## 3 Results and Discussion
### Analysis of Contour Reconstruction Reliability for \(S01\)  
Distribution of \(C_{f}\), \(\overline{D}\) and \(\sigma_{D}\) results as a function of \(S_{f}\), \(M\) and \(T\) corresponding to the \(S01\) scenario is presented in Figure 7. Each row in Figure 7 contains three graphs corresponding to the same edge detection method (\(M\)), corresponding each one to each MQI (\(C_{f}\), \(\overline{D}\) or \(\sigma_{D}\)). Each graph represents the distribution of its MQI values with respect to the filter size (\(S_{f}\)) and the threshold (\(T\)) by means of a colour scale. Thus, cooler colours represent better relative results than warmer colours. Figure 6 shows that all MQI showed high dependence on \(S_{f}\) and \(T\), whereas certain similarities were observed between different methods. Figure 6: Raw images (\(I0x\)) captured for \(S01\), \(S02\), \(S03\) and \(S04\) contrast scenarios. Figure 7: Measurement quality indicator (MQI) results as a function of \(S_{f}\) and \(T\) for every \(M\) calculated for SO1. Variations in results distribution regarding \(S_{f}\) and \(T\) were quite similar among first derivative methods ([PERSON], Prewitt and [PERSON]). These methods showed a high dependence of \(C_{f}\) with respect to \(T\). Medium-to-high \(T\) values severely reduced the contour coverage, except for several test combinations with extremely low \(S_{f}\) values. Severe coverage drops were observed for \(T>45\), while \(C_{f}\) was found to be far less sensitive to changes in \(S_{f}\). \(\overline{D}\) and \(\sigma_{D}\) also worsened for high \(T\) values, but this does not mean that best accuracy results corresponded to extremely low \(T\) values. In fact, a narrow interval of intermediate \(T\) values provided minimum \(\overline{D}\) and \(\sigma_{D}\) results, which implied the best similarity between the FBS digitising and the CMM reference. These intervals were wider and more homogeneous in the case of \(\overline{D}\), and thinner and more \(S_{f}\)-dependent in the case of \(\sigma_{D}\). Both Canny and ApproxCanny methods presented a broad range of \(S_{f}\) and \(T\) combinations providing a complete coverage of the test target contour. Nevertheless, \(\overline{D}\) showed minimum values for Canny when intermediate \(S_{f}\) and \(T\) were selected. For a given \(S_{f}\) value, combinations with extremely high or low \(T\) values provided poor \(\overline{D}\) results. Nonetheless, \(\overline{D}\) was found to be also sensitive to \(S_{f}\) variations for a given \(T\), although this effect was less noticeable for intermediate \(T\) values. A similar behaviour was observed regarding \(\sigma_{D}\). ApproxCanny, on the other hand, presented better \(\overline{D}\) and \(\sigma_{D}\) results for combinations of intermediate \(T\) and high \(S_{f}\) values. The interval of optimal combinations was narrower here than it was for Canny but was still far wider than the one observed in first derivative methods. Finally, ZeroCross showed a completely different distribution of results because, for the original test resolution, it seemed that no valid results could be achieved for \(T>5\) combinations (Figure 7). Moreover, even for \(T=5\), the coverage was very poor. Nevertheless, coverage was not the only problem with this method, because even optimal \(\overline{D}\) and \(\sigma_{D}\) results were very poor. It seemed that ZeroCross should be rejected, therefore these results were confined to such a small range of \(T\) that a second round of the test was performed in the \(0<T<15\) experimental range with a \(T=1\) sample step (Figure 8). Accordingly, ZeroCross was far more sensitive to \(T\) values than other methods. Slight variations in \(T\) caused quality results to vary abruptly. Conversely, an adequate selection of \(T\) and \(S_{f}\) provided excellent results which, in certain cases, could be even adopted for an optimal contour characterisation. Thus, combinations with \(T=3\) and \(S_{f}>35\) provided a good coverage and very low \(\overline{D}\) and \(\sigma_{D}\) values.