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THE USE OF A TWO DIMENSIONAL PROJECTIVE TRANSFORMATION TO SOLVE FOR THE PARAMETERS FOR 
THE ANTERIOR-POSTERIOR AND LATERAL SURVIEWS OF A CT SCAN 
Van Geems B.A.T Adams LP 1 Hough J.2 
1. Department of Biomedical Engineering, University of Cape Town Medical School, Observatory, 7925, South Africa, 
Phone: 27 21 4066547, Fax: 27 21 4483291, Emails: GTSBAR@ANAT.UCT.AC.ZA, ADAMS@ANAT.UCT.AC.ZA 
2. Department of Medical Physics, Groote Schuur Hospital, Observatory, 7925, South Africa 
Phone: 27 21 4046272, Fax: 27 21 4046269, Email: JANHOUGH@RAY.UCT.AC.ZA 
KEY WORDS: Computed tomography, two-dimensional projective transformation 
ABSTRACT 
The Biostereometrics Group in Cape Town has developed a simple pointing device mounted on a three legged stool for 
stereotactic biopsies of intracranial lesions (Adams et al 1994). Clinical trials are presently being undertaken. 
To be able to set the device and to correct for any patient movement, a total of eight points have to be marked on the 
patient's scalp. The Cartesian coordinates of the eight points and the centre of the lesion are determined using the 
computed tomography (CT) scan slice system, with a slice being required for each point to be coordinated. To 
streamline the CT scan procedure the Group has developed a method of calculating three dimensional coordinates of 
all the ball bearings using only two plan views, i.e. the anterior-posterior (AP) and lateral (LAT) surviews, using a two 
dimensional projective transformation algorithm. This transformation has to be employed since the central projection 
only applies along the horizontal axis of the surview with the vertical axis being a linear mapping. 
This paper will show how the two dimensional projective transformation is employed to determine parameters for the 
CT scan surviews; and how the parameters are used to determine the equivalent three dimensional / slice coordinates 
of points from the CT scan's surviews. 
1. INTRODUCTION 
Computed tomography (CT) has become commonplace in most large hospitals as a diagnostic tool and has, when 
combined with a stereotactic system, been used to determine the locations of intracerebral lesions for proton 
radiotherapy (Levin et al 1993). More recently, in an attempt to eliminate the use of cumbersome and invasive probe 
guidance frames traditionally used in stereotactically guided neurosurgery, a simple stereotactic pointing device - a 
three legged stool (Adams et al 1994) - has been developed to be used in conjunction with the CT scan. 
To set the device, the entry point selected by the surgeon, and the three points corresponding to the foot points of the 
three legs of the stool have to be marked on the patient's scalp using 2mm round radio-opaque ball bearings. These 
four points and the centre of the lesion are coordinated using the CT scan slice system. Their 3D coordinates are used 
in various calculations to produce a printout, which is used to set the pointing device of the stool. In theatre the three 
legs of the stool are placed on their corresponding markers on the scalp and by inserting the biopsy needle down the 
guide of the pointing device to a calculated depth the centre of the lesion is reached. 
Due to the duration of the CT scan procedures and the requirement of the neurosurgeon not to physically restrain 
patients, it is not always possible for patients to remain perfectly still during the procedures. Any movement on the part 
of the patient destroys the geometry of the system - the coordinates of the ball bearings measured from the CT scan 
slices no longer reflect the true relationship of the markers to one another. Video photogrammetry is employed to 
repeatedly determine the patient's position during the CT scan procedure (Adams et al 1994).. This is done by 
"tracking" four dual purpose markers ( video photogrammetric targets with ball bearing centres) attached to the 
patient's scalp. : 
To simplify the whole CT scan procedure, a new approach has been developed to coordinate all the markers. By 
treating the two pilot views, the anterior-posterior (AP) and the lateral (LAT) surviews, as PSEUDO PHOTOGRAPHS 
and using modified photogrammetric techniques, a method has been developed whereby the 3D coordinates of all 
markers are determined using only the two pilot views. The coordinates of the lesion centre must still be determined 
using an individual slice. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommiíssion Workshop "From Pixels to Sequences", Zurich, March 22-24 1995 
  
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