# Comparative Analysis of Discrete Subtraction and Cross-Correlation for Subpixel Object Tracking
## 4 Conclusions  
In this manuscript, we have analyzed the performance of the Discrete Subtraction method (DSM) for target tracking with subpixel accuracy. The method is based on calculating the difference between the grayscale intensity of a reference image and its displaced version [13]. The tracking results of this method, tagged as DSM, have been compared to those obtained with the more popular correlation method with local peak interpolation to achieve subpixel resolution. To this end, four different targets have been mounted on a motorized platform and horizontally displaced while a digital camera records all the process. The \begin{table}
\begin{tabular}{c c c c c} \hline  & **DSM** & **Correlation** & **DSM** & **Correlation** \\  & **Max Abs (Error)** & **Max Abs (Error)** & **Mean \(\pm\) STD** & **Mean \(\pm\) STD** \\ \hline Square & 0.042 & 0.073 & \(-\)0.003 \(\pm\) 0.013 & \(-\)0.029 \(\pm\) 0.018 \\ Circle & 0.032 & 0.021 & \(-\)0.011 \(\pm\) 0.007 & \(-\)0.004 \(\pm\) 0.006 \\ Gaussian & 0.145 & 0.102 & \(-\)0.036 \(\pm\) 0.035 & \(-\)0.006 \(\pm\) 0.030 \\ Male & 0.151 & 0.086 & \(-\)0.080 \(\pm\) 0.027 & \(-\)0.033 \(\pm\) 0.017 \\ \hline \end{tabular}
\end{table} 
Table 2: Displacement errors for the DSM and correlation methods for 2000 frames in the middle of the trajectory. All units are given in mm. experiment resulted in different sequences of moving targets with an expected frame-to-frame displacement of 1.3 \(\upmu\)m, or equivalently 0.002 px. The results indicate that the average performance of both DSM (Digital Speckle Method) and correlation-based methods is similar, but DSM is more sensitive to noise compared to correlation. This sensitivity to noise is reflected in a higher dispersion in the calculation of the target position, which can be up to five times worse for complex objects. Thus, the DSM method may be less accurate for complex objects that exhibit small distortions when captured at different positions. However, one advantage of DSM is that it does not require interpolation, which means it is not affected by peak-locking errors that can be observed in methods using squared targets when tracked with the correlation method. In terms of target morphology, the circular target is found to be the most suitable artificial target for subpixel tracking. It is easy to draw and yields clean and accurate results. Additionally, circular shapes are commonly found in natural objects such as perforations or bolts, making them suitable for image tracking using natural objects. Based on these findings, the DSM method can be considered a reliable alternative to the correlation method. It offers the advantages of simpler implementation and lower computational cost, although it requires previous calibration. However, it should be noted that DSM cannot recognize the direction of movement as currently formulated. Future studies could focus on analyzing the performance of the DSM method with textured targets, such as pseudo-speckled patterns used in Digital Image Correlation. Results obtained with complex targets suggest that the method may not provide optimal results, but the deviation of the curve from linear behavior can provide valuable information about object distortions that is not captured by the correlation method, where only the peak position is used as a parameter. In summary, the DSM method is a reliable alternative to correlation-based methods, offering simplicity and a lower computational cost. However, it is more sensitive to noise and may not perform optimally with complex targets. According to this, the choice of circular targets is recommended for subpixel tracking due to their ease of use and accuracy. Conceptualization, D.M. and J.T.S. ; methodology, D.M. ; software, M.-B.T. ; validation, M.W. ; formal analysis, B.F.; investigation, B.F.; writing--original draft preparation, B.F.; writing--review and editing, D.M., M.W. and M.-B.T. All authors have read and agreed to the published version of the manuscript. This research was funded by CELTA, No.