# Bisector-Based Tracking of In Plane Subpixel Translations and Rotations
## 5 Discussion and Conclusions  
We have presented a targetless noncontact measuring technique that completely locates both the position and orientation of an object describing a trajectory. Two nonparallel segments from the image of the object are used as features to compute, through a simplex minimization method, a location vector that comprises the intersection point and the orientation of the bisector of the angle between them. We have evaluated the performance of the method both with a numerical simulation and lab experiments that comprised practical applications. The algorithm provides a theoretical mean subpixel accuracy of 0.03 px for the position and 0.02 degrees for the orientation. In the practical application, we reached subpixel accuracy of 0.1 px and 0.04 degrees for the orientation, besides obtaining accuracies of hundredths of \(\deg/\mathrm{s}^{2}\) in the angular acceleration, and thousandths of \(\deg/\mathrm{s}\) in the angular velocity. The obtained resolutions equal the best ones reported in the literature. The technique could be used to test the performance of stage motors and engines. In the above example, we were able to distinguish the accelerated phases and the constant velocity phase. The obtained angular velocity value agrees with theoretical one, whereas both angular acceleration values are below the limit of the device. One could also establish the time necessary to reach constant velocity, evaluate the stability of the different phases of the movement (constant velocity, uniformly accelerated,... ), and model the acceleration and deceleration stages, etc. The technique has also been useful to measure the change of position in time of a structure under external loads. The instantaneous position is linked with stresses and strains in the structure, but usually only the final position can be measured due to the speed of the process. With this technique, using the fast-enough camera needed, the instant stress-strain process during the structure's loading can be measured, and additional information about the stress transmission can be obtained. One of the steps of the algorithm is an image processing block to obtain a binary image with some nonparallel segments. That block is susceptible to being changed depending on the application, thus providing a spread range of use. Indeed, even the condition of the object to remain unaltered in shape and having some nonparallel segments could be relaxed. Of course, it would imply an increase in the uncertainty of the measurement. The technique could be applied to track the translation and rotation of crawling cells in time-lapse video microscopy sequences [4]. We insist on the idea that the algorithm can be adapted and optimized depending on the application. It could be also modified to be addressed to a clinical application, such as image registration [19]. The sequences are processed offline; nevertheless, as future work, we expect to modify the algorithm to perform real-time processing, and then apply the technique to automatic target recognition research. The method is supported on the a priori knowledge of some structural information, that is that the object extracted from the image does not deform. If we extend that assumption not only to the image plane (\(XY\)) but to the \(Z\) direction, we could perform three-dimensional tracking. Instead of extracting only two intersecting segments on a plane, we would need three intersecting segments in a three-dimensional space. If the angles between segments do not change in time, we could compute the bisector and use it to track the movement, if the object does not change its shape. **Author Contributions:** [PERSON] conceived the main idea, the numerical models, and wrote the paper's draft. All programming for the theoretical models and the numerical analysis of the experiment was also done by him. [PERSON] helped to understand and apply the Nelder-Mead simplex algorithm. The first experiment was conceived and implemented by [PERSON].