**7. Conclusions**

In this work, a decoupled acquisition method for generating 3D thermal models is proposed. The integration is carried out using the triangulation laser scanner Konica Minolta Vivid 9i and the thermal camera Testo 882, but it can be exploited for generating 3D thermal models with a generic range sensor and a generic thermal camera. The two devices are kept independent during the acquisition phase, allowing the integration of 3D data and thermal data acquired at di fferent times.

With regard to the extrinsic calibration, two methods are used, a more standard one relying on a manual selection of homologous points, and an "automatic" one, the latter based on finding the optimum of a particular function which evaluates the degree of filling of the reprojection of the 3D points inside the object silhouette in the thermogram. The former method is used to assess the e ffectiveness of the latter, which is proven to work well in the case study, but has room for improvements, especially in terms of robustness. Concerning the data fusion, we propose an easy to implement algorithm which is able to deal with complex object shapes, handle occlusions and cases of incomplete data from the range finder. Furthermore, the viewing angle is computed, and it is used to calculate a weight for each ray, in order to assign a proper temperature value in the zones in which, when integrating multiple

thermograms, overlaps occur. It was shown how this can e ffectively reduce the error in the temperature due to the dependence of the emissivity on the viewing angle.

The integration methodology was first tested on a 3D-printed object and was then applied to a cultural heritage case study, and the results sugges<sup>t</sup> that this approach can be e ffective and useful with an eye to integration and restoration. We are planning further tests to better investigate the effectiveness of the method.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2076-3417/10/3/828/s1.

**Author Contributions:** The authors have given an equal contribution to all the di fferent parts of this article. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank Ing. Massimiliano Fantini (Romagna Tech S.C.P.A.) for his important contribution to 3D laser scanner survey about the statue of Agostino di Duccio.

**Conflicts of Interest:** The authors declare no conflict of interest.
