^ street_cycle_track connection inside encloses are_parallel
are_orthogonal common_ell common_tee common_stem
common_frk common_arw common_njn5 size_diff
distance_2 left_position top_position common_sides
same_polytyp %
[positiv yes no no yes no 1 2 1 0 0 0 2586.363894 43.73397
left.of top of 1.03 same. poly] ;;; [radwegb strasse3]
[positiv yes no no yes no 1 2 0 0 0 0 2940.824027 10.26592
left of under 5.63 same poly ] ;;; [radweg3 strasse3]
[negativ yes no no no yes 0 2 1 0 0 O 1411.443836 76.430477
right_of top_of 0.04 diff_poly ] ;;; [radweg3 strasse2]
From the given examples the following function (decision
tree) for the relation is automatically gained by ID3?:
vars street cycle track ;
define street cycle track (areai,area2) -» klasse ;
vars klasse , areal,area2 ;
undef -» klasse;
if (are parallel(areai,area2) -»» val) == "yes" then
if ( connection (areal,area2) ->> val) == "yes" then
’positiv’ -> klasse;
elseif (connection(areal,area2) ->> val) == "no" then
’negativ’ -> klasse;
endif;
elseif (are parallel(areai,area2) ->> val) == "no" then
’negativ’ -> klasse;
endif;
enddefine;
This function characterizes that for a neighborhood of streets
and cycle tracks a check has to be made as to whether they
are parallel and connected - which might be obvious after
reading it. Merely inventing such a rule, one might easily
have thought of parallelity alone and have forgotten to check
for a connection. In the same way, aggregations of objects
can be interactively and iteratively gained. E.g. the fact that
adjacent fields can be aggregated is learned as a part-of-
relation.
Figure 3 (left) visualizes the association street-cycle_track in
dotted lines and the part-of-relation field-field in solid lines.
The final result - after successive application of the field-field
relation and also the street-street relation - is shown on the
right hand side of Figure 3.
eia; MOSE fein Pre
|
fre i
5 yaeweg3 | | |. —
edi feld8 fas sirasse5
stress eld] ex feld feld13
elds
Figure 3: Association street-cycle_track in dotted lines; part-
of-relation field-field in solid lines (left); Final result of inter-
pretation (right)
So in the end a complete scene description evolves, together
with a corresponding model characterizing traffic and field ob-
jects. The derived model is given in Figure 4.
field13
Prop. Prop.
Meth. Meth.
street1 street6 cycle tr. cycle tr.
Prop. Prop. Prop. Prop.
Meth. | Meth. Meth. Meth.
Figure 4: Derived scene model: objects and relations
4.2 Concept for Learning Multiple Representation
Rules
The learning facility can easily be applied in multiple repre-
sentation on two methods:
Learning rules for object presence: Such a rule deter-
mines when and if an object is present on a certain
level of detail. This can be achieved by pointing at ob-
jects and classifying whether the object is existent in
the following scale or not. The system then generates
a decision tree that determines which attributes are re-
sponsible for this representation (e.g. size, form, type).
Learning aggregation rules: In the spirit of van Oosterom
[1995] a successive aggregation of the objects has to
be performed when going from one scale to the next.
In contrast to his method however, the rules for aggre-
gation are not fixed in terms of importance parameters,
but are learned directly from the given data set. The ex-
pectation is that such rules better reflect the underlying
structure in the data. In this way - analogous to the ag-
gregation of fields and streets in the previous example
- higher level methods for the generalization of objects
can be derived.
4.3 Similarities and Differences between the two
Problems
Between the problems model acquisition and multiple rep-
resentation the following similarities and differences can be
found:
Similarities: Both problem domains base on complex object
hierarchies. The relations between the individual ob-
jects (or object classes) are however object- and task
dependent. The system allows to identify these rela-
tions and learn corresponding rules depending on the
attributes.
?This is the automatically derived decision tree in the language POP11. The function is composed of the definition of the function variable
street cycle track and the function itself, enclosed by define and enddefine
772
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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