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.
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Manual of Photogrammetry, Fourth Edition, 1980. Two-dimensional projective transformation, p.729-731
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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
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IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995