münster gi-days 2004 – 1-2 july – germany 1 description, definition and proof of a qualitative...
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Münster GI-Days 2004 – 1-2 july – Germany 1
Description, Definition and Proof of a Qualitative State Change of Moving Objects
along a Road Network
Peter Bogaert, Nico Van de Weghe, Philippe De Maeyer
Ghent University
Münster GI-Days 2004 – 1-2 july – Germany 2
Spatial Reasoning
spatial reasoning
lot of work has been done in stating the topological dyadic relations between objects
Two approaches
artificial intelligence → GI Science1992 Randell, Cui, CohnRegion Connection Calculus
databases → GI Systems1991 Egenhofer, Franzosa4-Intersections model
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RCC - diagram
Assuming continuous motionConstraints upon the way the base relations can change
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Conceptual Neighborhood Diagram
Freksa (1992 )
Conceptual Neighbors
‘Two relations between pairs of events are conceptual neighbors, if they can be directly transformed into one another by continuously deforming (i.e. shortening, lengthening, and moving) the events in a topological sense’
Conceptual Neighborhood Diagram
Graphical representation of the conceptual neighbors
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QTC
Problem : How to describe disjoint objects
Van de Weghe et al. (2004)
QTC = Qualitative Trajectory Calculus
studies the changes in qualitative relations between two disconnected continuously moving objects.
based ondirection of movementmovement speed
resulting in transition-codes
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QTC – simplification to 1D space
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QTC - labeling
3. speed of K and L:D(Kt2,Kt1) > D(Lt2,Lt1) : +D(Kt2,Kt1) < D(Lt2,Lt1) : -
D(Kt2,Kt1) = D(Lt2,KL1) : 0
1. movement of K relative to original position of L:D(Kt2,Lt1) > D(Kt1,Lt1) : +D(Kt2,Lt1) < D(Kt1,Lt1) : -D(Kt2,Lt1) = D(Kt1,Lt1) : 0
2. movement of L relative to original position of K:D(Lt2,Kt1) > D(Lt1,Kt1) : +D(Lt2,Kt1) < D(Lt1,Kt1) : -D(Lt2,Kt1) = D(Lt1,Kt1) : 0
Kt1Kt2 Lt1 Lt2+ + 0
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Conceptual Neighborhood Diagram
Results in 3³ = 27 possible trajectories
CND can be represented by a cube
0
000
0
0
0 0 0
00
00
00
0
0
00
0
0
0
0 0
0
0
0
+0
0
+
char
acte
r 2
characte
r 2
0
+
character 1
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1 00
2 0-
3 0+
4 +0
5a --05 -- 5b --- 5c --+
6a -+06 -+ 6b -+- 6c -++
7 -0
8a +-08 +- 8b +-- 8c +-+
9a ++09 ++ 9b ++- 9c +++
QTC – 1D space
In 1D space : Only 17 real-life trajectories
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QTC – diagram (1D)
00
+ + + + + 0
+ - +
+ - -
- - - - - 0
-0
0+
+ + -
+0
0-
+ - 0
- - +
- + -
- + 0
- + +
Conceptual neighbourhood diagram
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QTC-N
Moreira et al. (1999): In real-life there are two kinds of moving objects
those having a free trajectory(e.g. a bird flying through the sky)
those with a constrained trajectory(e.g. a vehicle driving through a city along a road network).
QTC-N deals with object that have a constraint trajectory due to a network
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QTC-N
QTC-N
both objects are inserted as nodes in the graph representing the network.
the cost (e.g. Euclidian distance, time, etc.) between those two objects is measured along the shortest path
an object can only approach the other object, if and only if it moves along the shortest path between these two objects.
Münster GI-Days 2004 – 1-2 july – Germany 13
New definition of QTC - labeling
3. speed of K and L:D(Kt2,Kt1) > D(Lt2,Lt1) : +D(Kt2,Kt1) < D(Lt2,Lt1) : -
D(Kt2,Kt1) = D(Lt2,KL1) : 0
1. movement of K relative to original position of L:k does not move along the shortest path: +
k moves along the shortest path : -k stable : 0
2. movement of L relative to original position of K:l does not move along the shortest path : +
l moves along the shortest path : -l stable : 0
Kt1Kt2 Lt1 Lt2+ + 0
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QTC-N
QTC-N
If two objects on a network change their speed, they can reach each label in the QTC-1D
00
+ + + + + 0
+ - +
+ - -
- - - - - 0
-0
0+
+ + -
+0
0-
+ - 0
- - +
- + -
- + 0
- + +
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If speed is constant there can still be a transition
Passing a node change
node with a degree of minimum 3 only an object with label ‘–‘
Degree less than 3
can only choose to follow the shortest path
Label ‘+’
impossible because it can’t choose to follow an arc that belongs to the Shortest path
QTC-N
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QTC-N
If speed is constant there can still be a transition
Change in the shortest path between the objects
Only if one or both objects have label ‘+‘
Both Labels ‘-’
Impossible because this way there can’t be a change in the shortest path
Münster GI-Days 2004 – 1-2 july – Germany 17
CND of the QTC-N
0
000
0
0
0 0 0
00
00
00
0
0
00
0
0
0
0 0
0
0
0
+0
0
+
cha
ract
er 2
characte
r 2
0
+
character 1
00
0 00
00 0
000
0
Münster GI-Days 2004 – 1-2 july – Germany 18
CONCLUSION AND FUTURE WORKCONCLUSION
QTC can be used to describe moving objects on a networkobjects moving on a network can’t be treated as objects moving in 1D space.
17 vs. 27 possible trajectories
FUTURE WORK
QTC-N from 2 moving objects to n moving objects
Composition table
Calculating quatlitative trajectory using Shortest Path calulation tables
Münster GI-Days 2004 – 1-2 july – Germany 19
Description, Definition and Proof of a Qualitative State Change of Moving Objects along a Road Network
Geography Department – Ghent UniversityKrijgslaan 281 S8
B-9000 Gent
http://geoweb.ugent.be/research/carto.asp
Peter Bogaert
+ 32 (0)9 264 46 [email protected]