comparison, the correlation functions of two different AR- 
processes are shown in Figure 1. The corresponding 
generating processes are 
AR(1): z, = 0.934 9176 
i 10 meters 
AR(2): 2, = 1.957 2, 4 - 0.985 By pt 84 y AX = 10 meters 
4. DISCUSSION 
There are of course several limitations to the use of the 
Karhunen-Loeve expansion for terrain classification. 
Firstly, the original set of functions is basically 
expressed as linear combinations of orthogonal base 
functions. Other types of relations, for instance 
exponential functions (Frederiksen et.al, 1978), have to be 
transformed into a linear model for K-L expansion. : 
Secondly, the orthogonal base functions are Strictly 
empirical and not based on any theoretical model. The use of 
a theoretical model might improve the flexibility of the 
model for terrain classification. But until such theoretical 
base functions have been derived, empirical orthogonal base 
functions may be used. 
The main advantages with the K-L expansion is that it is an 
objective method and that it gives the opportunity of 
selecting the most significant part of the information. It 
is in other words a method for data compression with minimum 
loss of information. Since terrain classification to a great 
extent is a problem of data reductions, the latter feature 
of the method is of great importance. 
A third main advantage of the method is that the 
similarities and dissimilarities among different terrain 
types may be studied, without considering the problem of 
terrain classification at all. In the small example shown in 
this paper, the close relationship between the terrain 
elevations and autoregressive processes have been 
demonstrated. It should be emphasized that it is not shown 
that a terrain profile can be expressed by an autoregressive 
process, just that their autocorrelation functions are 
similar. There might be other processes as well that 
produces similar autocorrelation functions. 
This study is limited to the autocorrelation of the 
elevations of the terrain. Other descriptions of the terrain 
could be studied as well, for instance its power spectrum or 
its covariogran. 
It is in addition not only the elevations themselves that 
are of interest. For the specification of the geometric 
quality of digital elevation data, a classification of the 
errors has to be made, similar to the classification of the 
elevations. Today, when the exchange of geographical 
- 688 -