The discrepancy between the temperatures can be clearly appreciated since it reaches up to 1.5 \({}^{\circ}\)C in repetitions 1 and 10. Below are the standard deviation images with respect to the original mean thermal image. In this

Figure 1: Assignment of temperature to the point clouds for each rotation of the thermal camera. Spins are numbered from 1 to 8.

example, the outlier detection algorithm concludes that images 1, 2, 9 and 10 are _outlier images_. The average image of repetitions 3, 4, 5, 6, 7 and 8 is, therefore, taken as the corrected and representative thermal image corresponding to the first rotation of the thermal camera. Figure 2b presents the average original and standard deviation images before and after carrying out the outlier image filtering process. As can be seen, the average standard deviation image now has a mean value of 0.24 \({}^{\circ}\)C, which is a considerable improvement to the earlier value of 0.51 \({}^{\circ}\)C. The average image will later be used to calculate a partial thermal cloud corresponding to the first rotation of the platform. The same process is carried out for the images corresponding to the remaining nine rotations, thus obtaining the corresponding ten partial thermal point clouds. Note that the temperatures contained in these average thermal images are _apparent temperatures_ that will later be corrected with the calculated emissivity and the reflected radiation effects. Figure 2c shows a composition containing all the _apparent temperature images_, presented as a panoramic image, and the _apparent thermal cloud_ calculated with them. ### Obtaining Real Temperatures: Results of Stage 2

The _apparent thermal point cloud_ (ATPC) is used to calculate the _real thermal point cloud_ (RTPC). As mentioned in Section 4, the ATPC is segmented into points belonging to the walls, ceiling and floor (assuming that the scene is a standard room), and the

Figure 2: Outlier thermal image detection for turn i = 1. (**a**) Original thermal images (up) and standard deviation images (down). (**b**) Average thermal image and standard deviation average images before and after applying the correction algorithm. Note that the mean standard deviation is reduced from 0.51 \({}^{\circ}\)C to 0.24 \({}^{\circ}\)C when outlier images 1, 2, 9 and 10 are eliminated. (**c**) Resulting in average thermal images for all camera turns and an apparent thermal point cloud of Zone 1.

corresponding colour orthoimages (COs) and apparent thermal orthoimages (ATOs) are obtained automatically. Upon processing COs and ATOs, as explained in the four steps shown in Section 4, the real thermal orthoimages are eventually obtained. Figure 3 illustrates the COs and TOs corresponding to SEs #3, #6, #9 and #10 of Zone 1 (Room EastI), in which wrinkled pieces of aluminium foil and electrical tape have been placed on four faces of the room. All these targets are automatically recognised and delimited in the COs. The dual ATOs are then used to first calculate the _reflected apparent temperature_ by means of Equation (1). The real temperatures of pieces of electrical tape near a door frame (if any), a window frame (if any) and wall areas are calculated according to Equation (2). Figure 4 shows how the aluminium foil and electrical tape targets are automatically detected. The emissivity of the objects \"window frame\", \"door frame\" and \"wall area\" is obtained from Equation (3) using the mean temperature of narrow rings around the corresponding targets. Finally, the real temperatures of all the _objects_ are calculated using Equation (4). Table 1 shows the values of the apparent and real temperatures measured on the aluminium foil (T) and the electrical tape targets (AT and RT) on all the walls in the scene,

\[T_{tape\_real}=\left(\frac{T_{tape\_ap}^{4}-\left(1-\epsilon_{tape}\right)T_{ ref}^{4}}{\epsilon_{tape}}\right)^{\frac{1}{2}} \tag{2}\]0 **(a–c)** Visualization of apparent (left) and real (right) 3D thermal models for (**a**) door-frames, (**b**) window-frames and (**c**) wall areas.