method is one of the fastest gray level transformations approximation a high pass filter if one
uses table-look-up procedures (cf. Ehlers 1983). Einary or polarity correlation on the other side
aims at high speed, but usually leads to relatively poor results though the autocorrelation func-
tion due to the arcsin-law (cf. Papoulis 1965,p.484) is sharp peaked (cf. the broad discussion
by Helava 1976). Binary correlation should therefore only be used for determining approximate
values or in cases where ultimate precision is not demanded.
The modifications discussed up to now have frequently been applied and have made algorithms
more flexible and reliable when being confronted with varying types of templates. The method of
template matching however has to be embedded into more general tasks such as aerial triangulation
deformation measurements or mosaiking where not only one channel or one pair of images are to be
handled.
4. Multi-image object location occurs when several satellite images are simultaneously regi-
stered on the basis of well defined ground control points. The corresponding model is described
by eq. (3); but now the template g is given. The task is to identify the same object in two or
more images. The algorithmic solution reduces to simple object location only if the degrading
noises n, and 5, are uncorrelated. If however they have common terms, the estimation process for
the two shifts has to take into account the correlation. It might be caused by stochastic or deter-
ministic effects such as unmodelled geometric distortions or unknown filters h(x) and Rs (x) the
object is passed through.
i
p
5. More involving is the simultaneous relative rectification of three or more images using
multi-image correlatton.Eq. (3) then has to be complemented by one ore more further equations,e.g.
On
= aM
=
üt
(z- E.) * ns. Now again g is unknown. The relative shifts E95 2373378 and
1D; have to be determined. Obviously only two of them are independently estimable. This gives
se to a condition equation $,2'É55,:7$,,70 for the estimated shift differences. It can be intro-
duced into the estimation process (cf. Ackermann 1982) or it might at least serve as a triangle
check for detecting false correlations which proves to be very effective (Tanaka et. al. 1978,
Ackermann and Pert] 1982).
pu
r
-4
6. No severe problems causes the simultaneous correlation of several channels of an MSS or
colour image at least from the theoretical point of view. The multi-channel correlation can also
be described by eq. (1) but now gc, g, and n are vectors depending on x. Thus with e. g. two chan-
nels a and P one has to solve
H
N-
li
tC
x E
w bie, ~ BL +n (x)
a L
©
&
s».
+
|
e$
i
a
ry (7)
4
"
e
u
«Wy
*
e»
e
8
|
32
A.
+
8
me
©
i
U
ç
Dt
e
+
e
for £,, which is the discrete version of the estimation problem. Observe that we now have two tem-
plates g, and g, , only one unknown shift. Collecting the corresponding vectors in one vector, e.g.
ro
/), allows to rewrite eq. (7) and to obtain the discrete version of eq. (10: 25/2,2.5
j
;) * n. The matched filter obviously requires the covariance matrices Can. and
^
-
Ann
~
but also C, n,. If the noise vectors (n (z.)) and (rn, (z.)) are uncorrelated the shift can be sepa-
-
mated from both channels. The estimates then have to be averaged using their standard
£
i
colour images will not be correlated correlations between :
”
-—2
and z. might result from unmodelled
geometric distortions. s
Experiences by Anuta (1970) seem to prove that different channels of MSS images contain diffe-
rent geometric information, thus a combined estimation should lead to better results than
estimations from single channels. On the other hand the investigations of Prabhu and Netravali
(1982) show that the luminance component of colour images is sufficient for the prediction
