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Making choices in multi-dimensional parameter spaces PhD thesis - PowerPoint PPT Presentation

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Making choices in multi-dimensional parameter spaces PhD thesis defence Steven Bergner Model adjustment at different levels User-driven experimentation: Use cases for paraglide Criteria optimization: Lighting design Theoretical

  1. Sampling the region of interest • Tensor product of value levels for each dimension � Nested for -loops � Cost is exponential in #dims • Separate range specification from sample generation Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 8

  2. Sampling the region of interest • Tensor product of value levels for each dimension � Nested for -loops � Cost is exponential in #dims • Separate range specification from sample generation Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 8

  3. Paraglide summary • Longitudinal study showed use of parameter space partitioning • Requirements informed follow-up projects • Alternative user interaction � Dimensionally reduced slider embedding � Mixing board • Video demo Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 9

  4. Model adjustment at different levels • User-driven experimentation: Use cases for paraglide • Criteria optimization: Lighting design • Theoretical analysis: Sampling in volume rendering • Discretizing a region: Lattices with rotational dilation • Summary and conclusion Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 10

  5. Model adjustment at different levels • User-driven experimentation: Use cases for paraglide • Criteria optimization: Lighting design • Theoretical analysis: Sampling in volume rendering • Discretizing a region: Lattices with rotational dilation • Summary and conclusion Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 10

  6. Roadmap From light to colour Efficient light model Designing spectra for lights and materials Evaluation Applications 11 Bergner, Drew, Möller - Generating Light and Reflectance Spectra - ACM Trans. on Graphics 2009

  7. From Light to Colour !"#$% ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 &'(!')%*+)' ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 12

  8. From Light to Colour !"#$% !,- ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 &'(!')%*+)' !"#$"%&"'($)*+& ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 12

  9. From Light to Colour !"#$% !,- ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 '()*+,-./01-*),!-# &'(!')%*+)' !"# ! !"#$%&$% $%""& ! !"#$"%&"'($)*+& ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 '()" ! ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 12

  10. From Light to Colour !"#$% !,- ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 '()*+,-./01-*),!-# &'(!')%*+)' !"# ! !"#$%&$% $%""& ! !"#$"%&"'($)*+& ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 '()" ! ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 = B G R 12

  11. From Light to Colour !"#$% !,- ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 '()*+,-./01-*),!-# &'(!')%*+)' !"# ! !"#$%&$% $%""& ! !"#$"%&"'($)*+& ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 '()" ! ! !"" !#" !$" !%" &'" &&" &(" $)" $!" $*" *"" +,-./.012345067 component-wise = � product in RGB B G R 12

  12. Light 1 Use for Visualization Light 2 13

  13. Light 1 Use for Visualization { Metamers � Different Spectra give same RGB Light 2 13

  14. Light 1 Use for Visualization Metamers � Different Spectra give same RGB Constant Colours � Metamers under changing Light 2 light 13

  15. Light 1 Use for Visualization Metamers � Different Spectra give same RGB Constant Colours � Metamers under changing Light 2 light Metameric Blacks � Spectra give RGB triple = 0 13

  16. Light 1 Use for Visualization Metamers � Different Spectra give same RGB Constant Colours � Metamers under changing Light 2 light Metameric Blacks � Spectra give RGB triple = 0 Effective choice of light & material palette needed! 13

  17. Roadmap From light to colour Efficient light model Designing spectra for lights and materials Evaluation Applications 14

  18. Roadmap From light to colour Efficient light model Designing spectra for lights and materials Evaluation Applications 15

  19. Illumination Dependent Colour Picker ? ? ? ? ? ? ? 16

  20. Illumination Dependent Colour Picker ? ? ? ? ? ? ? 16

  21. Illumination Dependent Colour Picker ? ? ? ? ? ? ? 16

  22. Illumination Dependent Colour Picker ? ? ? ? ? ? ? 16

  23. Illumination Dependent Colour Picker 16

  24. Quality Criteria Colour – Fit the desired colour or metamer Smoothness – Regularize solution and reduce extrema Minimal error in linear model – Minimal colour difference when illumination bounce is computed in linear subspace Positivity – Produce physically plausible spectra 17

  25. Quality Criteria 18

  26. Quality Criteria Instead of equation system for spectrum � M � x = � x y Solve normal equation x � M � x − � y � argmin � 18

  27. Quality Criteria Instead of equation system for spectrum � M � x = � x y Solve normal equation x � M � x − � y � argmin �     m red c r � � � � – Colour: �  diag ( � argmin � S ) � c g m green x − � � x    � � m blue c b � � 18

  28. Quality Criteria Instead of equation system for spectrum � M � x = � x y Solve normal equation x � M � x − � y � argmin �     m red c r � � � � – Colour: �  diag ( � argmin � S ) � c g m green x − � � x    � � m blue c b � �     − 1 2 − 1 0 0 0 · · · � � 0 − 1 2 − 1 0 0 – Smoothness: · · · �     �  � argmin � �     � . ... x − . x �     � . � �    0 0 − 1 2 − 1 0 · · · 18

  29. Quality Criteria Instead of equation system for spectrum � M � x = � x y Solve normal equation x � M � x − � y � argmin �     m red c r � � � � – Colour: �  diag ( � argmin � S ) � c g m green x − � � x    � � m blue c b � �     − 1 2 − 1 0 0 0 · · · � � 0 − 1 2 − 1 0 0 – Smoothness: · · · �     �  � argmin � �     � . ... x − . x �     � . � �    0 0 − 1 2 − 1 0 · · · Weight the criteria and combine as stacked matrix – Global minimum error solution via pseudo-inverse of M – Positivity through quadratic programming 18

  30. Roadmap From light to colour Efficient light model Designing spectra for lights and materials Evaluation Applications 19

  31. Materials and lighting Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 20

  32. Materials and lighting Given: Output Goal: Input Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 20

  33. Materials and lighting Given: Output Goal: Input lights )*+,-./01)$# "&# ? ? " !"" #"" $"" %"" ? reflectances ? ? ? ? • 3x5 combination colours • 7x31 component SPDs with 3 components each Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 20

  34. Materials and lighting Given: Output Goal: Input lights )*+,-./01)$# 23,-04-./0' 23,-04-./0( )*+,-./01)$# ' ' "&# "&# "&# "&# ? ? " " " !"" #"" $"" %"" !"" #"" $"" %"" !"" #"" $"" %"" " ' !"" #"" $"" %"" ? "&# " !"" #"" $"" %"" reflectances ? "&' " !"" #"" $"" %"" ? "&# " !"" #"" $"" %"" ? "&( " !"" #"" $"" %"" "&# ? " !"" #"" $"" %"" • 3x5 combination colours • 7x31 component SPDs with 3 components each Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 20

  35. Image based re-lighting a) 21

  36. Image based re-lighting b) a) 21

  37. Image based re-lighting b) a) c) 21

  38. Applications in Graphics and Visualization D65 daylight sodium hp 0.2 0.4 0.1 0.2 0 0 400 500 600 700 400 500 600 700 refl 1 0.8 0.6 0.4 0.2 0 400 500 600 700 refl 2 1 0.5 0 400 500 600 700 Additional texture details appear under changing illumination 22

  39. Model adjustment at different levels • User-driven experimentation: Use cases for paraglide • Criteria optimization: Lighting design • Theoretical analysis: Sampling in volume rendering • Filling a region: Lattices with rotational dilation • Summary and conclusion Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 23

  40. Model adjustment at different levels • User-driven experimentation: Use cases for paraglide • Criteria optimization: Lighting design • Theoretical analysis: Sampling in volume rendering • Filling a region: Lattices with rotational dilation • Summary and conclusion Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 23

  41. Volume Rendering • Map data value f to optical properties using a transfer function g(f(x)) • Then shading+compositing Opacity g f f Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 24

  42. Volume Rendering • Map data value f to optical properties using a transfer function g(f(x)) • Then shading+compositing Opacity g f f Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 24

  43. Volume Rendering • Map data value f to optical properties using a transfer function g(f(x)) • Then shading+compositing Opacity g f f Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 24

  44. Volume Rendering • Map data value f to optical properties using a transfer function g(f(x)) • Then shading+compositing Opacity g f f Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 24

  45. Volume Rendering • Map data value f to optical properties using a transfer function g(f(x)) • Then shading+compositing Opacity g f f Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 24

  46. Intuition Analysis Application Example of g(f(x)) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 25

  47. Intuition Analysis Application Example of g(f(x)) Original function f(x) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 25

  48. Intuition Analysis Application Example of g(f(x)) Original function f(x) Transfer function g(y) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 25

  49. Intuition Analysis Application Example of g(f(x)) Original function f(x) g(f(x)) sampled by Transfer function g(y) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 25

  50. Intuition Analysis Application Example of g(f(x)) Original function f(x) g(f(x)) sampled by Transfer function g(y) g(f(x)) sampled by Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 25

  51. Intuition Analysis Application Composition in Frequency Domain y y · · Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  52. Intuition Analysis Application Composition in Frequency Domain · Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  53. Intuition Analysis Application Composition in Frequency Domain · H ( k ) = 1 � � G ( l ) e il · f ( x ) dle − ik · x dx 2 π R R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  54. Intuition Analysis Application Composition in Frequency Domain · H ( k ) = 1 � � G ( l ) e il · f ( x ) dle − ik · x dx 2 π R R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  55. Intuition Analysis Application Composition in Frequency Domain · H ( k ) = 1 � � G ( l ) e il · f ( x ) dle − ik · x dx 2 π R R H ( k ) = 1 � � e il · f ( x ) e − ik · x dxdl G ( l ) 2 π R R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  56. Intuition Analysis Application Composition in Frequency Domain · H ( k ) = 1 � � G ( l ) e il · f ( x ) dle − ik · x dx 2 π R R H ( k ) = 1 � � e il · f ( x ) e − ik · x dxdl G ( l ) 2 π R R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  57. Intuition Analysis Application Composition in Frequency Domain · H ( k ) = 1 � � G ( l ) e il · f ( x ) dle − ik · x dx 2 π R R H ( k ) = 1 � � e il · f ( x ) e − ik · x dxdl G ( l ) 2 π R R � e i ( l · f ( x ) − k · x ) dx P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 26

  58. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  59. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  60. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  61. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  62. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  63. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  64. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  65. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  66. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  67. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  68. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  69. Intuition Analysis Application Visualizing P(k,l) � H ( k ) = 1 e i ( l · f ( x ) − k · x ) dx 2 π < G ( · ) , P ( k, · ) > P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 27

  70. Intuition Analysis Application Visualizing P(k,l) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 28

  71. Intuition Analysis Application Visualizing P(k,l) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 28

  72. Intuition Analysis Application Visualizing P(k,l) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 28

  73. Intuition Analysis Application Visualizing P(k,l) • Slopes of lines in P(k,l) are related to 1/f‘(x) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 28

  74. Intuition Analysis Application Visualizing P(k,l) • Slopes of lines in P(k,l) are related to 1/f‘(x) • Extremal slopes bounding the wedge are 1/max(f’) Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 28

  75. Intuition Analysis Application Method of stationary phase � e i ( l · f ( x ) − k · x ) dx P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 29

  76. Intuition Analysis Application Method of stationary phase � e i ( l · f ( x ) − k · x ) dx P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 29

  77. Intuition Analysis Application Method of stationary phase � e i ( l · f ( x ) − k · x ) dx P ( k, l ) = R Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 29

  78. Intuition Analysis Application Method of stationary phase � e i ( l · f ( x ) − k · x ) dx P ( k, l ) = R • Taylor expansion around points of stationary phase • Exponential drop-off at maximum l · max | f ′ | = k Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 29

  79. Intuition Analysis Application Method of stationary phase � e i ( l · f ( x ) − k · x ) dx P ( k, l ) = R • Taylor expansion around points of stationary phase • Exponential drop-off at maximum l · max | f ′ | = k Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 29

  80. Intuition Analysis Application Adaptive Raycasting Same number of samples Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 30

  81. Intuition Analysis Application Adaptive Raycasting SNR Ground-truth: computed at a fixed sampling distance of 0.06125 Steven Bergner - Making choices in multi-dimensional parameter spaces - PhD thesis defence 31

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