T TEN
N E
3 a Rs. Je es Ze nus M
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algorithm, i.e. the multiquadric approach. The reference system can be chosen
arbitrarily, enabling also relative rectifications of imagery with respect to
another arbitrary reference image. A topographic data base (DEM) can be option-
ally included.
The base-integrated multi-sensor imagery forms together with the various
data base thematic layers a three-dimensional matrix structure, the two first
dimensions being the location-indices, and the third dimension being the the-
matic, topographic and sensor type index. Further processing of these relatively
registered "matrix elements" can be readily employed, as shown schematically
in Figure |.
2. GEOMETRIC PROCESSING OF ARBITRARY INPUT IMAGERY
2.1 Principle
The goal is to geometrically transform a (distorted) input image
dQu,Y4) into a (rectified) output image g(X;,Y;). The processing steps in-
volved are
- determination of pass point coordinates PL (Xo Y no Xo Yao, ke = 1,K
- deriving geometric transformation equations X, = X(X,,Y,) and Y, = Y(X,,Y,)
i i 1 222 1 2? à
from the k pass points, and
- the actual rectification, i.e. the quantization of the picture elements
g(X2,Y2) from the input elements d(X],YŸ1) - |
The transformation equations can be modelled by parametric /4,5,6/ or non-para-
metric techniques /6/. Parametric techniques explicitly model the sensor orien-
tation elements on the basis of the collinearity of image and object points,
while non-parametric approaches interpolate between pass points and do not
establish any explicit sensor orientation function.
In the following the non-parametric approach will be further presented
with emphasis on the specific interpolation function uscd.
2.2 Concept of multiquadric interpolation
The task is to interpolate a value z for an arbitrary point location x,y
for a given point set p Uni $z1,n.
Using the definitions
2 ; 2 2
s iE xx )^T"Cy-y. (1^
53 (x xj! (y y)
S 2 = (x -X 124 (y.- y* and (2)
Si i Yield s
G = 0,6 nin(s; ^), i5 hng-j*l,n (3)
the multiquadric approach first selects the interpolation functions as /7,8/
(855 7 6,7 o"? (4)
and computes the interpolation function matrix C- [f ds a
>
Denoting the average value of all z;- data by z, then the average-centered data
vector Z = lz}, 1 with pe 208 “is computed. The yet unknown interpolation
zu
, J
coefficients T 3 = 1,1 of the coefficient vector KK | are then solved
from the system of n linear cquations C K = Z.
Fina
equa
is p
Firs
as t
resp
niti
