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.

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.

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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

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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

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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

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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]