ant 
r 
id 
of 
ray 
n of 
on 
ith 
Comparison of the actual z-values (fig. 11, 12, 13) -as they result due to 
differing sensor characteristics -with the permissible solution interval 
defined in (4.4.5) shows that the condition z £7 is approximately satis- 
fied for an area size of 100 x 1080 pixels only,but by no means for the 
other area sizes. 
An all-positive eigenvector is given only if the secondary diagonal elements 
of the Q-matrix do not disappear simultaneously [2]. The values of the Q.. 
(i # j) decrease as the test areas grow small and the possibility of HJ 
nonexistent all-positive eigenvectors grows accordingly. The variation of 
the z-values can consequently be interpreted as a superposition of the 
sensor-speci fic behavior and the stability of the eigenvalue problem [34. 
5. Conclusion, Prospects 
The extensive investigation of the North Sea showed a significant depen- 
dence on position for the mean gray values and the largest eigenvalues. The 
sensor-dependence is particularly evident in the substantial variations 
observed in the all-positive eigenvector. This leads to the conclusion that 
at least for the land cover type ''open waters'' there is no typical error 
ellipsoid for the object. On the contrary, the determining parameters such 
as ellipsoid center, length and direction of the semimajor axis, are sub- 
ject to very large variations in some cases, a crucial factor being the 
size of the investigated area: Based on the three different area sizes used 
for analysis, the optimum as to eigenvalues was found to be at 100 x 100 
pixels, even if the remaining root mean square errors of orientation can 
amount to 709. This fact will certainly make classification considerably 
more difficult. In addition, the training areas used in general practice 
cover substantially less than 100 x 100 pixels which is likely to aggravate 
the problems pointed out in the above. 
As the analysis also shows, a relatively certain classification is only 
possible within small image submatrices (100 x 100 pixels). On account of 
their different properties the results fail to be transferable to adjacent 
areas. 
0f all influences affecting the accuracy of classification, position-depen- 
dent systematic gray value variations (see: mean values) as well as some 
random portions (see: ellipsoid dimensions) can be accounted for, resp. 
minimized, through reduction of the area of analysis, yet the ellipsoid 
function remains a position function. Improvement of sensor-dependent 
ellipsoid orientation, however, seems feasible only through employing either 
one single sensor or several sensors of identical calibration within a sen- 
sor array. The latter technical requirement for sensor array scanners on 
the one hand will probably be difficult to realize, on the other it con- 
stitutes an indispensable precondition for improving the discrimination of 
multispectral characteristics and consequently for object recognition. 
177