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Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH 290-04 Chris Tralie, Duke University 3/1/2016 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics Announcements Group Assignment 1 Full Submission Due Tomorrow

  1. Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH 290-04 Chris Tralie, Duke University 3/1/2016 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  2. Announcements ⊲ Group Assignment 1 Full Submission Due Tomorrow (Wednesday) 11:55 PM ⊲ Rank Top 3 Final Project Choices By Friday 3/5 (Groups of 3-4) ⊲ Attendance Policy Clarification ⊲ Midterm Next Thursday 3/10 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  3. Table of Contents ◮ Shape Statistics / Algorithms ⊲ Comparing Shape Statistics ⊲ Classification / Performance Evaluation COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  4. Random Sampling By Area Goal: Given a shape, return similar shapes in a database Tralie 2010 ⊲ Focus on point clouds ⊲ Focus on shapes similar under rigid motion COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  5. Random Sampling By Area COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  6. Centroid Centering / RMS Scaling x i } N For a point cloud { � i = 1 ⊲ Subtract off centroid ⊲ Root mean square scale. Want � N � � 1 � � x i || 2 = 1 || � N i = 1 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  7. Shape Matching Criteria ⊲ Concise To Store ⊲ Quick to compute ⊲ Efficient to match ⊲ Discerning ⊲ Noise tolerant ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  8. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  9. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  10. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  11. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  12. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  13. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  14. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  15. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  16. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  17. Shape Histogram: Shells ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  18. Shape Histogram: Shells ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  19. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  20. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  21. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  22. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  23. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  24. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  25. Shape Histogram: Shells What can’t it tell apart? SHOW VIDEO COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  26. Shape Histogram: Shells And Sectors SHOW VIDEO COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  27. Shape Histogram: Shells And Sectors Still Rotation Invariant? COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  28. Shape Histogram: Shells And Sectors ⊲ Sort sectors within each shell ⊲ Record PCA eigenvalues within each shell COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  29. Spin Images Johnson/Herbert 1999, Figure Huang 2010 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  30. Spin Images: Rubber Duck Johnson/Herbert 1999 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  31. Spin Images ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  32. Spin Images ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  33. Spin Images ⊲ Quick To Compute ⊲ Concise To Store COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  34. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  35. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  36. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  37. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  38. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  39. D2: Distance Histograms Osada 2003, Figure from Huang 2010 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  40. D2: Primitive Examples Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  41. D2: Real Examples Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  42. D1: Randomly Sample Points Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  43. D3: Randomly Sample Areas Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  44. D4: Randomly Sample Volumes Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  45. A3: Randomly Sample Angles Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  46. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  47. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  48. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  49. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  50. Extended Gaussian Image ⊲ Efficient To Compute / Concise To Store Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  51. Extended Gaussian Image ⊲ Efficient To Compute / Concise To Store Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  52. Extended Gaussian Image ⊲ Discerning Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  53. Extended Gaussian Image ⊲ Discerning (Only fully describes convex objects) Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  54. Extended Gaussian Image ⊲ Rotation Invariant Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  55. Extended Gaussian Image ⊲ Rotation Invariant (Rotate To Align With PCA Axes) Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  56. Extended Gaussian Image ⊲ Robust To Noise? Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  57. Extended Gaussian Image ⊲ Not Robust To Noise! Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  58. Table of Contents ⊲ Shape Statistics / Algorithms ◮ Comparing Shape Statistics ⊲ Classification / Performance Evaluation COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  59. Normalize Histograms By Mass h [ i ] h ′ [ i ] = � N k = 1 h [ k ] In other words, all bins should sum to 1 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  60. Histogram Euclidean Distance For histograms h 1 and h 2 � N � � � ( h 1 [ i ] − h 2 [ i ]) 2 d E ( h 1 , h 2 ) = � i = 1 Just thinking of h 1 and h 2 as high dimensional Euclidean vectors! Each histogram bin is a dimension COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  61. Histogram Cosine Distance � � h 1 · � � h 2 d C ( h 1 , h 2 ) = cos − 1 || � h 1 |||| � h 2 || COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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