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The Double-Cross and the Generalization Concept as a Basis for Representing and Comparing

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)

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The Double-Cross and the Generalization Concept as a Basis for Representing and Comparing

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  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@ugent.be peter.bogaert@ugent.be

  2. Overview • Problem statement • QTC versus QTCs • QTCs Central Concepts Double-Cross Concept Generalization Concept Shape Similarity • QTCs versus Closely Related Calculi • Further Work

  3. 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.

  4. QTC versus QTCs QTC QTC shape = QTCs

  5. 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

  6. 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.

  7. QTCs Double-Cross Concept

  8. QTCs Double-Cross Concept – 0 – +

  9. QTCs Double-Cross Concept – – 0 – +

  10. QTCs Double-Cross Concept – – – – 0 +

  11. QTCs Double-Cross Concept – – – – + 0 –

  12. Qualitative Trajectory Calculus (QTC)QTCB2D QTCs

  13. Qualitative Trajectory Calculus (QTC)QTCB2D QTCs

  14. Qualitative Trajectory Calculus (QTC)QTCB2D QTCs

  15. QTCs Double-Cross Concept –

  16. QTCs Double-Cross Concept – +

  17. QTCs Double-Cross Concept – + 0

  18. QTCs Double-Cross Concept – – + 0

  19. QTCs Double-Cross Concept (e1 ,e2) – – + 0

  20. QTCs Double-Cross Concept (e1 ,e2) – – + 0 Shape Matrix (Ms)

  21. QTCs Double-Cross Concept (e1 ,e2) – – + 0

  22. QTCs Problems with Boundary Based Approaches I II

  23. QTCs Generalization Concept

  24. QTCs Generalization Concept

  25. QTCs Generalization Concept

  26. 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

  27. QTCs Shape Similarity the relative number of different entries in the Ms

  28. QTCs QTCs versus Closely Related Calculi

  29. QTCs QTCs versus Closely Related Calculi

  30. QTCs QTCs versus Closely Related Calculi

  31. QTCs QTCs versus Closely Related Calculi ()S ( + )S

  32. 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

  33. 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@ugent.be peter.bogaert@ugent.be

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