## 4 Results and Discussion
### Deep Learning Approach vs. Statistical Analytical Approach  
The review of the current deep learning approaches shows they have definite constraints. As an example of a deep learning approach, let us consider the ICCV 2019 paper by [PERSON] and [PERSON] [43]. It describes a non-iterative and non-gradient method based \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Description** & \multicolumn{3}{c}{**Mapping Error**} & \multicolumn{3}{c}{**Time to Run**} & \multicolumn{1}{c}{**\% of Data**} \\ \cline{2-7}  & **Avg** & **Std** & **Max** & **Avg** & **Max** & \\ \hline Our algorithm & 0.14 & 0.07 & 2.98 & 8 & 51.7 & 100 \\ \hline ICP (whole dataset) & 1.30 & 0.82 & 16.52 & 0.18 & 5.47 & 100 \\ \hline ICP for max(ME) \(\leq\) 0.14 & 6 \(\times\) 10\({}^{-4}\) & 4.6 \(\times\) 10\({}^{-3}\) & 0.13 & 0.18 & 5.47 & 53 \\ \hline ICP for max(ME) \textgreater{} 0.14 & 2.73 & 2.06 & 16.52 & 0.18 & 2.79 & 47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: ICP vs. our algorithm. The threshold for maximum ME is 0.14. It divides the dataset [78] into two parts. For ME, the mean value (avg), standard deviation (std), and maximum (max) are calculated for all the considered datasets. Also, the average and the maximum time to process 3D objects by the algorithm (in seconds) are provided. The ICP statistics are given for the whole dataset and parts of the dataset with maximum mapping error max(ME) \(\leq\) 0.14 and max(ME) \textgreater{} 0.14. The part of the considered dataset is provided in the column named “\(\%\) of data”. Figure 4: (**a**) A model of a feline with fangs, (**b**) a feline without fangs, (**c**) the ICP mapping of both models. on applying deep learning. The deep learning model should be trained on a dataset of 3D objects, and later, the transformation to map the objects will be produced. In the mentioned manuscript, the following are pointed out:  
* Current deep learning networks can only handle object-level point clouds (each usually has around 500 to 5000 points); this is a common limitation of recent point cloud learning methods. * The deep learning model can be improved by iteration or \"polishing\" via the classical ICP (iterative closest point algorithm). * The deep learning model is trained on some input data. The application of the method to unseen categories of objects shows a sharp drop in accuracy. * The extraction of the rigid motion is performed by solving 3 \(\times\) 3 SVD eigenproblems. This solution might be unstable due to the multiplicity of eigenvalues and sensitivity to outliers, as was shown by [PERSON] [13] (Appendix B). Usually, the proposed method is compared with the state-of-the-art ICP method and its modification, the Go-ICP method [36]. The ICP method may converge to the global or local extremum. The convergence to the local extremum could show a huge discrepancy with the ground truth solution. Calculation of the average accuracy of converged and non-converged (local extremum convergence) cases could show the inferiority of the ICP, even if it has higher or comparable accuracy in an overwhelming majority of all the cases in comparison with the deep learning method. We think the accuracy should be calculated separately for the category of globally converged data, with the percentage of locally converged cases in the dataset mentioned. We would like to mention the following:  
* Our algorithm does not depend on the end-to-end trained model, and we propose a solution based on a statistical analytical approach. * It does not matter to our algorithm which class of objects it uses; its accuracy does not depend on whether it has seen this class before. * Our algorithm was able to process 3D models with tens of millions of vertices and find global extrema, even when the ICP cannot, and the memory requirements for a deep learning approach are excessive. * It considers the internal architecture of the object, not only the tiny amount of surface points.