-—6- 
For a strip image in x' direction the number of needed coefficients may be reduced by comparing 
ground coordinate differences in terms of image coordinates; for example: 
3 
Ax. =c te6,.X! t6,.y! t o.x!y! 6.515 4 (ex! 
3 i 273 2 j'1 9 
© 1 4H hsv) (9a) 
3 
2 
1 ' ' ' ' 1 
A, d, + dx] + dy! + d,xiyi : + (à5x1 4...) 
with more than 5 (or6) points being needed for the determination of coefficients; 
Ax, 
x - X. 
i i known computed 
A 
Yay 
(9b) 
i known ^ "i computed 
z 1 : 
Xi compu ted = X cosec + = tg e sinoC + X. 
1 Z yi 
Ji computed = sin t c te c caso + ME: 
most simple analyses have been conducted using either (8) or (9), particularly for the first tests 
for satellite scanners (Bähr & Schuche/5/, Forrest /30/,Wong /86/),for airborne scanners 
(konecny /42, 44, 45/) and for radar (Bosman et al /11, 12/,Derenyi /24/, Konecny /44, 46/, 
Leberl /57/ ). 
5.2. Interpolation by spline functions 
  
Polynomials have the disadvantage that while they may be made to fit well at the points from 
which coefficients are determined, they may strongly deviate, where no data are present. As 
better regional correction therefore spline functions have been suggested (Anuta fA; Baker & 
Mikhail /7/, Bosman et al /11/ ). They permit to use low order polynomials within bounded 
regions, thus avoiding the tendency toward ill conditioning when solving high order polynomial 
coefficient matrices. 
The following types of splines may be used for an area bounded by 4 points 
a) piecewise linear functions (first order splines) 
Ax} 
(10a) 
Ay! : 
they have discontinuities at the regional boundaries just as functions of the type 
Ax] - + a 
a 4% tay + azxy 
(10b) 
! = 
Ay! [A * b,x + by * b,Xy 
b) biquadratic polynomials (second order splines) 
Ax! = + àa,X + A,Y + 8,Xy + a x +8 y^ + a ny + a xy^ + a xy 
i 0 1 2 3 4 5 6 7 8 
Ay! b + b,x + by * by xy + b x? + buy * bex^y + boxy’ + Dax y 
i 0 4 
they have contious first derivatives at the boundaries