limiting each motion phase. * Mechanical torsion and bending in a beam In this experiment, we obtained two video sequences: one from the camera recording the beam, and another one from the camera recording the contact distance measure. On the one hand, the processing of the first video is again directed to obtain an edge binary image. The object to be tracked is the U-shape beam profile, so, from each frame, we cropped a region around the point A, where we expected to extract two intersecting segments. Then, we equalized the histogram of the image to enhance contrast and we binarized it. Straightaway, we extracted the edges using the Canny method [18], and applied an opening filter to remove small objects (those shorter than 200 px, in this case). In the final processed image, we manually selected two regions that contained the two nonparallel segments (\(s_{1}\) and \(s_{2}\)), and got the coordinates of both segments. These regions were automatically transformed frame to frame following the relative movement. With those, we computed the location vector (\(x_{c}\), \(y_{c}\), \(\beta\)) for each frame of the sequence through the presented minimization method. In Figure 9, we show a frame of the sequence with the selected segments (blue), the computed intersection (red square), which coincided with the corner of the beam as expected, and the bisector (pink). Figure 8: Variation in time of the orientation of the computed bisector for the selected segments from the rotation stage experiment. The curve was divided into three, approximately distinguishing between the linear (blue circles) and nonlinear parts (red circles). The blue line and the red dashed lines represent the best curve fitting to each part. In Table 1, we present the results for the location vectors' parameters computed separately solving (5), with those obtained by applying the proposed minimization method and the theoretical values obtained from (8) and (9). We can compare the errors and deviations obtained with both methods at point A with reference to the theoretical one. The torsional angle coincides with the variation of \(\beta\). Its value obtained with the proposed method is quite similar to the theoretical one, with an absolute difference of \(4\times 10^{-3}\) radians and a relative deviation of 18%, whereas the result obtained solving (5) differed around 0.02 radians with a relative deviation of 78%. The errors of the fittings in (5) probably accumulate, a fact that leads to a bad angle estimation, and therefore the method is dismissed. By comparing the theory and the minimization method regarding the displacements, one can see that the deviation in the \(x\)-direction is similar to that of the angle. However, the deviation in the \(y\)-direction is quite higher. Note that the displacement magnitudes are low, so the signal-to-noise ratio is high and the measurements inaccurate, although the estimation is not bad. It is not worth comparing displacement values because those magnitudes are related to the torsional angle in Equation (9). Indeed, they are more sensitive to errors in the theoretical calculations. Note that the structure is not ideal (welding, holes, not squarely welded pieces, irregularities in the shape pieces, inhomegeneities in the material,...).