1. CS 563 Advanced Topics in Computer Graphics Spectral BRDF by Cliff Lindsay

2. Overview “The ultimate aim of realistic graphics is the creation of images that provoke the same responses that a viewer would have to a real scene.”

3. Topics Covered  Color Theory (Colorimetry)  Techniques and Examples for Using Spectra in Rendering  Future of Spectral Rendering

4. Color Theory  Dominant Wavelength  Color Matching  CIE XYZ Terminology:  Luminance – total power in the light, by the total we mean area under the Spectral curve  Dominant Wavelength – specifies the hue of the color, usually represented by a spike or dominating portion of the spectral curve  Saturation (purity) – of a light is defined as the % of luminance that resides in the dominant wavelength

5. Dominant Wavelength  Color is a Spectral Curve (intensity vs. Wavelength)  Response (in general) = k  w( )L( )d [1]  Color is determined by Spectra, mostly the Dominant  Different Spectral Power Distributions can map to the same color, for ex.: Red Laser, SPD w/ Red dominating, Red w/ White (AKA Metamers).

6. Tristimulus Theory  Human Visible light  380nm – 800nm  3 Different Cone Sizes  Response for each Cone Size [1] :  S =  s( )A( )d  M =  m( )A( )d  L =  l( ) A( )d

7. Tristimulus Theory For Each Cone :  A( ) = rR( )+ gG( )+bB( )  S =  s( )A( )d =  s( )(rR( )+ gG( )+bB( )) = r  s( )R( )d +g  s( )G( )d +b  s( )B( )d = rS R + gS G + bS B Equations were taken from pages 302-303 of [1]  The equations are the same for M & L, and RGB, and rgb contribute to all Cones separately. Where s( ) is the Response function for a Short Cone.

8. CIE  Commission Internaionale de l’Eclairage (CIE)  Created a Standard color system in 1931 (XYZ)  Based on the human eye's response to RGB  Device-independent colors  Positive combinations of colors

9. CIE XYZ CIE Tristimulus values  X = 683  x( )L( ) d  Y = 683  y( )L( ) d  Z = 683  z( )L( ) d  Y is luminance  Integrate over 380nm – 800nm  Affine Equation for Color Definition:  Affine – means all components add to 1.

10. CIE Chart

11. Mapping CIE XYZ  RGB [1]

12. Current Display Issues  Representation of Light is RGB based  Low Dynamic Range of Monitors  Disparate Range Values Image acquired from [8]

13. Dealing With Display Issues  Tone Reproduction  Spectra to Color Mapping  Mapping Color to Spectra

14. Tone Reproduction (Mapping)  Methods for scaling luminance values in a real world to a displayable range.  Mimics perceptual qualities  cd (candela) – lumen per steridian ~10 5 cd/m 2 ~10 -5 cd/m 2 ~100 cd/m 2 ~1 cd/m 2 Same Visual Response ? [11]

15. Tone Reproduction (Mapping)  Spatially Uniform (global)  Spatially Varying (local)  Time Dependent

16. Spatially Uniform (global operator)  Tumblin, Rushmeier, & Ward  Histogram Equalization Technique  HVS Imitation Technique  Luminance as Textures  And more …

17. Tumblin & Rushmeier, 1993  B = k (L – L 0 ) , where k is a constant, L 0 is min Luminance, and  =.333 –>.49 [4]  Linear on a log-log scale similar to HVS  Computationally Efficient LowMediumHigh [4]

18. Ward, 1994  Linear transform L d = mL W  Matching contrast between real and image  L d = display Luminance, L w = world, and m = scale factor. Min-MaxWard

19. Spatially Varying (local operator)  Chiu, 1993, Schlick 1994  Zone System (Ansel Adams ‘80, ‘81?) [10]  Low Curvature Image Simplifier  Local-linear Mapping  And More …

20. Chiu, 1993  Eye is more sensitive to reflectance than luminance  Blur the image to remove high frequencies  Inverting the Result  S(i, j) = 1/(k*f blur (i,j)) where f blur = e.01r [9]  S*f, where S() – inversion, f() – raster position Where:  r = is the distance (in one pixel width equals one) from the center of the kernel  K = is a visual adjustment weight

21. Chiu, 1993  Original image  Image with blurring and and inversion scaling [9]

22. Schlick, 1994  Rational rather than logarithmic  Big speed advantage over Chiu et al.  F = p * Val/p*Val – Val + HiVal Where:  HiVal - the highest tonal value in the image  Val = current tonal value  P = M*HiVal/N*LoVal, where M = the darkest gray level that can be distinguished from black, and N is the largest value for the display device.

23. Schlick, 1994 [10]

24. Time Dependent Ferwerda et al, 1996  Threshold visibility  Changes in colour appearance  Visual Acuity  Temporal Sensitivity [11]

25. Time Dependent

26. Spectra Representation  Direct Sampling (Sparse)  Polynomial Representation  Adaptive Techniques  Hybrid (composite)  And More…

27. Direct Sampling Where:  K is a normalization coefficient  64 = segments of the visible domain [380nm- 700nm] in 5nm widthband  x( ), y( ) and z( ) are the color matching functions of the XYZ colorimetric system  S r – SPD * reflectence under normal incidence

28. Polynomial Representation  Piecewise cubic polynomials  Inter-reflections are reduced to polynomial multiplications  Degree reduction technique based on Chebyshev polynomials  Spectral multiplications are O(n 2 )

29. Mapping Color to Spectra  If Light is defined as RGB, then what and we want to model situations that require Spectra: Light interference (Soap Bubbles, hummingbird wings, film coated objects)  Then We Need to Go Back to Spectra from RGB, But Many different Spectra Map to the Same Color???  We can do it!  Definitions:  Metamers - One color that maps to more than one Spectral Power Distribution.

30. Mapping Color to spectra Remember: S =  s( )A( )d =  s( )(rR( )+ gG( )+bB( )) = r  s( )R( )d +g  s( )G( )d +b  s( )B( )d = rS R + gS G + bS B Equations From Slide 7  Given Colors we want to go back to a 3 component Spectrum (image slide 6): S =  j=1-3 t ji x j, where t ji = k  A( )f j ( ) d and f j = some linearly independent functions

31. Mapping Color to spectra Equations From Slide 7 S =  j=1-3 t ji x j, where t ji = k  A( )f j ( ) d  f j = some linearly independent functions  What this gives us a 3X3 matrix of coefficients that we need for reconstruction of the SPDs.  We can use Delta functions, Box functions, or Fourier Functions

32. What is Spectral BRDF  Just Like Regular BRDFs (but different)  Rendering equation  Function of 4 angles (incident, reflection)  Conservative  Different Color Interaction  Different Material Interaction  Different Viewer Interaction (non-reciprocal)

33. Now What Can We Do With Spectra?  Polarization  Interference  Dispersion  Florescence [4]

34. Polarization  Caused by light interaction with an optically smooth surface  Electromagnetic Wave  Retardance of incident light, relative Phase shift [4]

35. Interference Factors that Affect Light Interference:  Refractive index and thickness of the thin film  Refractive indices of the media  Incident Angle and incident SPD (Spectral Power Distribution) [6]

36. Dispersion  Light is split into spectral components  Dielectric Materials: diamonds, lead crystal, glass  Results: colored fringes, rainbow caustics, etc. [4]

37. Florescence  Re-emission of photons at different energy levels  Re-emission has at a time delay(typically 10 -8 secs.) [4]

38. Conclusion  Spectral Rendering is gaining momentum in the industry :-)  We Have Ways Around Display Devices Limitations  Necessity for Realistic Image Rendering  Getting Closer to a Physically Based System

39. Insights, Future, and Were to Go From Here  Something to look into:  Paul Debevec’s “High Dynamic Range Paper”  Ward’s “High Dynamic Range Imaging”  OpenEXR – An Opensource HDR image file format developed by Industrial Light & Magic Image courtesy of ILM, http://www.openexr.com/about.html

40. References  [1] Shirley, Peter, “Fundamentals of Computer Graphics”,  [2] Hill, F.S., “Computer Graphics Using OpenGL”,  [3] Akenine-Möller, Thomas, Haines, Eric, “Real-time Rendering”,  [4] Devlin, Kate, “State of The Art Report Tone Reproduction and Physically Based Spectral Rendering”, Eurographics, 2002  [5] Rougeron G., P'eroche B.,” An adaptive representation of spectral data for reflectance computations”, Rendering Techniques '97 (Proceedings of the Eighth Eurographics Workshop on Rendering)  [6] Sun Y, “Deriving Spectra from Colors and Rendering Light Interference”  [7] Ward, Matt, “Color Theory and Pre-Press”, http://www.cs.wpi.edu/~matt/courses/cs563/talks/color.html  [8] Devlin, Kate, “A review of tone reproduction techniques”, Technical Report CSTR-02-005, November 2002

41. References  [9] K Chiu, M Herf, P Shirley, S Swamy, C Wang, K Zimmerman, “Spatially Nonuniform Scaling Functions for High Contrast Images”,  [10] Erik Reinhard, Erik, Stark, Michael, Shirley, Peter, Ferwerda, James, “Photographic Tone Reproduction for Digital Images”,  [11] McNamara, Ann, “Visual Perception in Realistic Image Synthesis: State of the Art Report”, PowerPoint Presentation,  [12] Schlick, C, “ Quantization Techniques for Visualization of High Dynamic Range Pictures”, 1994