1. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Object Description and Decomposition by Symmetry Hierarchies Kai Huebner Safe and Secure Cognitive Systems (SSCS) GermanResearch Center for Artificial Intelligence (DFKI) Bremen, Germany. now at: Computational Vision and Active Perception Lab (CVAP) Royal Institute of Technology (KTH) Stockholm, Sweden.

2. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007  Short Motivation  A Range-Based Symmetry Operator  Symmetry Hierarchies  Experiment  Conclusion 1 Overview

3. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Motivation [Locher & Nodine (1989)] Motivation 2 Architecture Art Nature

4. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 A Range-Based Symmetry Operator Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. 3

5. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. A Range-Based Symmetry Operator 3

6. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. A Range-Based Symmetry Operator 3

7. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. A Range-Based Symmetry Operator 3

8. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. A Range-Based Symmetry Operator 3

9. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. A Range-Based Symmetry Operator 3

10. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Computation of the whole search space: A Range-Based Symmetry Operator A Dynamic Programming approach. A Range-Based Symmetry Operator 3

11. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007  Result: Iteration stop at l = 4 (max) Iteration stop at l = 4 (max) Mapping index (4 / 4)  S = 8 Mapping index (4 / 4)  S = 8  Parameters: Band mask width w B = 2 Band mask width w B = 2 Absolute threshold T = 5 Absolute threshold T = 5 Weights W i = 1 Weights W i = 1 Iterative computation with threshold: A Range-Based Symmetry Operator 4 [Huebner, Westhoff, Zhang (2005)]

12. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Low vertical symmetry (0) High vertical symmetry (w) A Range-Based Symmetry Operator 5

13. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 A Range-Based Symmetry Operator 5 Low vertical symmetry (0) High vertical symmetry (w)

14. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Hierarchies are generally considered w.r.t different operator sizes in symmetry strength-based approaches (multi-scalar or multi-resolution): Symmetry Hierarchies [Zabrodsky et al. (1992)] Multi-scalar hierarchy: Symmetry Hierarchies Multi-resolution hierarchy: 6

15. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 The range-based operator allows to consider hierarchies of symmetries theirselves instead: Symmetry Hierarchies 7

16. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies The range-based operator allows to consider hierarchies of symmetries theirselves instead: 7

17. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies The range-based operator allows to consider hierarchies of symmetries theirselves instead: 7

18. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies The range-based operator allows to consider hierarchies of symmetries theirselves instead: 7

19. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies The range-based operator allows to consider hierarchies of symmetries theirselves instead: 7

20. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies The range-based operator allows to consider hierarchies of symmetries theirselves instead: 7

21. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies The range-based operator allows to consider hierarchies of symmetries theirselves instead: 7

22. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Symmetry Hierarchies 8  Image decomposition using symmetry hierarchies

23. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007  Platform: Rolland 3, Cognitive Robotics working group  Embedded into the SFB/TR8 research project  Goal: autonomous, secure and safe driving in dynamic environments Rolland 3 9 Experiment Experiment

24. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007  Panoramic image decomposition using symmetry hierarchies 10 Experiment Experiment → →

25. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007  Panoramic image decomposition using symmetry hierarchies  Sector color matching: 10 Experiment Experiment → →

26. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007  Panoramic image decomposition using symmetry hierarchies  Sector color matching  Result: Intuitive, dynamic image sectoring based on symmetry  Future work: Combination of hierarchies & Regional Symmetry Features, towards a more general description of symmetric image content 10 Experiment Experiment → →

27. German Research Institute of Artificial Intelligence (DFKI), Bremen Lab. Safe and Secure Cognitive Systems Group 15th WSCG International Conference Plzen, 31. January 2007 Thanks for your attention!