## 3 Materials and Methods
### Thermal Study of the Envelope: Probes and Cameras  
In addition to the construction of the thermal model of the envelope, a complete interior and exterior survey of the walls was carried out. The thermal probes and the two cameras were used. Forty points were chosen at the same distance apart (300 mm). Twenty points correspond to the exterior walls and 20 points to the interior ones. All were labelled and selected from areas where no discontinuities existed. The thermometer was placed on top of each point to measure the surface temperature, and photographs were taken with the two thermal cameras, placed 3 m apart while keeping the point in the centre of the image.  
Figure 7: Phases in the construction of the 3D-RGB model of the cellar.  
The results obtained are shown below: Figure 7 shows different views of the 3D model built with RGB images, Figure 8 shows the procedure for measuring the temperature of the walls using thermal probes and Figure 9 shows the thermal images with the sensitive points selected for the study.  
To check the validity of the study and to determine the accuracy that could be obtained by radiometric thermal imaging, the temperature values provided by the cameras at the reference points were compared with those obtained from the thermal probes in direct contact with the walls. The study was carried out for both cameras, inside and outside the envelope. Figures 10 and 11 show, on the ordinate axis, the temperature measured by the probes, and on the abscissa axis, those obtained from the thermal images. Figure 10 shows the outside temperature results and Figure 11 shows the inside temperature results.  
In order to check the validity of the radiometric measurements made with the two thermal cameras, the Pearson's correlation coefficient was calculated between the matrices formed by the temperature values measured directly on the walls and the radiometric values. The correlation coefficient of two variables is a measure of their linear dependence. If each variable has \(N\) scalar observations, then the [PERSON]'s correlation coefficient (Equation (1)) is defined as [58]:  
\[\rho(A,B)=\frac{1}{N-1}\sum_{i=1}^{N}\biggl{(}\frac{A_{i}-\mu_{A}}{\sigma_{A}} \biggr{)}\biggl{(}\frac{B_{i}-\mu_{B}}{\sigma_{B}}\biggr{)} \tag{1}\]  
where \(\mu A\) and \(\sigma A\) are the mean and standard deviation of \(A\), and \(\mu B\) and \(\sigma B\) are the mean and standard deviation of \(B\). Alternatively, it is possible to define the correlation coefficient (Equation (2)) in terms of the covariance of \(A\) and \(B\):  
\[\rho(A,B)=\frac{cov(A,B)}{\sigma_{A}\sigma_{B}} \tag{2}\]  
Figure 8: Measurement procedure.  
Figure 9: Thermal images, points of measurement and anomalies (different colour patterns).  
Table 1 shows the results obtained both indoors and outdoors with the two cameras. As can be seen, even in the case of the lowest correlation, the results are more than acceptable.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Pearson’s Coefficient** & **Indoor** & **Outdoor** \\ \hline B335 & 0.785 & 0.813 \\ \hline VUE PRO & 0.803 & 0.52 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Correlation coefficients.  
Figure 11: Comparison between the indoor temperatures measured with the probes and those extracted from the two thermal cameras.  
Figure 10: Comparison between outdoor temperatures measured with the probes and those extracted from the two thermal cameras.  
In the following, the procedure for the construction of the 3D thermal model will be presented. Then, the points or regions where anomalies were found will be highlighted, and finally, the conclusions and proposed improvements will be detailed.