## 3 Geometrical Calibration  
When a thermal camera is involved, the term \"calibration\" could refer to two different types of calibration--the geometrical calibration and the radiometric calibration. The latter (which was not the object of this work) consists of a procedure that models the relationship between the digital output  
Figure 1: (**a**) Thermal camera Testo 882. (**b**) Laser scanner Konica Minolta Vivid 9i. Figure 2: High-level workflow of the integration process. of the camera and the incident radiation. Hereinafter, if the term \"calibration\" is used, \"geometrical calibration\" is intended. The geometrical calibration is a fundamental process used to compute intrinsic and extrinsic parameters of the system components. Intrinsic parameters model the optic imaging process and are divided into two groups--four parameters defining the camera matrix, based on the pinhole camera model, and other parameters defining radial and tangential camera distortions caused by the physical properties of lenses [23]. There are six extrinsic parameters which describe the relative pose of the sensors, i.e., the transformation from world coordinates to camera coordinates. In the vast majority of methods, the intrinsic parameters are computed first, and then they are exploited to determine extrinsic ones. For the determination of both intrinsic and extrinsic parameters, the best-known techniques involve the use of a target with a chessboard pattern, a method first presented by [PERSON] in [24]. Note that, in the case of thermal cameras, the pattern has to be detected in the IR spectrum. Several solutions have been presented for this purpose, involving, for example, a heated chessboard pattern or marker detectable in IR; a more detailed state of art can be found in [10]. In the last few decades, however, some work has been done in order to develop the so-called automatic or targetless extrinsic calibration methods, that exploit natural scenes' features (see [11; 25; 26; 27]). Concerning the intrinsic calibration, we adopted the method developed by [PERSON] et al. in [28], which relies on a mask-based approach and does not require specialized equipment. Regarding the extrinsic calibration, since our aim was to keep the two devices unlinked, the classical approach (consisting of acquiring several frames of the target in a fixed configuration of the two sensors) did not appear very suitable. For cases in which the identification of some homologous point is easily feasible, the extrinsic parameters are computed by means of a manual selection routine of homologous points, and then by exploiting the Matlab function \"estimateWordCameraPose\", which solves the perspective-\(n\)-point (PnP) [29]. However, this method might fail or achieve a very low accuracy in scenarios in which homologous points cannot be clearly identified. To address this limitation and to be able to consider more various scenarios, we developed an alternative method exploiting the detection of the object silhouette in the thermogram. In the literature, some silhouette-based calibration methods can be found, for instance in [30] and [31]. In [30], the pose of a known object is estimated through a hierarchical silhouette matching and unsupervised clustering, whereas in [31] the calibration of a stereo camera system was carried out by defining and minimizing a function that computes the distance between viewing cones, which are known from the silhouettes. The developed method has some similarities with the one presented in [11], in which the extrinsic parameters were obtained by minimizing an objective function that measures the alignment between edges extracted from RGB-D images (obtained by a depth camera) and the ones extracted from thermograms. Like that method, ours is suitable for thermograms in which the object contour can be easily identified, and so the object can be extracted from the background, a fairly common situation when dealing with thermograms.