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)

Peter BogaertSeBGIS 2005 Overview  Problem statement  QTC versus QTC s  QTC s Shape Similarity  QTC s versus Closely Related Calculi  Further Work Double-Cross Concept Generalization Concept Central Concepts

Peter BogaertSeBGIS 2005 The Qualitative Trajectory Calculus for Shapes (QTC s ) 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 = QTC s QTC versus QTC s

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 QTC s

Peter BogaertSeBGIS 2005  Freksa, Ch., 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 QTC s

Peter BogaertSeBGIS 2005 Double-Cross Concept QTC s

Peter BogaertSeBGIS – Double-Cross Concept + – QTC s

Peter BogaertSeBGIS – + Double-Cross Concept –– QTC s

Peter BogaertSeBGIS – Double-Cross Concept ––– QTC s

Peter BogaertSeBGIS –––– – + Double-Cross Concept QTC s

Peter BogaertSeBGIS 2005 Qualitative Trajectory Calculus (QTC) QTC B2D QTC s

Peter BogaertSeBGIS 2005 Qualitative Trajectory Calculus (QTC) QTC B2D QTC s

Peter BogaertSeBGIS 2005 Qualitative Trajectory Calculus (QTC) QTC B2D QTC s

Peter BogaertSeBGIS 2005 – Double-Cross Concept QTC s

Peter BogaertSeBGIS 2005 –+ Double-Cross Concept QTC s

Peter BogaertSeBGIS 2005 –+ 0 Double-Cross Concept QTC s

Peter BogaertSeBGIS 2005 –+ 0 – Double-Cross Concept QTC s

Peter BogaertSeBGIS 2005 –+ 0 – (e 1, e 2 ) Double-Cross Concept QTC s

Peter BogaertSeBGIS 2005 –+ 0 – (e 1, e 2 ) Shape Matrix (M s ) QTC s Double-Cross Concept

Peter BogaertSeBGIS 2005 –+ 0 – (e 1, e 2 ) QTC s Double-Cross Concept

Peter BogaertSeBGIS 2005 QTC s Problems with Boundary Based Approaches I II

Peter BogaertSeBGIS 2005 Generalization Concept QTC s

Peter BogaertSeBGIS 2005 Generalization Concept QTC s

Peter BogaertSeBGIS 2005 Generalization Concept QTC s

Peter BogaertSeBGIS 2005 Generalization Concept QTC s M s 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 Similarity QTC s the relative number of different entries in the M s

Peter BogaertSeBGIS 2005 QTC s versus Closely Related Calculi QTC s

Peter BogaertSeBGIS 2005 QTC s versus Closely Related Calculi QTC s

Peter BogaertSeBGIS 2005 QTC s versus Closely Related Calculi QTC s

Peter BogaertSeBGIS 2005 QTC s versus Closely Related Calculi QTC s (  +   ) S (   )S(   )S

Peter BogaertSeBGIS 2005 Further Work  Handling breakpoints in QTC S using a snapping technique  Handling closed polylines (i.e. polygons) Non-oriented polygon  Data reduction by selecting a minimal subgraph  Presenting changes by QTC S handled as a polyline, with v 1 = v n '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)