# Geometrical Calibration of a 2.5D Periapical Radiography System
## 4 Discussion  
According to a joint statement by the American Association of Endodontists and the American Academy of Oral and Maxillofacial Radiology in 2015, the optimal imaging choice for root canal evaluation is intraoral X-ray [24]. Therefore, image quality often influences dentists' diagnosis and treatment methods. The 2D periapical film images commonly used in clinics cannot provide sufficient information for dentists due to image superposition limitations. Our team previously developed a 2.5D Periapical Radiography System but failed to obtain clear images because of limitations in the accurate adjustment of hardware positions. However, the calibration methods for CT cannot be applied to the 2.5D Periapical Radiography System. Therefore, in this study we proposed a two-step calibration method that enables the linking line of the X-ray tube and rotation axis to intersect orthogonally with the sensor's center point. This calibration method can be applied to a machine with medium or large sensors in digital tomosynthesis systems in the future. Several studies have applied digital tomosynthesis to dentistry [25; 26; 27; 28; 29; 30; 31; 32], but it has not been widely applied to clinical use due to the limits of the technology at this time. Our team proposed the 2.5D Periapical Radiography System in 2018 [8] and developed a high-frame-rate sensor. This device enables placing a digital X-ray sensor in the mouth of a patient and can reconstruct images in different depths using shots at limited angles. However, during shooting, the research team discovered that the imaging speed of all commercially available digital X-ray sensors excluded their application to the developed system. Using commercial digital X-ray sensors results in excessively long shooting times unsuitable for practical clinical applications. The long shooting time not only causes discomfort for patients but also generates artefacts in the reconstructed images due to natural breathing motions or unconscious tiny swings of patients during shooting. Therefore, our team also developed a high-frame-rate intraoral \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Group 3**} \\ \hline
**Parameter** & **Ideal** & **Estimate** & **Error (\%)** \\ \hline Pz & 350 & 350.000001 & 0.00000 \\ B’x & \(-\)12.1756613 & \(-\)12.1756622 & 0.00001 \\ B’y & 1.65729352 & 1.65729336 & \(-\)0.00001 \\ Bx & 7.80766134 & 7.80766052 & \(-\)0.00001 \\ By & 0.84070648 & 0.84070632 & \(-\)0.00002 \\ Px & \(-\)2.438 & \(-\)2.43802854 & 0.00117 \\ Py & 6.892 & 6.8919944 & \(-\)0.00008 \\ \hline \multicolumn{4}{c}{**Group 4**} \\ \hline
**Parameter** & **Ideal** & **Estimate** & **Error (\%)** \\ \hline Pz & 370.83 & 370.829997 & 0.00000 \\ B’x & 9.25091935 & 9.25092049 & 0.00001 \\ B’y & \(-\)0.13745354 & \(-\)0.13745374 & 0.00015 \\ Bx & \(-\)10.7109194 & \(-\)10.7109182 & \(-\)0.00001 \\ By & 1.09745354 & 1.09745334 & \(-\)0.00002 \\ Px & \(-\)0.54 & \(-\)0.53995807 & \(-\)0.00776 \\ Py & 0.19 & 0.18999275 & \(-\)0.00382 \\ \hline \multicolumn{4}{c}{**Group 5**} \\ \hline
**Parameter** & **Ideal** & **Estimate** & **Error (\%)** \\ \hline Pz & 350 & 349.999997 & 0.00000 \\ B’x & 7.50455987 & 7.50456092 & 0.00001 \\ B’y & 0.81019259 & 0.81019316 & 0.00007 \\ Bx & \(-\)12.4845599 & \(-\)12.4845588 & \(-\)0.00001 \\ By & 1.46980741 & 1.46980797 & 0.00004 \\ Px & \(-\)2.92 & \(-\)2.91996328 & \(-\)0.00126 \\ Py & 1.66 & 1.6600196 & 0.00118 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._periapical sensor [12] which can reach a shooting speed of 15 Hz and reduce the shooting time to within 10 s.  
CT and digital tomosynthesis systems require accurate calibration of main hardware component positions; otherwise, errors in the hardware component positions will generate artefacts in the reconstructed images.