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Peter BogaertSeBGIS 2005
The Double-Cross and the Generalization Concept
as a Basis for Representing and Comparing
Shapes of Polylines
Presentation: Peter Bogaert
Authors: Nico Van de Weghe, Guy De Tré, Bart Kuijpers and Philippe De Maeyer
Ghent University - Hasselt University (Belgium)E-mail: [email protected]
Peter BogaertSeBGIS 2005
Overview
Problem statement
QTC versus QTCs
QTCs
Shape Similarity
QTCs versus Closely Related Calculi
Further Work
Double-Cross Concept
Generalization Concept
Central Concepts
Peter BogaertSeBGIS 2005
The Qualitative Trajectory Calculus for Shapes (QTCs)Van de Weghe, N., 2004, Representing and Reasoning about Moving Objects: A Qualitative Approach, PhD Thesis, Belgium, Ghent University, 268 pp.
Problem Statement
Shape comparison is important in GIS (Systems and Science)
Approaches
Quantitative approach
Qualitative approach
: Statistical Shape Analysis
Region-based approach
Boundary-based approach
global descriptors (e.g. circularity, eccentricity and axis orientation)
string of symbols to describe the type and position of localized features (e.g. vertices, extremes of curvature and changes in curvature)
Peter BogaertSeBGIS 2005
QTC
QTC shape = QTCs
QTC versus QTCs
Peter BogaertSeBGIS 2005
Central Concepts
Double-Cross Concept
a way of qualitatively representing a configuration of two vectors
Generalization Concept
a way to overcome problems that are inherent on traditional boundary-based approaches
QTCs
Peter BogaertSeBGIS 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 ConceptQTCs
Peter BogaertSeBGIS 2005
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
0
–
Double-Cross Concept
+
–
QTCs
Peter BogaertSeBGIS 2005
0
– +
Double-Cross Concept
– –
QTCs
Peter BogaertSeBGIS 2005
0+–
Double-Cross Concept
– – –
QTCs
Peter BogaertSeBGIS 2005
0
– – – –
–+
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
Qualitative Trajectory Calculus (QTC)QTCB2D
QTCs
Peter BogaertSeBGIS 2005
Qualitative Trajectory Calculus (QTC)QTCB2D
QTCs
Peter BogaertSeBGIS 2005
Qualitative Trajectory Calculus (QTC)QTCB2D
QTCs
Peter BogaertSeBGIS 2005
–
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
– +
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
– + 0
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
– + 0 –
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
– + 0 –
(e1 ,e2)
Double-Cross ConceptQTCs
Peter BogaertSeBGIS 2005
– + 0 –
(e1 ,e2)
e 2 e 3 e 4
e 1 – + 0 – – + – + – + – +e 2 – + 0 + – + + +e 3 – + 0 +
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
e 2 e 3 e 4
e 1 – + 0 – – + – + – + – +e 2 – + 0 + – + + +e 3 – + 0 +
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
Shape Matrix (Ms)
QTCs
Double-Cross Concept
Peter BogaertSeBGIS 2005
– + 0 –
(e1 ,e2)
e 2 e 3 e 4
e 1 – + 0 – – + – + – + – +e 2 – + 0 + – + + +e 3 – + 0 +
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
e 2 e 3 e 4
e 1 – + 0 – – + – + – + – +e 2 – + 0 + – + + +e 3 – + 0 +
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
0 0 0 0+ – + 0+ – + ++ – + –e4
– + 0 +0 0 0 0+ – + 0+ – + –e3
– + + +– + 0 +0 0 0 0+ – – 0e2
– + – +– + – +– + 0 –0 0 0 0e1
e4e3e2e1
Table 1: Similarity Matrix
QTCs
Double-Cross Concept
Peter BogaertSeBGIS 2005
QTCs
Problems with Boundary Based Approaches
I
II
Peter BogaertSeBGIS 2005
Generalization ConceptQTCs
Peter BogaertSeBGIS 2005
Generalization ConceptQTCs
Peter BogaertSeBGIS 2005
Generalization ConceptQTCs
Peter BogaertSeBGIS 2005
Generalization ConceptQTCs
Ms representing the same polyline at different levels can be compared
Analogous locations on different polylines can be compared with each other
Polylines containing curved edges as well
Peter BogaertSeBGIS 2005
Shape SimilarityQTCs
the relative number of different entries in the Ms
Peter BogaertSeBGIS 2005
QTCs versus Closely Related CalculiQTCs
Peter BogaertSeBGIS 2005
QTCs versus Closely Related CalculiQTCs
Peter BogaertSeBGIS 2005
QTCs versus Closely Related CalculiQTCs
Peter BogaertSeBGIS 2005
v1 v2
v3
v4
v5
v1 v2 v3
v4
v5
e1
e4
e1
e4
Polyline 1 Polyline 2
QTCs versus Closely Related CalculiQTCs
( + )S( )S
Peter BogaertSeBGIS 2005
Further Work
Handling breakpoints in QTCS using a snapping technique
Handling closed polylines (i.e. polygons)
Non-oriented polygon
Data reduction by selecting a minimal subgraph
Presenting changes by QTCS
handled as a polyline, with v1 = vn
'every' orientation should be handled. But, what is 'every'?
Oriented polygon
From an Shape Matrix to a type of shape
Cognitive experiments
Peter BogaertSeBGIS 2005
The Double-Cross and the Generalization Concept
as a Basis for Representing and Comparing
Shapes of Polylines
Presentation: Peter Bogaert
Authors: Nico Van de Weghe, Guy De Tré, Bart Kuijpers and Philippe De Maeyer
Ghent University - Hasselt University (Belgium)E-mail: [email protected]
