## 3 Theoretical Framework
### Albedo Factor and Surface Emissivity  
Figure 2 shows that the heating step had an amplitude of \(\sim\)320 W/m\({}^{2}\) for horizontal surfaces and \(\sim\)300 W/m\({}^{2}\) for vertical surfaces at 200\({}^{\circ}\). These values represent the total amount of incident radiation. However, as every surface absorbed only a part of the incoming energy (called the emissivity factor), this irradiation was only absorbed by blackbodies. As incident radiation energy (sunlight) is primarily visual and near infrared (NIR) energy [10], the factor used in this work to refer to the amount of reflected sunlight was albedo \(\alpha\), and the term describing the energy factor absorbed (and emitted) in the LWIR range was determined as emissivity \(\epsilon\).  
As the albedo of white plaster is approximately \(\sim\)0.65 [11], the actual absorbed energy is 35% of the total incident irradiation. On grey surfaces, the albedo is \(\sim\)0.55 [11], which results in an energy absorption of 45%. The albedo of grey pavement is \(\sim\)0.60 [11].  
As common building materials such as plaster and concrete are considered to have high emissivity (\(\geq\)0.95) in the LWIR range [12] p. 316, an emissivity correction for the LWIR camera was not performed. Instead, the factors researched imposed an albedo correction first.  
For Table 1 and all corrected figures, the albedo correction was performed using the aforementioned values.  
The scene in Figure 3 shows the composition of a common street with houses, garages, trees, a car and a paved road. Due to this composition, not all of the four selected regions  
Figure 2: Correction of GHI to GVI as before, zoomed in to show the relevant part of the dataset containing step heating.  
of interest are perpendicular to the optical axis of the thermography camera. For further inspections, it was necessary to perform a projective transformation from the observed angle to a plane that is perpendicular to the optical axis. For the creation of the transformation matrix, two assumptions were made. First, it was assumed that the observed ROIs were flat surfaces, and second, the two building walls and the garage sidewall in particular had a rectangular shape. For each ROI, the four edge points of the studied object were selected and registered to a rectangular geometry with the aspect ratio of the observed object [13]. The projective mapping was carried out with MATLAB, using the \"image processing toolbox\". Figure 4 shows a typical thermogram of the scene, with an overview over the ROIs chosen.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Temperature**} & \multicolumn{2}{c}{**Excitation**} & \multicolumn{2}{c}{**Surface Heat**} & \multicolumn{3}{c}{**Effusivity**} \\ \cline{2-7}  & **Difference** & **Gradient** & **Intensity** & **Capacity** & **SHT** & **LEF** & **Reference \({}^{\dagger}\)** \\ \hline Region of interest & K & K/min & W/m\({}^{2}\) & kJ/\(\left(\text{Km}^{2}\right)\) & & \(\text{J}/\left(\text{Km}^{2}\sqrt{\text{s}}\right)\) & \\ (1) Wall left & 7 & 0.6 & 300 & 6 & 324 & 1024 & 490–780 \\ (2) Wall right & 5 & 0.4 & 300 & 14 & 454 & 1061 & 490–780 \\ (3) Concrete road & 4 & 0.3 & 320 \({}^{\ddagger}\) & 27 & 2132 & 1971 & 1730–2120 \\ (4) Garage & 3 & 0.25 & 300 & 19 & 1362 & 1581 & 1100–1400 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Overview of the different estimations. Note this table corrects for the albedo factor of the different image parts.  
\({}^{\ddagger}\) The reference values are taken from [14; 15; 16]\({}^{\ddagger}\) as the concrete road lay horizontally. GHI is the excitation intensity (see Figure 2).  
Figure 3: Optical overview over the scene.