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Based on the assumption that the angle between the AP and LAT imaging planes is exactly 90 degrees, that the 
principal points of the AP and LAT images are coincident and that the principal distances are known, it should be 
possible to calculate the X, Y coordinates of the surface marker P (figure 2), with the Z coordinate equal to the table 
position. On testing the theory, it was found that errors were often greater than the expected accuracy of 1.5mm. It was 
found that the angle between the AP and LAT imaging planes was not 90 degrees; that the principal points of the AP 
and LAT images were not coincident and that the principal distances for the AP and LAT surviews were not known. 
Therefore an alternative mathematical approach has been developed using a modified two dimensional projective 
transformation algorithm (Manual of Photogrammetry, 1980) to solve for the point P. 
3. THE CT SCAN VIDEO PHOTOGRAMMETRIC SYSTEM COMBINED WITH THE CT SCAN SYSTEM 
As the lesion centre's 3D coordinates can only be obtained from the CT scan slice system, the 3D coordinates 
determined from the AP and LAT surviews have to be in the CT scan slice system. Therefore, to correct for any patient 
movement, the video photogrammetric system has to be made coincident with the CT scan slice system. 
A dual purpose control is used to determine camera and CT scan parameters. Some of the control points in the one 
plane of the photogrammetric control are also marked with radio opaque ball bearings. In the same plane are 
additional CT control points only marked with ball bearings. The control frame is set up in such a manner that the 
single plane of the CT control frame is coincident with the single plane in which the CT scan operates. 
Images of the control frame are captured by the video photogrammetric system. An AP and LAT surview of the CT 
control are scanned. Only a single CT scan slice is required to image all the control points, as they all lie in one plane. 
Once the control has been removed, the patient, with the eight surface markers attached, lies on the CT scan table 
with his head in the area that the control occupied. As the AP surview is scanned, camera images are captured of the 
head. The same procedure is repeated for the LAT surview and the slice taken through the centre of the lesion. The 
video photogrammetric system, and the manner in which its control parameters and the 3D coordinates of objects 
points are determined, has been described in Adams et al 1994. The movement of the object between the successive 
surviews is resolved using the same procedures as described in Van Geems et al 1994, where a single X-ray source 
was combined with a close-range photogrammetric system to be able to eliminate patient movement between 
successive X-ray exposures. 
  
  
  
  
_ Glass backing 
o o . 
o o 5mm Thick perspex disc 
Oo 
o o T Control Point EC m Ball bearing 
9 9 Side view of control point 
  
Figure 3: CT scan control with nine control points all lying in the same plane 
To develop the algorithms and to test the accuracies obtained from the CT scan's surviews a two dimensional control 
(figure 3) was constructed and tests run using a phantom head with only the three leg points and the entry point 
marked on the surface of the phantom. A ball bearing placed inside the phantom served as lesion centre. The two 
dimensional control is made of thick glass to ensure that all control points lie in the same plane. As glass is very radio 
opaque, the ball bearings were mounted on perspex discs. On surviews the glass appears as a solid straight line, with 
the ball bearings suspended in space in front of it as the discs do not image. 
4. THE TWO DIMENSIONAL PROJECTIVE TRANSFORMATION 
s. )-*) (1) 
A linear transformation, equation (1), of homogenous coordinates in space is known as a projective transformation 
when the matrix A is non-singular. In terms of non-homogenous coordinates it takes the form of equations (2), i.e. the 
equations for a two dimensional projective transformation (Manual of Photogrammetry 1980), where ai is a typical 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995 
  
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