Ds=Min{ |IX-Yi]|. Xi £ Objects} 
  
  
  
  
  
  
  
  
  
  
Raster Voronoi Diagram of spatial objects. 
3. The description cf topological relations based cn Voronoi diagram. 
Kainz[1990], Egenhofer and Franzosa [1991] made more systematic investigation on the 
definitions of spatial topological relations. They proposed a formal framework, as 
follows in term of the intersections of the boundaries and interiors of two point- 
sets. 
JAN IB JAN DB° 
A° N 3b A n. 
But this kind of description framework exists drawbacks, some relations can’t be 
represented by them. For conquering the deficients, Chen, Sun[1994} take the 
conplement besides interior and boundary into a count and construct a new framework 
in terms of the intersections of boundaries, interior and complements of two sets. 
3A ^ 38 ANB’ 34 A91 
M A 35 A^ nw a° N 87 
AN an An 8° As? 
In nature. the new framework has no considerable changes.The lateral ad jacent 
relations still are not represented. Therefore, we introduce the Voronoi Diagram into 
the discrete space and modify the description framework as follows: 
JAN 28 2An 5? JAN Vs 
A? ^30 A? A9 AN Vg 
Va nao Va ^ B? Va NV 
Va, Vb are raster Voronoi regions cf spatial objects. Making use of this framework 
it is possible for description lateral adjacent relations besides general spatial 
relations. In the follows two examples are given, the first is to find nearest object 
near to one location, the second is tco find adjacent objects near to the center 
object in the term cf Vcronci diagram adjacency. 
229 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996