## 3 Results  
The method was tested on 12 scoliosis cases. The first case, a 16-year-old male with mild single curve thoracolumbar scoliosis, was used to verify the method's accuracy. The superimposed spinous processes lines were determined by the acquired 3D ST data (Figure 6). In the biplanar view, the spinous processes line is located in the frontal view (the \(xy\) plane in Figure 3) as shown in Figure 6a; the sagittal view is shown in Figure 6b. The spinous processes line is shown in the sagittal view (the \(yz\) plane in Figure 3). The distribution of the deviation without the decomposition on the \(x\)- and \(z\)-axes is shown in Figure 7a and is shown with the decomposition in Figure 7b. Figure 6: The graph showing the spinous processes line calculated using the developed methodology (X-ray and 3D ST scanning) and data obtained based on the 3D ST data analyses alone. Frontal (**a**) and sagittal (**b**) views. The ordinate and abscissa values are presented using different scales to visualize the abscissa axis data better. The mean deviation between the points of the lines was 2.84 mm. The maximal deviation was 4.34 mm. Because the spinous processes line is usually analyzed in two perpendicular planes (frontal and sagittal), the values of the deviations for the individual axes are crucial, as illustrated in Figure 7b. The mean deviations in the \(x\)- and \(z\)-axes were 2.54 mm and 1.01 mm, respectively, and the maximal deviations in the \(x\)- and \(z\)-axes were 4.17 mm and 2.40 mm, respectively, in the presented cases. The results for all twelve patients (PT1-PT12) in the study are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Patient** & **Max (\(\mathbf{x}\))** & **Max (\(\mathbf{z}\))** & **Max** & **Mean (\(\mathbf{x}\))** & **Mean (\(\mathbf{z}\))** & **Mean (\(\mathbf{z}\))** \\ \hline PT1 & 4.17 & 2.40 & 4.34 & 2.54 & 1.01 & 2.84 \\ PT2 & 14.20 & 1.70 & 14.20 & 0.59 & 7.90 & 7.94 \\ PT3 & 12.35 & 1.48 & 12.36 & 6.34 & 0.64 & 6.40 \\ PT4 & 16.35 & 8.13 & 17.83 & 4.91 & 1.58 & 5.31 \\ PT5 & 18.67 & 9.19 & 18.90 & 8.20 & 2.72 & 8.82 \\ PT6 & 11.50 & 1.91 & 11.50 & 6.79 & 0.74 & 6.87 \\ PT7 & 1.23 & 4.38 & 4.45 & 0.38 & 1.38 & 1.50 \\ PT8 & 5.00 & 4.84 & 6.95 & 0.66 & 2.80 & 2.97 \\ PT9 & 0.88 & 6.01 & 6.03 & 0.34 & 1.46 & 1.55 \\ PT10 & 2.88 & 7.78 & 7.83 & 0.65 & 3.22 & 3.35 \\ PT11 & 4.65 & 6.64 & 6.65 & 0.77 & 3.27 & 3.50 \\ PT12 & 1.99 & 9.00 & 9.21 & 0.51 & 1.73 & 1.89 \\ \hline \hline \end{tabular} Legend: Max—maximal deviation; Max(\(x\)) and Max(\(z\))—maximal deviation from the decomposition on the \(x\)- and \(z\)-axes, respectively; Mean—mean deviation; Mean(\(x\)) and Mean(\(z\))—mean deviation from the decomposition on the \(x\)- and \(z\)-axes, respectively;  
\end{table} 
Table 1: Maximal and mean deviations of the results taken as total value and decompositions on the \(x\)- and \(z\)-axes [mm]. Figure 7: Distribution of differences in distances between points belonging to the reference and subject spinous processes lines (**a**) and the \(x\)- and \(z\)-axes (**b**). The ordinate and abscissa values are presented using different scales to visualize the abscissa axis data better. The maximal deviation between the lines' points was found in the patient (PT5), who had a maximal deviation of 18.9 mm. In most cases, the \(x\)-axis component was more deviated than the \(z\)-axis component. The mean deviation was 4.41 mm, and values for individual patients and axes are presented in Table 1. The group's maximal deviations in the \(x\)-axis and \(z\)-axis were 18.67 mm and 9.19 mm, respectively. The method developed here was intended for use in cases where it is impossible to calculate the spinous processes line using data only from the cloud of points obtained using 3D ST scanning.