new 
onal 
own 
AP 
sed 
nm 
  
371 
for both the X and the Y values was obtained. The Z axis, being linear, does not form part of the calculations to 
determine the h parameters. 
The 3D coordinates of the three leg points, the entry and lesion centre of the phantom were determined from the AP 
and LAT surviews and compared with their equivalent CT scan slice coordinates, see table 1 below. 
  
  
  
  
X (mm) Y (mm) Z (mm)-Table Position 
Mean error -0.9 0.3 1.4 
Std. Deviation 0.5 0.5 0.6 
  
  
  
  
Table 1: Comparing 3D coordinates of the phantom obtained from the CT scan slices to those obtained from the AP 
and LAT surviews 
Both the CT control and the phantom head were measured in a reflex metrograph (Scott, 1981), which has a 
measuring resolution of 0.1mm, and compared to the CT scan slice system using Cayley's formula and Rodrigues 
parameters (Thompson, 1969). This was to determine the accuracy of the CT scan slice system, as the lesion centre 
can only be determined from the CT scan slices. The results are listed in table 2 and 3 below. The values obtained by 
the metrograph are "considered" error free. 
  
  
CT control X (mm) Y (mm) Z (mm)=Table Position 
Std. Deviation 0.6 0.6 0.2 
  
  
  
  
  
  
  
Table 2: Comparing 3D coordinates of the CT control obtained by the reflex metrograph and the CT scan slice system 
  
Phantom Head X (mm) Y (mm) Z (mm)=Table Position 
  
  
  
  
  
Std. Deviation 0.2 : 0.7 0.7 
  
Table 3: Comparing 3D coordinates of the phantom head obtained by the reflex metrograph and the CT scan slice 
system 
7. CONCLUSION 
The CT scan system has a 1mm measuring resolution for X and Y coordinates and a minimum slice thickness of 2mm, 
with an overall expected accuracy of target fixation of 1.5mm. The determination of 3D coordinates from the AP and 
LAT surviews using a two dimensional projective transformation algorithm is well within the accuracy limit expected for 
the CT scan slice coordinate system, which is the normal method of CT scan coordinate determination. Thus the AP 
and LAT surviews can be utilised for 3D coordinate determination. The ability to use the AP and LAT surviews to obtain 
CT scan slice coordinates of marked points on the patient's scalp reduces the actual CT scan time, which reduces the 
computational procedure in removing any movement the patient might undergo during the scan and is beneficial to the 
patient. 
REFERENCES 
Adams, LP., van Geems, B.A, Jaros, G.G., Peter, J., Wynchank, S., 1994. A stereophotogrammetric controlled 
pointing device for surgical use. Int. Archs. of Photogrammetry and Remote Sensing, 30(5):1-7. 
Adams, L.P., 1981. X-ray stereophotogrammetry locating the precise, three dimensional position of image points. 
Medical and Biological Engineering and Computing, 19 :569-578. 
Hallert, B., 1970. X-ray photogrammetry. Elsevier Publishing Company, Amsterdam. 
Levin, C.J., Hough, J., Adams, L.P., Boonzaier, D., Rüther, H., Wynchank, S., 1993. Determining locations of 
intracerebral lesions for proton therapy. Phys. Med.Biol, 38:1393-1401. 
Manual of Photogrammetry, Fourth Edition, 1980. Two-dimensional projective transformation, p.729-731 
Scott, P.J., 1981. The reflex plotters: measurement without photographs. Photogrammetric Record Vol.X:435-446 
Thompson, E.H., 1969. An introduction to the algebra of matrices with some applications. Adam Hilger, London. p.142 
van Geems, B.A., Adams, L.P., Gold, B., Spirakis, A., Learmonth, I.D., 1994. The use of X-ray stereo photogrammetry 
to ascertain early failure of a total hip replacement using a single X-ray source. Int. Archs. of Photogrammetry and 
Remote Sensing, 30(5):420-425. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995