176 
ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
Table 9: Different neighbour order of disjoint relations 
B(a.h) 
Semantic 
Figure 
f c (aOb) =(-0 0 -0 -0 -0) 
Neighbour Order V* - 1 
1-order neighbour 
■■ 
ft (a8b) =(-0 0 -0 -0 -0) 
WÊiéÊ 
Neighbour Order - 2 
2-ordcr neighbour 
1 m 
f c (aOb) =(-0 0 -0 -0 -0) 
Neighbour Order V" = 3 
3-order neighbour 
7. CONCLUSIONS 
In this paper, a novel approach for the description of spatial 
relations is employed. It consists of three strategies as follows: 
(a) appropriate operators from set operators (i.e. union, 
intersection, difference, difference by, symmetric 
difference, etc) are utilised to distinguish the spatial 
relations between neighbouring spatial objects; 
(b) three types of values are used for the computational 
results of set operations, -- content, dimension and 
number of connected components; 
(c) a spatial object is treated in a whole but the Voronoi 
region of an object is employed to enhance its 
interaction with neighbours; 
This approach overcomes the shortcomings of both 
decomposition-based and whole-based approaches. With this 
strategy, a generic algebraic model is developed to distinguish 
and determine spatial relations in geographical databases. 
Such a model includes mainly three integrands, i.e. spatial 
objects themselves, their Voronoi regions and proper set 
operators. Spatial objects here mainly refer to points, lines and 
areas in planar space. The set operators are primitive 
operations in GIS, especially in raster based systems. From 
theoretical point of view, this model is a more general model 
than all existing models. It also overcomes the deficiencies of 
both the whole-based and decomposition-based models. From 
practical viewpoint, using this approach, the integration of the 
description and computation of spatial relations in both vector 
and raster space can be realised in a natural way. Such model 
has applications in spatial analysis and reasoning such as 
digital map generalisation in GIS. 
ACKNOWLEDGEMENT 
The work described in this paper was substantially supported 
by a grant from the Research Grants Council of the Hong Kong 
Special Administrative Region (Project No. PolyU 5048/98E). It 
is also partially supported by a grant from the National Science 
Foundation under No. 69833010. 
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