CS 563 Advanced Topics in Computer Graphics Spectral BRDF

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CS 563 Advanced Topics in Computer
GraphicsSpectral BRDF

• by Cliff Lindsay

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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.

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Topics Covered

• Color Theory (Colorimetry)
• Techniques and Examples for Using Spectra in
  Rendering
• Future of Spectral Rendering

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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

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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).

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Tristimulus Theory

• Human Visible light ? 380nm 800nm
• 3 Different Cone Sizes
• Response for each Cone Size1
• S ? s(?)A(?)d?
• M ?m(?)A(?)d?
• L ? l(?) A(?)d?

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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?
• rSR gSG bSB

• 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.

Equations were taken from pages 302-303 of 1
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CIE

• Commission Internaionale de lEclairage (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

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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.

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CIE Chart
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Mapping CIE XYZ ? RGB
1
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Current Display Issues

• Representation of Light is RGB based
• Low Dynamic Range of Monitors
• Disparate Range Values

Image acquired from 8
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Dealing With Display Issues

• Tone Reproduction
• Spectra to Color Mapping
• Mapping Color to Spectra

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Tone Reproduction (Mapping)

• Methods for scaling luminance values in a real
  world to a displayable range.
• Mimics perceptual qualities
• cd (candela) lumen per steridian

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Tone Reproduction (Mapping)

• Spatially Uniform (global)
• Spatially Varying (local)
• Time Dependent

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Spatially Uniform (global operator)

• Tumblin, Rushmeier, Ward
• Histogram Equalization Technique
• HVS Imitation Technique
• Luminance as Textures
• And more

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Tumblin Rushmeier, 1993

• B k (L L0)?, where k is a constant, L0 is min
  Luminance, and ? .333 gt .494
• Linear on a log-log scale similar to HVS
• Computationally Efficient

4
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Ward, 1994

• Linear transform
• Ld mLW
• Matching contrast between real and image
• Ld display Luminance, Lw world, and m scale
  factor.

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Spatially Varying (local operator)

• Chiu, 1993, Schlick 1994
• Zone System (Ansel Adams 80, 81?)10
• Low Curvature Image Simplifier
• Local-linear Mapping
• And More

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Chiu, 1993

• Eye is more sensitive to reflectance than
  luminance
• Blur the image to remove high frequencies
• Inverting the Result
• S(i, j) 1/(kfblur(i,j)) where fblur e.01r
  9
• Sf, 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

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Chiu, 1993

• Original image

• Image with blurring and and inversion scaling

9
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Schlick, 1994

• Rational rather than logarithmic
• Big speed advantage over Chiu et al.
• F p Val/pVal Val HiVal
• Where
• HiVal - the highest tonal value in the image
• Val current tonal value
• P MHiVal/NLoVal, where M the darkest gray
  level that can be distinguished from black, and N
  is the largest value for the display device.

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Schlick, 1994
10
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Time DependentFerwerda et al, 1996

• Threshold visibility
• Changes in colour appearance
• Visual Acuity
• Temporal Sensitivity

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Time Dependent
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Spectra Representation

• Direct Sampling (Sparse)
• Polynomial Representation
• Adaptive Techniques
• Hybrid (composite)
• And More

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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
• Sr SPD reflectence under normal incidence

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Polynomial Representation

• Piecewise cubic polynomials
• Inter-reflections are reduced to polynomial
  multiplications
• Degree reduction technique based on Chebyshev
  polynomials
• Spectral multiplications are O(n2)

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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.

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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? rSR gSG bSB

• Given Colors we want to go back to a 3 component
  Spectrum (image slide 6)
• S ?j1-3tjixj , where tji k ? A(?)fj(?) d?
• and fj some linearly independent functions

Equations From Slide 7
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Mapping Color to spectra

• S ?j1-3tjixj , where tji k ? A(?)fj(?) d?
• fj 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

Equations From Slide 7
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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)

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Now What Can We Do With Spectra?

• Polarization
• Interference
• Dispersion
• Florescence

4
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Polarization

• Caused by light interaction with an optically
  smooth surface
• Electromagnetic Wave
• Retardance of incident light, relative Phase
  shift

4
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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
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Dispersion

• Light is split into spectral components
• Dielectric Materials diamonds, lead crystal,
  glass
• Results colored fringes, rainbow caustics, etc.

4
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Florescence

• Re-emission of photons at different energy levels
• Re-emission has at a time delay(typically 10-8
  secs.)

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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

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Insights, Future, and Were to Go From Here

• Something to look into
• Paul Debevecs High Dynamic Range Paper
• Wards High Dynamic Range Imaging
• OpenEXR An Opensource HDR image file format
  developed by Industrial Light Magic

Image courtesy of ILM, http//www.openexr.com/abou
t.html
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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/co
  lor.html
• 8 Devlin, Kate, A review of tone reproduction
  techniques, Technical Report CSTR-02-005,
  November 2002

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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