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Landmark Selection for Vision-Based Navigation

Landmark Selection for Vision-Based Navigation. Pablo L. Sala, U. of Toronto Robert Sim, U. of Toronto/U. of British Columbia Ali Shokoufandeh, Drexel U. Sven Dickinson, U. of Toronto. Intuitive Problem Formulation. Intuitive Problem Formulation. Intuitive Problem Formulation.

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Landmark Selection for Vision-Based Navigation

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  1. Landmark Selection for Vision-Based Navigation Pablo L. Sala, U. of Toronto Robert Sim, U. of Toronto/U. of British Columbia Ali Shokoufandeh, Drexel U. Sven Dickinson, U. of Toronto

  2. Intuitive Problem Formulation

  3. Intuitive Problem Formulation

  4. Intuitive Problem Formulation

  5. Intuitive Problem Formulation

  6. Intuitive Problem Formulation

  7. Intuitive Problem Formulation

  8. Intuitive Problem Formulation

  9. Intuitive Problem Formulation

  10. Intuitive Problem Formulation

  11. A Graph Theoretic Formulation Problem Definition: The -Minimum Overlapping Region Decomposition Problem (-MORDP) for a world instance <G=(V,E), F, {v}vV> consists of finding a minimum size -overlapping decomposition D = {R1, …, Rd} of V into regions such that:

  12. A Graph Theoretic Formulation Problem Definition: The -Minimum Overlapping Region Decomposition Problem (-MORDP) for a world instance <G=(V,E), F, {v}vV> consists of finding a minimum size -overlapping decomposition D = {R1, …, Rd} of V into regions such that: Theorem 1: A -MORDP can be reduced to an equivalent 0-MOVRDP, and the solution to this latter problem can be extended to a solution for the original problem.

  13. A Graph Theoretic Formulation Problem Definition: The -Minimum Overlapping Region Decomposition Problem (-MORDP) for a world instance <G=(V,E), F, {v}vV> consists of finding a minimum size -overlapping decomposition D = {R1, …, Rd} of V into regions such that: Theorem 1: A -MORDP can be reduced to an equivalent 0-MOVRDP, and the solution to this latter problem can be extended to a solution for the original problem. Theorem 2: The decision problem <0-MORDP, d> is NP-complete. (Proof by reduction from the Minimum Set Cover Problem.)

  14. Heuristic Methods for 0-MORDP • 0-MORDP is intractable. • Can we efficiently find an effective approximation? • We developed and tested six greedy approximation algorithms.

  15. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region:

  16. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 25

  17. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 25

  18. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

  19. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

  20. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

  21. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

  22. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 17

  23. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 17

  24. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 14

  25. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 14

  26. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 11

  27. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 11

  28. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 9

  29. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 8

  30. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 8

  31. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 6

  32. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 4

  33. Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 4

  34. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region:

  35. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 1

  36. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 1

  37. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 1

  38. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 1

  39. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 1

  40. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 1

  41. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 2

  42. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 2

  43. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 2

  44. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 2

  45. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 2

  46. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 3

  47. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 4

  48. Algorithms B.x and C: O(k|V|2|F|) k = 5 Features commonly visible in region: 5

  49. Results Simulated Data

  50. Simulated Data (cont.) • Two types of Worlds: Irregular (Irreg) and Rectangular (Rect). • average diameter: 40m. • pose space sampled at 50 cm intervals. • average number of sides: 6. • average number of obstacles: 7. • Two types of Features: Short-Range and Long-Range. • visibility range N(0.65, 0.2) to N(12.5, 1) m, • and angular range N(25, 3) degrees. • Visibility range N(0.65, 0.2) to N(17.5, 2) m, • and angular range N(45, 4) degrees.

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