- 
It is to note that for a strict treatment of radar images all ground range representations should 
be refferred to slant ranges. 
The relations constitude the basis for a strict restitution if the orientation parameters are 
known. Present sensor designers are however not in the position, nor do they seem to care too 
much, to record the sensor orientation parameters to the desired accuracy. 
A practical solution to restitute scanner and other dynamic imagery will today therefore rest 
on the possibility to model the orientation or its effects as errors by aid of ground control 
points. 
3. Mathematical Models for the Restitution of Scanner Imageries 
  
The choice of a mathematical model for the determination of orientation parameters or for the 
elimination of coordinate discrepancies between control point values transformed to the imag 
by some approximation and the image coordinates will depend on a number of factors such as the 
assumption of a deterministic or a stochastic nature of the variations of parameters or dis- 
crepancies, the magnitude to be expected of such variations, the effort of computation and last 
not least the accuracy of representation desired. 
3.1. Interpolation by polynomials 
The simplest deterministic approach is to use polynomials for the correction of image coordinate 
discrepancies 
X! - & + a,X, + à. y. + a 
4 i 27i 
o 1i 3*iJ4 
ta, say + (a Xy. 4 A.X y. 
4*i 57i Gy t eux 131 
5 5 
+ &gXi * 8,05 
gi 
+...) 
+ ax. 
8*i”i 
+ b,x. + boy; + b 
17% 37175 
2 2 2 2 
+ b Xi * boi * (boxiy; + baXiY; 
2 + b X^ + b + 
+ b Xe 
8*i7i 9*i 1074. * *** 
The coefficients a. to bg (or b.) are conveniently determined for the more than 6 (or 11) control 
points i by & least squares fit. 
Ax! sx! -ox! 
i i computed i measured 
' - 1 
Ayi i computed Ji measured 
in which 
nd y 
x! a ! : : ; : : ; 
i computed i computed is determined from the collinearity equations with the best known or 
most convenient approximation (usually straight and level flight) available: 
x! xS. (x; - x, ) cos - ( 
i computed zZ to Ji 
ii^ Yio) sine 
i 
(84) 
1 = En? 
i computed * e Arc t5 zo 7 7, (x; 
y - X2) sine + (vy, - 3:0) cos« 
Such a formulation is appropriate for an image with about the same x' and y' extensions.