SELECTIVE REPRESENTATION 
  
  
  
  
SEMIAUTOMATED REPRESENTATION 
  
  
  
  
EVALUATION 
  
  
  
Fig. 3 Main stages of optimum representation 
2. TERRAIN MORPHOLOGY CLASSIFICATION 
In the context of optimum representation for terrain 
morphology modelling, the purpose of classification is to 
provide some initial information on the terrain morphology 
for specifying the presentation process. Thus, formulation 
of a suitable model for a quantitative terrain morphology 
classification is necessary. The terrain morphologic 
information is differentiated according to the skeleton and 
filling sub-sets (Charif, 1991). 
The skeleton information (Z) is represented by distinct 
morphologic features. They represent, mathematically, lines 
where the spatial derivatives are discontinuous. It is 
possible to extract the morphologic features from a 
photogrammetric stereo model, if they are distinct enough. 
The problem is to define an objective criterion for detecting 
those morphologic features. In this context, however, a 
method based on the concept of profile analysis by 
applying the second difference criterion, is used. 
The second difference in height of a triplet of points (AZ) is 
compared with a certain preselected threshold value. In 
the case (À, ) is greater than the threshold, the point 
belongs to the skeleton (2), otherwise, to the filling (F1) 
information. 
Hence, the total terrain morphologic information (T) is 
composed of the skeleton (2) and the filling (M), such as: 
T= + (1) 
3. QUALITY MEASURES 
The quality assessment of terrain morphologic 
representation is differentiated according to the 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
performance (accuracy, fidelity), reliability, and efficiency 
(Charif, 1991). 
3.1 Performance 
The performance is one of the main criteria influencing the 
estimation of the quality of terrain morphologic 
representation products. Performance was differentiated 
further according to completeness of E information, 
accuracy of 2 and [1 information, and fidelity of E and M 
information. 
In optimum representation, the terrain morphology is 
represented by the > and M sub-sets. Consequently, the 
accuracy estimation should be differentiated according to 
the standard error. 
The standard error Oy, of modelling by the X set depends 
on: image quality and scale, precision of instrument, 
operator skill and care, and sampling mode(stationary, 
dynamically) 
The standard error 0; of modelling by the IM set depends 
on: apriori 2 set and Oy, grid interval, pointing error, and 
interpolation algorithm. 
3.2 Sources of errors 
The accuracy of terrain morphology modelling is influenced 
by two main sources of errors: error of sampling and 
interpolation 0, and the measuring errors 6 
Assuming f(x) is the terrain profile, and f(x)is the correct 
height of a point and g(X)is the modelled height, then 
g(X) - f(x) + mx) (2) 
In photogrammetric measurement, m;(x) is considered 
partly systematic and partly random, thus the latter part of 
My;(x) can be defined as a sequence of uncorrelated 
values, which are normally distributed, with the mean equal 
; 2 ; 
to zero and the varianceO,,. Assuming that f(x) and 
m (x) are mutually independent and thus uncorrelated, the 
variance of the error of the modelling is: 
2 
Op=0,+ 0 (3) 
3.3 Accuracy of morphologic modelling 
Accuracy of terrain morphologic modelling can be estimated 
by analytical, semi analytical, or experimental approaches. 
Quality of the modelling of the ideal geometric primitives 
can be assessed using the following criteria: 
- The mean error Oy of selective representation is 
determined for all the grid points on the morphologic 
modelled surface.