# A Termination Criterion for Probabilistic Point Clouds Registration
## 4 Results
The result is expressed in terms of median and 0.75 and 0.95 quantiles of the scaled mean squared error, as described in [6]. In Table 3 we compare the median of the results on the various datasets of the benchmark, using PPCR with a high fixed number of iterations (100 iterations) and using the cost drop as termination criterion (stopping when the cost drop is less the 1% of the initial cost for more than 10 iterations). For the cost drop, in the column named _Number of iterations_, we show the mean number of iterations required to solve the registration problems. The same results are shown in Figure 7 as histograms. For most sequences, the differences between the results obtained using the two methods are negligible. Indeed, the medians among all the registration problems of all the sequences (that is, the row named _total_ in Table 3) are very close. However, there are notable exceptions. For the _box_met_ and the _urban05_ sequences, the cost drop leads to much better results (a lower median means a better alignment). This is the same behaviour we observed for the _Corridor_ dataset in the previous set of experiments. On the other hand, on the _p2 at_met_ and the _plain_ sequences the high number of iterations leads to better results. Nevertheless, it has to be considered that, even when the cost drop is not the best termination criterion, its results are still very good. At the same time, the average number of iterations required using the cost drop is 18.55 and, considering the sequences individually, never greater than 31; therefore there is a great reduction in computational time, w.r.t. using 100 iterations. Table 4 shows that, using the cost drop, we obtain even more consistent results, since its 0.95 quantile is less than that of the 100 iterations. The 0.75 quantiles, instead, are very similar. The proposed termination criterion requires two parameters--the percentage of drop and the number of iterations during which the condition described by Equation (7) should hold. However, the experiments show that using 1% and 10 iterations as thresholds leads to good results in a very large and varied set of registration problems. Therefore, this values should be adequate for most cases and should not require any further fine-tuning. In Table 5, we show the results using 1% and 20 iterations as thresholds. The median result is very close to that obtained using 100 iterations, although the mean number of iterations used is less than 30; therefore, there is a great saving in computational time. However, in our opinion, the difference w.r.t. using 10 iterations as threshold is so negligible that it is not worth the extra computational time. Anyway, it is still an option if a very accurate result is desired. PPCR using the proposed termination criterion, along with instructions on how to use it, is available on GitHub: [[https://github.com/iralabdisco/probabilistic_point_clouds_registration](https://github.com/iralabdisco/probabilistic_point_clouds_registration)]([https://github.com/iralabdisco/probabilistic_point_clouds_registration](https://github.com/iralabdisco/probabilistic_point_clouds_registration)) (accessed on 17 Mar 2021).