## 6 Discussion  
The work presented includes methodologies to address each integration step, with the final aim of achieving 3D thermography by maintaining the decoupling of the devices. Concerning the extrinsic calibration, we proposed an automatic method that exploits the object silhouette. An evaluation of the accuracy of the method is presented in Table 2. Since our automatic method does not exploit the concept of homologous points (and thus, MRE cannot be computed), the evaluation of its accuracy was made by a comparison with the extrinsic parameters (considered the ground truth) obtained by the manual selection of homologous points, executed on a test object purposely designed. A comparison can be made with the automatic calibration method based on a silhouette developed by [PERSON] and [PERSON] [11]. The error concerning the \(x\) and \(y\) translations (\(\Delta t_{1}\) and \(\Delta t_{2}\) in Table 2) in our work is about one order of magnitude lower (the max obtained is around 1 mm); concerning the \(z\) translation (\(\Delta t_{3}\) in Table 2), our maximum error stays within 12 mm, against the over 50 mm reported in [11]. Regarding the error on the rotations (\(\Delta\alpha\), \(\Delta\beta\) and \(\Delta\gamma\) in Table 2), our errors are higher, with a mean of 0.58 degrees against the 0.3 degrees reported in [11]. We want to point out that this comparison is made between integration procedures that suit different integration modalities. In [11], indeed, the authors carried out a real-time integration between thermograms and depth-maps (2.5D), whereas we integrate (offline) thermograms with 3D point clouds. The difference in the type of the range data integrated entails, among other things, the following fact--the accuracy of the method used in [11], as the authors said, depends on the scene coverage, that is to say the percentage of the area covered by the object of interest with respect to the background. The higher the coverage is, the higher the edge variability is, and the lower the error in the extrinsic parameters. In our case, since we did not work  
Figure 17: Results of the integration of twelve thermograms. (**a**) Three different views coloured with the colormap “hot”. (**b**) Frontal view coloured with the colormap “jet”. with an edge map but with 3D point cloud, the concept of edge variability is not similarly defined and the error did not depend on this parameter. Unfortunately, regarding the accuracy, a direct comparison with the decoupled method presented by [PERSON] al. [22] is not possible because the automatic calibration procedure they used was based on the automatic matching of interest points and was evaluated by the classical MRE. Apart from the calibration method, other differences from the work [22] include the fact that they used the 3D data in the form of a polygonal mesh, whereas we keep the 3D data as a point cloud during the whole integration process. For visual purposes, if need be, the results may be converted into a coloured mesh at a later time. Concerning the handling of the points in which more temperatures are superimposed, we computed the temperature to be assigned as a weighted average, where the weight decreases in an exponential way if the viewing angle increases, which was the method exploited by [PERSON] and [PERSON] in [9]. In [22], conversely, the weight of each point temperature was computed as a function of the position of the point inside the view frustum of the camera (the weight increases if nearer to the optical axis or to the optical centre). A flaw of this latter approach is that it did not take into account the object geometry (i.e., the normal vectors in each point) and so it was prone to fail to compensate for the variation of the emissivity at high viewing angles. Figure 14 clearly shows that at high viewing angles the temperature can be underestimated (in that specific case up to one degree).