## 3 Results and Discussion
### Analysis of Contour Reconstruction Reliability for S03
These effects can be also observed through the polar plots of the radial differences (\(R_{d}\)) presented in Figure 16.  
Polar graphs illustrate how multiple-contour detection issues negatively affect the contour reconstruction accuracy (Figure 16). At lower \(T\), the algorithm included comparatively weak gradients as contour candidates, causing the existence of multiple-contour candidates within the same angular sector and allowing a full contour coverage. When \(T\) increased, fewer multiple-contour issues occurred, but several sectors did not provide any valid contour point. This phenomenon is directly linked to a higher \(T\), causing the loss of a larger sector (nearly 120\({}^{\circ}\) for \(T60\)) and rendering contour reconstruction useless. Nevertheless, this loss of information was not randomly distributed along the contour. In fact, only lower sectors were affected while upper sectors retained an adequate coverage despite growing \(T\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Coverage Priority**} & \multicolumn{4}{c}{**Accuracy Priority**} \\ \cline{2-10}  & \(T\) & \(S_{f}\) & \( \begin{array}{c}C_{f}\\ \text{(\%)}\end{array} \) & \( \begin{array}{c}\overline{D}\\ \text{(\upmu)}\end{array} \) & \( \begin{array}{c}\sigma_{D}\\ \text{(\upmu)}\end{array} \) & \(T\) & \(S_{f}\) & \( \begin{array}{c}C_{f}\\ \text{(\%)}\end{array} \) & \(\begin{array}{c}\overline{This circumstance suggested that the observed behaviour was related to an anisotropic phenomenon. Consequently, the lack of uniformity in contrast between the target contour and the surrounding background regarding local contour orientation was thereafter analysed (Figure 17). Figure 16: Polar graphs of \(R_{d}\) calculated for S03 including reference CMM data (red dots) and three different test conditions (blue dots). Figure 15: Samples of \(S03\) contour points obtained with Canny for different angular positions and test configurations: \(T05/S_{f}15\) (**upper row**), \(T20/S_{f}15\) and \(T60/S_{f}15\) (**lower row**). Linear samples of grey-level intensity distribution in the original \(I\)03 are presented in Figure 17. In two of those orientations (45\({}^{\circ}\) and 90\({}^{\circ}\)) there were clearly defined isolated greyscale transitions (details C and D). Conversely, other orientations reveal multi-transition issues (details A and B in 0\({}^{\circ}\) orientation) and weak transition issues (detail E in 180\({}^{\circ}\) orientation). Accordingly, a relevant anisotropic behaviour of contrast was present. The FBS directional illumination brightened background areas next to the lower sectors of the target contour. Simultaneously, the 3D geometry cast a shadow in the background areas next to the upper sectors. Intermediate orientations showed an intermediate behaviour. Accordingly, the contrast anisotropy caused an evident lack of uniformity of greyscale transitions. This phenomenon was not just restricted to the contour itself, but also caused variations in the local grey intensity of the upper layer related to manufacturing characteristics (deposited material topography) and defects (seams). Multiple transitions caused multi-contour detection issues. These transitions must present certain differences (contour transition should be sharper than the rest, see A and B details), therefore lower T values would not properly discriminate them. On the other hand, using higher T values to minimise this problem would neglect low-contrasted contour sectors (see detail E). Due to T being the same for the whole image, contrast anisotropy was a major issue for the contour reconstruction. Arguably, the higher the anisotropic behaviour of contrast in the whole contour, the harder it is for an edge-detection algorithm to provide an appropriate reconstruction.