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. 2020 Apr 30;12(4):e7904. doi: 10.7759/cureus.7904

Table 7. Solutions computed from PP Matrices derived from Table 6 reveal the geometry of the biplanar imaging. Here we are able to compute the point source in AP and LAT. In addition, K-matrix (intrinsic matrix) components are shown including principal point, skew angle (theta), and a simple average between alpha and beta. The planes are computed using the focal distance obtained from a quadratic solution and the normal of the detector plane. The normal of the computed detector plane relative to the normal of the normalized plane is also shown as the "AP/LAT Normal to Normal Angle.".

AP = Antero-Posterior; LAT = Lateral; VERT = Vertical; PP = Perspective Projection; Combined = Simple average of Alpha and Beta for focal length calculation; Alpha = Alpha length from intrinsic matrix for focal length calculation; Beta = Beta length from intrinsic matrix for focal length calculation; 

Inline graphic

Theta = Angle used to determine skew angle (here presented in radians);

Distance from Point Source to Plane = Focal Length, which was calculated using Quadratic Solution;

AP/LAT Normal-to-normal Angle (degrees) = normal of computed detector plane relative to the associated normal of a normalized plane.

Solutions in AP and LAT Computed from PP  
AP Point Source (AP, LAT, VERT):         
655.7883 -6.05706 93.15404      
Combined Alpha Beta Uo Vo Theta
1173.785 1177.416 1170.154 146.9495 16.4229 1.581723
AP Plane Calculation using Intrinsic Matrix from PP (AP, LAT, VERT):   
-511.98 0 0      
-513.434 0 100      
-516.476 -100 0      
Focal Distance AP (Quadratic Solution):     
1168.091          
AP Normal-to-Normal Angle (degrees): 2.70572703691867
LAT Point Source (AP, LAT, VERT):         
-4.4651 -657.583 5.275153      
Combined Alpha Beta Uo Vo Theta
1171.379 1169.453 1173.304 209.5675 101.2284 1.571102
LAT Plane Calculation using Intrinsic Matrix from PP Reverse Cross Product (AP, LAT, VERT): 
0 515.5404 0      
0 510.9394 100      
-100 516.9381 0      
Focal Distance LAT (Quadratic Solution): 
1171.589          
LAT Normal-to-Normal Angle (degrees): 2.75303244159637