## 4 Results  
The results with each method used in the study were obtained independently and by different analyzers and were supervised by two experts in the fields of dentistry and/or maxillofacial radiology, with extensive clinical experience to ensure the effectiveness of the procedure. The volumes of the pulp chamber according to the different methods used in the study are in Table 1. The data obtained with micro-CT were established as ideal and \"true volumes\" because of the high resolution of the images that were acquired due to the high dose of radiation used; those results were the most reliable. The values obtained for samples 1, 2, and 4 were quite similar (Figure 2), while those for samples 3 and 5 were almost double (Figure 3). The range of the values was completely suitable and normal and was independent of the maxilla and place. From the CB-CT images manipulated by the specialist (set CB-CT threshold), the values were similar to those obtained by micro-CT except for samples 4 and 5, whose values were considerably lower. However, the volumes obtained with the automatic CB-CT threshold are always lower than those obtained with the established CB-CT threshold and with micro-CT, especially samples 4 and 5. Likewise, the volumes obtained with the algorithm are very similar to those obtained with micro-CT, with the exception of sample 5, whose value is very close to that obtained with the automatic CB-CT threshold, except for sample 3. The volumes generated by the mathematical formula resulted reliable in 4 of the 5 samples analyzed, with an error of 3.65% on average, and matched those obtained with micro-CT. Only in sample number 5 did the results calculated by the algorithm clearly differ from those obtained with micro-CT.  
From the point of view of the algorithm, it can only be said that the method of detection of the pulp chamber is performed automatically using as data the distance between planes, the initial plane, and the control parameter k. For the algorithm to work, it is also necessary to know the location of a pixel belonging to the pulp chamber of the first image, which can be given by the user; otherwise, the central value of the image is taken. Based on these data, the pulp chamber is automatically detected in the planes where it exists, along with the corresponding volume. Therefore, from the perspective of the algorithm, there are no differences between sample 5 and the others (Figure 3); accordingly, it is not possible to justify the discrepancy between the volume provided by micro-CT and the calculated volume. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Micro-CT** & **CB-CT Viewer** & **CB-CT Viewer** & \\  & **(mm3)** & **(mm3)** & **(mm3)** & **CB-CT** \\  & **(mm3)** & **Set Threshold** & **Automatic Threshold** & **Algorithm** \\ \hline Sample 1 & 11.13 & 11 & 7 & 11.76 \(\pm\) 0.6 \\
2 MU & 11.79 & 13 & 8 & 12.4 \(\pm\) 0.78 \\ Sample 3 & 24.36 & 25 & 21 & 23.36 \(\pm\) 1.26 \\
2 ML & 14.1 & 9 & 4 & 14.36 \(\pm\) 0.38 \\ Sample 5 & 21.4 & 14 & 5 & 4.67 \(\pm\) 0.22 \\
2 MU & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative volumes obtained with the different methods used. 1: first; 2: second; M: molar. U: upper maxillary; L: lower maxillary. Software automatic threshold: 300. Several authors have calculated the pulp chamber volume for various purposes using different methods: one study measured the volume of the pulp cavity from cone-beam computed tomography (CB-CT) images by comparing them with the micro-CT reference standard, utilizing results from various radiological units and comparing 3D reconstructions using statistical methods [13]; some studies aimed to understand internal anatomy relationships prior to performing endodontic therapy using artificial intelligence techniques, training a U-Net network for automatic pulp segmentation [14; 15]; one study calculated the pulp chamber volume for estimating human age using statistical methods [16; 17].