The DoubleCross and the Generalization Concept

1
The Double-Cross and the Generalization Concept
as a Basis for Representing and Comparing
Shapes of Polylines
Authors Nico Van de Weghe, Guy De Tré, Bart
Kuijpers and Philippe De Maeyer
Presentation Peter Bogaert
Ghent University - Hasselt University
(Belgium) E-mail nico.vandeweghe_at_ugent.be peter.b
ogaert_at_ugent.be
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Overview

• Problem statement

• QTC versus QTCs

• QTCs

Central Concepts
Double-Cross Concept
Generalization Concept
Shape Similarity

• QTCs versus Closely Related Calculi

• Further Work

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Problem Statement
Shape comparison is important in GIS (Systems and
Science)
Approaches
Quantitative approach
Statistical Shape Analysis
Qualitative approach
Region-based approach
global descriptors (e.g. circularity,
eccentricity and axis orientation)
Boundary-based approach
string of symbols to describe the type and
position of localized features (e.g. vertices,
extremes of curvature and changes in curvature)
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.
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QTC versus QTCs
QTC
QTC shape QTCs
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QTCs
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
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QTCs
Double-Cross Concept

• 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.

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QTCs
Double-Cross Concept
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QTCs
Double-Cross Concept

0


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QTCs
Double-Cross Concept


0


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QTCs
Double-Cross Concept




0

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QTCs
Double-Cross Concept





0

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Qualitative Trajectory Calculus (QTC)QTCB2D
QTCs
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Qualitative Trajectory Calculus (QTC)QTCB2D
QTCs
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Qualitative Trajectory Calculus (QTC)QTCB2D
QTCs
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QTCs
Double-Cross Concept

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QTCs
Double-Cross Concept


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QTCs
Double-Cross Concept


0
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QTCs
Double-Cross Concept


0

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QTCs
Double-Cross Concept
(e1 ,e2)


0

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QTCs
Double-Cross Concept
(e1 ,e2)


0

Shape Matrix (Ms)
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QTCs
Double-Cross Concept
(e1 ,e2)


0

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QTCs
Problems with Boundary Based Approaches
I
II
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QTCs
Generalization Concept
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QTCs
Generalization Concept
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QTCs
Generalization Concept
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QTCs
Generalization Concept
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
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QTCs
Shape Similarity
the relative number of different entries in the
Ms
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QTCs
QTCs versus Closely Related Calculi
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QTCs
QTCs versus Closely Related Calculi
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QTCs
QTCs versus Closely Related Calculi
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QTCs
QTCs versus Closely Related Calculi
(? ? ?)S
(? ? ? ?)S
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Further Work

• Handling breakpoints in QTCS using a snapping
  technique

• Handling closed polylines (i.e. polygons)

Oriented polygon
handled as a polyline, with v1  vn
Non-oriented polygon
'every' orientation should be handled. But, what
is 'every'?

• Data reduction by selecting a minimal subgraph

• Presenting changes by QTCS

• From an Shape Matrix to a type of shape

• Cognitive experiments

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The Double-Cross and the Generalization Concept
as a Basis for Representing and Comparing
Shapes of Polylines
Authors Nico Van de Weghe, Guy De Tré, Bart
Kuijpers and Philippe De Maeyer
Presentation Peter Bogaert
Ghent University - Hasselt University
(Belgium) E-mail nico.vandeweghe_at_ugent.be peter.b
ogaert_at_ugent.be