## 1 Introduction
One advantage of 3D thermal models is that, for each 3D point, one can compute the so-called viewing angle (i.e., the angle between the surface normal vector in that point and the vector joining the point and the optical center). This information can be used to correct the error in the temperature caused by the dependence of the emissivity on the viewing angle. Indeed, for a given material, the emissivity is usually not constant, but depends on several factors, such as the surface condition, the wavelength, the temperature, the presence of concavities and the viewing angle (a viewing angle-dependent emissivity is often called \"directional emissivity\"). A detailed explanation of how these factors affect the emissivity can be found in [1] (pp. 35-45). Whereas the role of many of these factors can be in general considered negligible, the dependence on the viewing angle is normally relevant, and can bias the results, as outlined, for example, in [20] and [5]. Therefore, by knowing both the directional emissivity and viewing angle, it is possible to correct the temperature accordingly. Examples can be found in [4; 6] and moreover in [21], where the internal reflections due to concave surfaces of a complex test setup were also taken into account. It is worth noticing that in these publications the different sensors were rigidly linked together (mainly for calibration purposes and real-time data integration), and the trend was to strengthen this physical union (until obtaining, in the final form, a unique device such as \"HeatWave\" [9]). However, in some cases, it can be more convenient to keep the two devices decoupled and independent. This is especially true in outdoor surveys, where there is often the need to perform the thermographic analysis at a specific day-time or night-time and/or weather conditions, which requires high versatility (e.g., for the assessment of the damages and energy efficiency of the building envelope [18]). Laser scanners, on the other hand, can be bulky and heavy; their handling and the regulation of their position and orientation (usually are mounted on a tripod) may be time consuming and requires caution. Fixing a thermal camera to this type of scanner would make them even more difficult to regulate, and the easiness of handling of the thermal camera would be compromised. Furthermore, the two devices may have very different optics, which make the optimal distance of acquisition distinct. Conversely, with a decoupled acquisition, the integration can be applied in a flexible way, namely only when it is useful, based on previously recorded data, and does not affect the stand-alone capability of each device. In the literature, works based on this approach are uncommon. One exception is the work of [PERSON] et al. [22], which consisted of a method for generating 3D thermal models with decoupled acquisition, which relies on structure from motion and particle swarm optimization. Our paper focuses as well on a decoupled type of integration, but it differs from [22] in several aspects, such as the calibration method, the data fusion technique and the management of the superimposition of multiple thermograms. This paper is organized as follows: the system architecture is outlined in Sections 2-4 explain the geometrical calibration and data fusion procedure adopted, respectively, and Section 5 presents the results. In the first experimental case of Section 5, the effectiveness of our approach is tested on a 3D-printed object properly designed. The second example of application belongs to the cultural heritage field. In the last few years, we have carried out a many-sided research project aimed at preserving and restoring the ancient sanctuary of [PERSON], built toward the middle of the 15 th century, in the place of Forn o near the city of Forli (Italy). In particular, we have applied thermal imaging and laser scanning both to the building at large and to the ornamental elements.