map - 
This procedure is shorter than transforming equation (1) into: 
  
2 2 2 2. 
(X — Xp) + (Y- Y + (7 = Ze) - 8^ m0 
2 2 ; 2 
i4. x-Xx3 1 (vr-y)J3^.1 (9-7) 
3 F 12 F 13 = "e reg 
. . . 2 
CE EE ins ia (2-25) ) 
as proposed by Rosenfield [51], and solving (X, Y) from the two non- 
linear equations by assuming Zp = 0. Obviously, before applying the above 
algorithms, the slant ranges should, if necessary, be corrected for earth 
curvature and refraction. 
If the elements of exterior orientation are not measured, there exists 
the theoretical possibility to compute them as unknowns from the projection 
equations by using a large number of control points. For this purpose, the 
exterior orientation could be assumed as piecewise linear function ( see 
e.g. Masry [T1] ). Applying this to the equations (12), one would obtain: 
en V 2 2 2 2 
Ax =a 1X + ay - a h y - n - e « À y - Zi + e + e X 
= e 2,3 2 ai. + 
Ay 73 Jor ta, ra, (y^ - Le) /y + a. X. (y = Ze) /y 
+ ay zy + a, x. zs (15) 
The coefficients as 05, oy describe a general rotation, scale change 
and y-shift of the whole strip of imagery. The remaining coefficients 
change with the pieces of the imagery. 
Alone x = x. 
8 joint one enforces 
. . ] . = +0, 
Ca” +g x) piece, ( a. + a. 
i i 4 ) piece 
* 1 j T1? 
1 o£612,44:0,:8,. 10. 
Instead of applying formula (15), in which the unknowns are computed 
with the help of control points, it is also possible to perform first 
a parametric transformation, to eliminate the systematic effect of 
viewing geometry and squint only (i.e. assuming exterior orientation 
to be ideal). Following that control points may be used for interpolation 
purposes. 
1.2.9, 
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