to these classes. 
With these observations we find the class hierarchical 
structure of figure 3. In literature on semantic modelling 
(Brodie 1984, Brodie e.a. 1984, Egenhofer e.a. 1989, 
Oxborow e.a. 1989) the upward links of the classification 
hierarchy are labelled respectively as "ISA" links. These 
links relate each particular object to a class and to super 
classes. 
  
cree 
i 
CE at 
AB Be By | 
k >n 
a isvalue of A 
  
  
  
  
fig 3. The hierarchical relationships between objects 
and classes and their attributes. 
It is possible to add more hierarchical levels to the struc- 
ture of figure 3. At each level the classes inherit the 
attribute structure of their superclass at the next higher 
level and propagate it normally with an extension to the 
next lower level. At the lowest level in the hierarchy are 
the terrain objects, at this level the attribute structure is 
not extended any more, but here the inherited attributes 
are evaluated. In this case we find for e: 
LISTIe) « fay 97, aJ 
where: 
a, = Alle) is value of A, 
A, SLISTICU LISTISCHU.... 
thus A, is an attribute of the class or superclass(es) of e. 
If the classes at each level are disjoint so that the 
hierarchy has a tree structure then the terrain objects will 
get their attribute structure only through one inheritance 
line in the hierarchy, i.e. they have a unique thematic 
description. We will work under this assumption in this 
paper. 
The terrain objects occur at the lowest level in the 
classification hierarchy. They can be seen as the elemen- 
tary objects within the thematic field represented by the 
classification system. This implies that the decision, 
whether certain terrain objects should be considered as 
elementary or not, should always be made within the 
frame work of athematic field. Objects that are considered 
as elementary in one thematic field are, however, not 
necessarily elementary in another thematic field. 
2.3 Object Aggregation 
Objects can be aggregated to build composite objects at 
several levels of complexity. These may form aggregation 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
hierarchies which are quite distinct from classification hierar- 
chies. An aggregation hierarchy shows how composite 
objects can be built from elementary objects and how these 
composite objects can be put together to build more 
complex objects and so on. In literature on semantic 
modelling (Brodie 1984; Brodie e.a. 1984; Egenhofer e.a.19- 
89: Oxborrow e.a.1989) the upward relationships of an 
aggregation hierarchy are called "PARTOF" links. These 
links relate a particular set of objects to a specific composite 
object and on to a specific more complex object and so 
on. For example, ‘James Park is PARTOF Westminster is 
PARTOF London.’ 
For composite spatial objects the PARTOF links might be 
based on two types of rules involving the thematic and 
the geometric aspects of the elementary objects. 
Consequently the generic definition of a type of an aggrega- 
tion should consist of the following rules (Molenaar 1993): 
- rules specifying the classes of the elementary 
objects building an aggregated object of this type, 
- rules specifying the geometric and topologic relation- 
ships among these elementary objects. 
Suppose that aggregated objects of a type T should be 
formed. To do that we should first identify the objects O, 
that could be part of such aggregates. These objects should 
fulfil certain criteria, which according to the two sets of 
rules given earlier will often be based on the thematic data 
of the objects. Let these criteria be expressed by a decision 
function 
DIO,, T) = 1 if the object fulfils the criteria 
= O otherwise 
Regions can now be formed by applying two rules: 
> allobjects in the region satisfy the decision function 
for T 
fvO,| O;j€ R,) 5 DIO, T) « f 
> All objects that satisfy the decision function for T 
and that are adjacent to objects of the region belong 
to the region 
IvO,|D(O,, T) - 1)(80, € R,. | ADJACENTIO,, Oj] - f) 
=:(0;€ R.) 
The second rule implies that a region can be formed when 
atleast one object has been identified that fulfils the first 
rule. This object is then the seed around which the region 
can grow by identification of the other objects that fulfil 
both rules. 
A region R, can be expressed as a set of objects, i.e.: 
The objects of the region can be aggregated to form an 
aggregated or composite object O,, the suffixes express 
that the object is of aggregation type a and r is its 
identification number. The operation will be expressed by 
O,, = AGGR(R,) = AGGRI({…… Qj.) 
The fact that O;is part of O, is expressed by 
Part, [0;, O,1 = 1 
546 
    
The rev 
of ther 
are the 
COMP| 
The ge 
geome 
elemen 
aggreg 
steps, 
object 
first st 
Part, i 
this fur 
aggreg 
functio 
equatic 
assigne 
if itis 
the lefi 
the fun 
The se 
Parts, 
If there 
ofana 
1, othe 
evaluat 
the obj: 
For the 
be eval 
can be 
topoloc 
The ge 
someti 
faces. 
Ble,, O 
are not 
they d 
aggreg 
The exi 
througl 
all invo 
tions o 
case w 
object 
througl 
Itis pos 
constrt 
form a 
aggreg 
3.2 the 
the yie 
desagg 
becaus