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element of A in (1). The two dimensional projective transformation relates the points on one plane to their 
correspondingly projected positions on another plane. 
84 4X - 242 Y - 843 2 a54X + a99Ÿ + 293 
= (2) 
8434X + azoY * 843 
x Y! 
T 844X + ano Y + 833 
The CT scan surview however introduces a singular transformation (figure 4) for to distinct lines in the plane there 
corresponds one, and only one line, the line on the CT scan surview. Such a transformation cannot be uniquely 
inverted for to every picture point there corresponds an infinity of space points. 
CT surview image line - x 
ES 
Y | 
| 
| 2. 
| 
| 
| 
Space ray 
| * 
Space points 
| Space lines 
i 
[e LO 
Figure 4: Illustration of singular transformation 
In figure 5 consider the one-dimensional space - i.e. the line E. Line E represents one of the horizontal sections of a 
surview. On line E, P has a coordinate x in one dimension. One can interpret X, Y as rectangular coordinates in two 
dimensional space, i.e. X, Y in the CT scan slice system, and in this space one can choose a line Y=k parallel to the X 
line as the line E. If one joins the point P on E to the origin O by a straight line, then for points on this line X/Y are 
constant. If one lets Y=k=1 say, in general one can write: 
—=Xx (3) 
Accordingly the introduction of homogeneous coordinates signifies the representation of the line E into a space pencil 
of rays with the origin O as centre, of which E is a section; i.e. the homogenous coordinates of a point are the space 
coordinates of the points of the projecting ray of that point. 
  
Y 
AN n i > x LineE 
vx] . 
vL > X 
  
0 
Figure 5: lllustrating homogeneous coordinates 
The equations (2) are in terms of X, Y. but for the one-dimensional coordinates x and using the homogenous 
coordinates one can rewrite equation (3): 
xeu AM Min De ie Alt 7 aY ta (4) 
Y' 44X*842Y 843 894X-*8505Y 893  894X*855Y tao 
5. TREATING THE AP AND LAT SURVIEWS AS A TWO DIMENSIONAL PROJECTIVE TRANSFORMATION 
As the geometry of the central projection pertaining to the surviews only holds true in the XY plane of the CT scan slice 
system, the AP and LAT images can be viewed as a whole series of two dimensional projections "stacked together 
along the Z axis" (figure 6 ). 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences”, Zurich, March 22-24 1995