* 
2. GENERAL DESCRIPTION OF THE ALGORITH! 
The relations between image coordinates (x', y') and object 
or model coordinates (x, y, z) can be represented by two 
inage equations 
x! s f (x, y, 2) 7 + f X4 X. 5) (2.1) 
The image equations (2.1) can be generally further treated 
by applying the theorem of Taylor. | 
If the theorem of Taylor is applied to (2.1) with nz1, then 
the following equations in matrix notation result for the 
inage coordinates x' and yt 
XN olin yo x E = ext Re 
= : + Fes dy + = T + 
yt £a (x ,y, 3 ) dz RA orsa dy! Hy! 
(2.2) 
2 f Lia are the partial derivatives of 
+ J f, and I, with respect to x, Ze 
dx, yy dz dre the coordinate differences to the point 
P(x, 1¥, 125) in measurements in the environment of this point. 
The remainder terms are obtained to be 
$4 dx? 
ael 2dxdy 
1/2* Fe * 2dxdz (2C 35 
By 3 dy? 
2dydz 
dz* 
ap hg fa ios ifa AR 
barf 
XX 
Fi 
ae ip id hu hy 
fax Co fayy C rp. vay, ze idz),... CO < aÂ< 1) 
are the 2nd derivatives of f, and fs with respect to xz y; z. 
The difficulty lies in tne determinaton o? the coefficients 
af, which in the general case depend on X5, yo, Ze and 4x, 
dy. dz, i.e. they change from point to point. 
Another possibility of determining the remainder terms con- 
Sists in the inversion of (2.2) 
(2.4) 50 (2:3) save (varie independent of wether the pictures 
were taken with a metric camera, strip camera, panoramic ca- 
mera or a scanner. If the remainder terms cannot be rigorous- 
ly calculated, the remaining errors must be ascertained and 
considered in the determination of the spatial segments (i.o. 
of the environment of the local zero points Pose 9). 
Thus, the differences be ween the individual image types are 
no longer a constituent part of the real-time process, but or 
a preceding prosram, in which the local zero points in the 
model Bj are fixed and the appertaining local zero points 
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