Full text: XVIIIth Congress (Part B3)

  
  
  
  
  
  
   
   
   
   
  
  
  
   
  
  
  
  
  
    
  
   
  
  
   
  
  
   
  
  
   
    
  
    
  
  
  
   
  
  
   
   
  
   
   
   
   
  
    
    
  
  
    
   
  
   
  
   
    
Fig.12 is another example which shows the transformation of 
the representation of area features in scale dimension. 
Si Y " 
(a) Original feature (b) Result of 10x reduction (c) final result 
Fig.12 Another example of area aggregation (Su et al, 1996) 
7. CONCLUDING REMARKS 
Digital generalization of spatial data can be decomposed into 
two processes, ie. a digital-to-digital transformation and a 
digital-to-graphic transformation. The latter is about 
cartographic presentation, thus cartographic knowledge can be 
formalised and knowledge-based systems used at this stage. 
Some of multi-purpose requirements might be also be applied 
here. 
The digital-to-digital transformation is a transformation in scale 
dimension and thus the process itself should be objective. It 
has been argued in this paper that the transformation in scale 
dimension is guided by a natural principle (Li and Openshaw, 
1993) and this natural principle can be best depicted by the 
operators developed in mathematical morphology, which is a 
science dealing with shape, form and structure of objects. It 
means that, upon the two basic operators -- i.e. dilation and 
erosion -- in mathematical morphology, some basic 
mathematical models for transforming spatial representation in 
scale dimension can be built. These models, like affine, 
projective, conformal transformation efc in space dimension, 
will be of fundamental importance to generalization. If and 
only if these basic transformation models are developed, will 
one be able to develop a system which will be capable of 
producing consistent results. 
Indeed, the development of such basic mathematical models for 
transformation in scale dimension based on morphological 
operators has been carried out by the author and his 
collaborators since the first study by the author (Li, 1994b) and 
some promising results have also been obtained (Li and Su, 
1995; Su and Li, 1995; Su et al, 1996). 
It is a commonplace that there are many routes available for 
travelling from Hong Kong to Vienna although some are with 
longer distance while others may have shorter distance. But 
there is only one unique shortest distance between these two 
cities, i.e. the geodetic line. In practice, this line may be either 
difficult to determine or difficult to travel along. This paper is 
yet another attempt to find a feasible route for digital 
generalization in GIS environment but certainly this route is 
still not the geodetic line of digital generalization. Indeed, it is 
the author's hope that this paper will somehow contribute to 
the discovery of this geodetic line. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
ACKNOWLEDGMENTS 
The author would like to thank Mr. B. Su for producing 
diagrams used in Fig.6 and Fig.7 of this paper. 
REFERENCES 
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