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Lecture 7: Image Sources, Convolution, Scene Graphs COMPSCI/MATH 290-04 Chris Tralie, Duke University 2/4/2016 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs Announcements Mini Assignment 2 Due Next Monday 11:55

  1. Lecture 7: Image Sources, Convolution, Scene Graphs COMPSCI/MATH 290-04 Chris Tralie, Duke University 2/4/2016 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  2. Announcements ◮ Mini Assignment 2 Due Next Monday 11:55 PM ◮ Group Assignment 1 will be released before Monday ◮ Find partners! COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  3. Table of Contents ◮ 3D Rotations Continued ⊲ Image Sources ⊲ Convolution ⊲ Scene Graphs COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  4. 3D Rotations: Coordinate Frame Interpretation COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  5. 3D Rotations: Euler Angles Visualization COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  6. Table of Contents ⊲ 3D Rotations Continued ◮ Image Sources ⊲ Convolution ⊲ Scene Graphs COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  7. Ray Casting for Specular Reflections ⊲ Project onto normal, flip normal component, preserve parallel component COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  8. Ray Casting for Specular Reflections COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  9. Ray Casting for Specular Reflections COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  10. Ray Casting for Specular Reflections COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  11. Ray Casting for Specular Reflections COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  12. Ray Casting for Specular Reflections COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  13. Ray Casting for Specular Reflections ⊲ Dilution of precision ⊲ Need fine angle resolution to capture! COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  14. Image Sources COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  15. Image Sources COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  16. Image Sources COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  17. Image Sources: Proof COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  18. Image Sources: More Examples COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  19. Image Sources: Second Order COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  20. Image Sources: Second Order COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  21. Image Sources: Second Order COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  22. Image Sources: Second Order COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  23. Image Sources: Third Order (!) 1 2 3 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  24. Image Sources: Third Order 1 2 3 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  25. Image Sources: Third Order 1 2 3 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  26. Image Sources: Third Order 1 2 3 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  27. Image Sources: Third Order 1 2 3 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  28. Image Sources: Third Order COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  29. Image Sources: Occlusions COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  30. Image Sources: Occlusions Ray needs to hit target before anything else COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  31. Image Sources: Point Containment COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  32. Image Sources: Point Containment Intersection with line (plane in 3D) must be in interior of polygon COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  33. Table of Contents ⊲ 3D Rotations Continued ⊲ Image Sources ◮ Convolution ⊲ Scene Graphs COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  34. Impulse Response ⊲ Convert lengths of all paths into times, amplitude records decay Direct Path COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  35. Impulse Response ⊲ Convert lengths of all paths into times, amplitude records decay Direct Path ⊲ What causes decay? COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  36. Convolution ⊲ Convolution: What do sounds sound like in this environment? Direct Path COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  37. Convolution ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  38. Convolution ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  39. Convolution ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  40. Convolution ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  41. Convolution ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  42. Convolution ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  43. Convolution: Result ⊲ Add overlapping signals, delayed and decayed COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  44. Convolution: Notation / Equation x [ n ] : Discretely sampled signal describing the sound h [ n ] : Discretely sampled signal describing impulse COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  45. Convolution: Notation / Equation (RAFFLE POINT) x [ n ] : Discretely sampled signal describing the sound h [ n ] : Discretely sampled signal describing impulse COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  46. Convolution: Notation/Equation x [ n ] : Discretely sampled signal describing the sound h [ n ] : Discretely sampled signal describing impulse N � ( x ∗ h )[ n ] = h [ k ] x [ n − k ] k = 0 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  47. Convolution: Notation/Equation x [ n ] : Discretely sampled signal describing the sound h [ n ] : Discretely sampled signal describing impulse N � ( x ∗ h )[ n ] = h [ k ] x [ n − k ] k = 0 Roles can switch! COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  48. Gaussian Interpolation Given non-integer bin index n 0 with amplitude a   k = 2 σ h [ n ] = ae − ( n − n 0 ) 2 / 2 σ 2 / e − ( n − n 0 ) 2 / 2 σ 2 �   k = − 2 σ COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  49. Convolution Examples Interactive demo COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  50. Table of Contents ⊲ 3D Rotations Continued ⊲ Image Sources ⊲ Convolution ◮ Scene Graphs COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  51. Scene Graph: Human body Figure courtesy of http://www.euclideanspace.com/physics/kinematics/joints/ COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  52. Scene Graph: Human body MOCAP interactive example COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  53. Scene Graph: Bedroom Liu, Tianqiang, et al. ”Creating consistent scene graphs using a probabilistic grammar.” ACM Transactions on Graphics (TOG) 33.6 (2014): 211. COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  54. Scene Graph: Library Liu, Tianqiang, et al. ”Creating consistent scene graphs using a probabilistic grammar.” ACM Transactions on Graphics (TOG) 33.6 (2014): 211. COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  55. Scene Graph: Euler Angles Visualization COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

  56. Designing Scene Graphs Interactive Example COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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