rubber mask technique. The corresponding estimate for the standard deviation the median absolute 
deviation (MAD) has been applied by Bailey et. al. (1976), whose results however do not go quite 
conform with the expectation, because using the MAD as optimization criterium only is superior 
to the covariance maximization when the signal to noise ratio is high. Martin and McGath (1974) 
have applied robust techniques for detecting signals in noise assuming the probability density 
function of the noise to be a mixture of Gaussian density functions. Their limiter-quadratic 
detector belongs to class c. where large discrepancies do not influence the results. (cf. also 
Kuznetsov 1976) 
4. The impact of robust estimators on template matching lies in the fact that during line 
following the influence of unpredictable disturbancies (clouds, reseau-crosses, shadows) onto the 
unknown parameters can be totally eliminated, not only partly reduced as when using the phase 
correlation technique. Hence, these disturbancies need not be treated with methods of pattern re- 
cognition unless they.are robustified themselves. This also holds for cases where parts of the 
object are hidden by another one. Here the residuals, i. e. the gray level differences will be 
large enough to be weighted down thus having no impact onto the estimated shift. This allows to 
reach the segmentation borders without too much loss in accuracy. 
2.3 Extensions of the matched filter 
In this section we want to discuss several modifications and extensions of the matched filter 
which are already in use or could be used to advantage in standard applications of photogrammetry 
and remote sensing. 
1. The most important application of the filters for object location is their use for point 
transfer. This seems to be trivial but in view of the optimality criteria it is not. The model 
for point transfer is 
g; sg *o(x=x,) +n 
(3) 
2,7g9g*5(x-2,) + 1, 
no 
where now the shifts £, and Z,, the noises n, and z, but also the template ç are unknown. The task 
— v 
a 
Ut 
is to estimate the unknown shift difference Z,,7 2,- Z,. It is easy to rewrite eq. (3) into a 
T 9 
r^ 
form very similar to eq. (1) using the estimates 2,,, A, and 2 = (g,-7,): 
16 
-— He 
; 
= fe =: 
3» 
* 
H» 
T. 
fà» 
Co 
(4a) 
© 
2 
) 
a” 
28 
QO 
X 
| 
d 
But now the difference becomes apparent: The optimization of object location assumes the object 
to be deterministic whereas point transfer, using an estimate 2 as template, has to cope with 
an object having stochastical properties. Of course the filters derived for object location can 
be applied here substituting 2:7 £ and g g . But then at least g has to be restored, 
estimated from 2; (or g, or both) making some assumptions about 2) and Ras using a Wiener filter 
and solving eq. (4) for Z,, while keeping Z fixed. Of course this is an approximation. A rigorous 
solution still has to be found. 
2. Object location and point transfer in two dimensional images or sequences cannot be restric- 
ted to estimating shifts. The images usually are more or less distorted radiometrically or geo- 
metrically (cf. e.g. Bernstein and Ferneyhough 1974). Though one could think also of correlating 
three dimensional objects we will restrict the discussion to the two dimensional case. Here 
(D 
q. (1) should be generalized to 
e , 3 " ^" 
fA i M 1 f fever 40 a yh 3 fa 35) dy > (5) 
i — H L ) / v of / 
42i. z/ -—— a 733, BS 4 jew, y. ri - 
+ > I g e 
Gy 
res 
"3 
Fa