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Peter BogaertGeos 2005
A Qualitative Trajectory Calculus
and the Composition of its Relations
Authors: Nico Van de Weghe, Bart Kuijpers,
Peter Bogaert and Philippe De Maeyer
Department of Geography, Ghent University, Belgium{nico.vandeweghe, peter.bogaert, philippe.demaeyer}@ugent.be
Theoretical Computer Science, Hasselt University, [email protected]
Peter BogaertGeos 2005
Overview
Problem statement
The Qualitative Trajectory Calculus –Double Cross (QTCC)
Composition Table
Composition Rules Table
Concluding Remarks
Peter BogaertGeos 2005
Problem Statement
• Qualitative Reasoning: Region Connection Calculus (RCC)
• Database: 9-Intersection Model
Randell, D., Cui, Z, and Cohn, A.G., 1992. A Spatial Logic Based on Regions and Connection, In: Nebel, B., Swartout, W., and Rich, C. (Eds.), Proc. of the 3rd Int. Conf. on Knowledge Representation and Reasoning (KR), Morgan Kaufmann, San Mateo, USA, 165‑176.
Egenhofer, M. and Franzosa, R., 1991. Point‑Set Topological Spatial Relations, International Journal of Geographical Information Systems, 5 (2), 161‑174.
• a lot of work has been done in stating the dyadic topological relations between two polygons
• Two approaches
Peter BogaertGeos 2005
Problem Statement
DC(k,l) EC(k,l) PO(k,l)
TPP(k,l) NTPP(k,l)
TPPI(k,l) NTPPI(k,l)
EQ(k,l)
• 8 possible topologic relations
• Constraints upon the ways these relations change
Peter BogaertGeos 2005
Problem Statement
Developing a calculus for representing and reasoning about movements of objects in a qualitative framework.
continuously moving objects: often only “disconnected from”
“How do we handle changes in movement between moving objects, if there is no change in their topological relationship?”
DC(k,l)
Peter BogaertGeos 2005
QTC
(Van de Weghe, N. (2004) Representing and Reasoning about Moving Objects:A Qualitative Approach, PhD thesis, Belgium, Ghent University,
Faculty of Sciences, Department of Geography, 268 pp.)
QTCB
1D2D
Distance, speed
QTCC
2D
Double Cross Concept
A calculus for representing and reasoning about movements of two disconnected point-like objects
in a qualitative framework.
Peter BogaertGeos 2005
QTC – Simplification
Peter BogaertGeos 2005
Freksa, Ch., 1992. Using Orientation Information for Qualitative Spatial reasoning, In: Frank, A.U., Campari, I., and Formentini, U. (Eds.), Proc. of the Int. Conf. on Theories and Methods of Spatio‑Temporal Reasoning in Geographic Space, Pisa, Italy, Lecture Notes in Computer Science, Springer‑Verlag, (639), 162‑178.
Double-Cross Concept
Peter BogaertGeos 2005
QTCCDouble-Cross Calculus (Freksa)
QTC – DOUBLE-CROSS (QTCC)
l
k
Peter BogaertGeos 2005
Double-Cross Calculus (Freksa)
QTCC
l
k
l
k
QTC – DOUBLE-CROSS (QTCC)
Peter BogaertGeos 2005
Double-Cross Calculus (Freksa)
QTCC
l
k
l
k
l
k
QTC – DOUBLE-CROSS (QTCC)
Peter BogaertGeos 2005
QTC – DOUBLE-CROSS (QTCC)
l
k
Peter BogaertGeos 2005
0
–+
–
QTC – DOUBLE-CROSS (QTCC)
l
k
Peter BogaertGeos 2005
– +
– –
0
QTC – DOUBLE-CROSS (QTCC)
l
k
Peter BogaertGeos 2005
0–
– – –
+
QTC – DOUBLE-CROSS (QTCC)
k
l
Peter BogaertGeos 2005
0–
+
– – – –
–
+
QTC – DOUBLE-CROSS (QTCC)
l
k
Peter BogaertGeos 2005
Qualitative Trajectory Calculus (QTC)QTCB2D
QTCC
Peter BogaertGeos 2005
Qualitative Trajectory Calculus (QTC)QTCB2D
QTCC
Peter BogaertGeos 2005
Qualitative Trajectory Calculus (QTC)QTCB2D
QTCC
Peter BogaertGeos 2005
R1(k,l) R2(l,m) = R3(k,m)
originate from temporal reasoning (Allen 1983)
encodes all possible compositions of relations
simple table look‑up
useful from a computational point of view
Composition Table
Idea: to compose a finite set of new facts andrules from existing ones
Peter BogaertGeos 2005
Composition Table
Peter BogaertGeos 2005
Composition Table
QTCC defines 81 different relations
Difficult visual presentation
A composition table would have 81*81 (6561) entries
Peter BogaertGeos 2005
Useful for visual presentation
Instrument to help generate the composition table
Composition Rules Table
Reduction of the number of entrances
Peter BogaertGeos 2005
Composition Rules Table
Based on 2 rules
Which rotation do we need,such that l of R2 matches l of R1?
How is k moving with respect to l in R1, and how is m moving with respect to l in R2?
Peter BogaertGeos 2005
Which rotation do we need,such that l of R2 matches l of R1?
Composition Rules Table
(k,l)(– + + –)C (l,m)(– – – +)C
k l
l m
(k,m)
Peter BogaertGeos 2005
(case 1 of n)(k,l)(– + + –)C (l,m)(– – – +)C
k l
l m
l
(k,m)
k
m
Composition Rules Table
Peter BogaertGeos 2005
(k,l)(– + + –)C (l,m)(– – – +)C
(case 1 of n)(k,m)
k
m
k ll m
Composition Rules Table
Peter BogaertGeos 2005
m
k
–
(k,m)(– )C
(k,l)(– + + –)C (l,m)(– – – +)C
(case 1 of n)(k,m)
k ll m
Composition Rules Table
Peter BogaertGeos 2005
k ll m
m
k
+
(k,m)(– + )C
(k,m)(– )C
(k,l)(– + + –)C (l,m)(– – – +)C
(case 1 of n)(k,m)
Composition Rules Table
Peter BogaertGeos 2005
m
k–
(k,m)(– + )C
(k,m)(– )C
(k,m)(– + – )C
(k,l)(– + + –)C (l,m)(– – – +)C
(case 1 of n)(k,m)
k ll m
Composition Rules Table
Peter BogaertGeos 2005
k ll m
m
k
+(k,m)(– + )C
(k,m)(– )C
(k,m)(– + – )C
(k,m)(– + – + )C
(k,l)(– + + –)C (l,m)(– – – +)C
(case 1 of n)(k,m)
Composition Rules Table
Peter BogaertGeos 2005
k ll m
m
k l
(k,l)(– + + –)C (l,m)(– – – +)C
(case 2 of n)(k,m)
Composition Rules Table
Peter BogaertGeos 2005
k ll m
k
(k,l)(– + + –)C (l,m)(– – – +)C
(case 2 of n)(k,m)
m
Composition Rules Table
Peter BogaertGeos 2005
k ll m
k
(k,l)(– + + –)C (l,m)(– – – +)C
(case 2 of n)(k,m)
m (k,m)(– – + +)C
Composition Rules Table
Peter BogaertGeos 2005
(k,l)(– + + –)C (l,m)(– – – +)C
> 180°
k l
ml
(k,m)
l
(n of n cases)
Composition Rules Table
Peter BogaertGeos 2005
(k,l)(– + + –)C (l,m)(– – – +)C
> 180°
< 360°
k l
m
l
l
k l
m
(n of n cases)(k,m)
Composition Rules Table
Peter BogaertGeos 2005
> 180° and < 360°
(n of n cases) (k,l)(– + + –)C (l,m)(– – – +)C(k,m)
Composition Rules Table
Peter BogaertGeos 2005
Which rotation do we need, such that l of R2 matches l of R1
> 180° and < 360°
(n of n cases) (k,l)(– + + –)C (l,m)(– – – +)C(k,m)
Composition Rules Table
Peter BogaertGeos 2005
How is k moving with respect to l in R1, and how is m moving with respect to l in R2
(n of n cases) (k,l)(– + + –)C (l,m)(– – – +)C(k,m)
Composition Rules Table
Peter BogaertGeos 2005
How is k moving with respect to l in R1, and how is m moving with respect to l in R2
(n of n cases) (k,l)(– + + –)C (l,m)(– – – +)C(k,m)
Composition Rules Table
Peter BogaertGeos 2005
Composition Rules Table
Peter BogaertGeos 2005
independent
goal: movement of object k with respect to object n (R3)
incomplete data
incomplete answer
two scientific teams
'Puzzling the Past'
(k,n)?
Peter BogaertGeos 2005
(k,l)(– + + –)C (l,n)(– – – +)C
Team I
Team II(k,m)(– + – +)C (m,n)(– + – +)C
k l
l
mm
n
nk
(k,n)
(k,n)
'Puzzling the Past'
Peter BogaertGeos 2005
Team III Team IV
Team I Team II
Team III
Team IV
(k,n)
'Puzzling the Past'
Peter BogaertGeos 2005
Team V (k,n)(– + – +)C
Team III Team IV
'Puzzling the Past'
Peter BogaertGeos 2005
Complex researches (huge number of anchor points, teams, measurements per team, updates, etc.)
Cuncluding Remarks
IMPLEMENTATION OF QTCC
The composition-rules table forms a basis for reasoning about
incomplete spatio-temporal knowledge in information systems.
Can be used in a variety of research domains: geomorphology, geology, archaeology, and biology.
Peter BogaertGeos 2005
A Qualitative Trajectory Calculus
and the Composition of its Relations
Authors: Nico Van de Weghe, Bart Kuijpers,
Peter Bogaert and Philippe De Maeyer
Department of Geography, Ghent University, Belgium{nico.vandeweghe, peter.bogaert, philippe.demaeyer}@ugent.be
Theoretical Computer Science, Hasselt University, [email protected]