CS 563 Advanced Topics in Computer Graphics Spectral BRDF by Cliff Lindsay.
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Transcript of CS 563 Advanced Topics in Computer Graphics Spectral BRDF by Cliff Lindsay.
CS 563 Advanced Topics in Computer Graphics
Spectral BRDF
by Cliff Lindsay
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.”
Topics Covered
Color Theory (Colorimetry) Techniques and Examples for Using Spectra in
Rendering Future of Spectral Rendering
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
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).
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
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
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.
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
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.
CIE Chart
Mapping CIE XYZ RGB
[1]
Current Display Issues
Representation of Light is RGB based
Low Dynamic Range of Monitors
Disparate Range Values
Image acquired from [8]
Dealing With Display Issues
Tone Reproduction
Spectra to Color Mapping
Mapping Color to Spectra
Tone Reproduction (Mapping)
Methods for scaling luminance values in a real world to a displayable range.
Mimics perceptual qualities cd (candela) – lumen per steridian
~105cd/m2~10-5
cd/m2
~100 cd/m2~1 cd/m2
Same VisualResponse ?
[11]
Tone Reproduction (Mapping)
Spatially Uniform (global)
Spatially Varying (local)
Time Dependent
Spatially Uniform (global operator)
Tumblin, Rushmeier, & Ward
Histogram Equalization Technique
HVS Imitation Technique
Luminance as Textures
And more …
Tumblin & Rushmeier, 1993
B = k (L – L0), where k is a constant, L0 is min Luminance, and = .333 –> .49[4]
Linear on a log-log scale similar to HVS Computationally Efficient
Low Medium High [4]
Ward, 1994 Linear transform
Ld = mLW
Matching contrast between real and image Ld = display Luminance, Lw = world, and m = scale factor.
Min-Max Ward
Spatially Varying (local operator)
Chiu, 1993, Schlick 1994
Zone System (Ansel Adams ‘80, ‘81?)[10]
Low Curvature Image Simplifier
Local-linear Mapping
And More …
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*fblur(i,j)) where fblur = 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
Chiu, 1993
Original image
Image with blurring and and inversion scaling [9]
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.
Schlick, 1994
[10]
Time DependentFerwerda et al, 1996
Threshold visibility Changes in colour appearance Visual Acuity Temporal Sensitivity
[11]
Time Dependent
Spectra Representation
Direct Sampling (Sparse)
Polynomial Representation
Adaptive Techniques
Hybrid (composite)
And More…
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
Polynomial Representation
Piecewise cubic polynomials
Inter-reflections are reduced to polynomial multiplications
Degree reduction technique based on Chebyshev polynomials
Spectral multiplications are O(n2)
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.
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
Equations From Slide 7
Given Colors we want to go back to a 3 component Spectrum (image slide 6):
S = j=1-3tjixj , where tji = k A()fj() d
and fj = some linearly independent functions
Mapping Color to spectra
Equations From Slide 7
S = j=1-3tjixj , 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
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)
Now What Can We Do With Spectra?
Polarization
Interference
Dispersion
Florescence
[4]
Polarization
Caused by light interaction with an optically smooth surface
Electromagnetic Wave Retardance of incident light, relative Phase
shift
[4]
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]
Dispersion
Light is split into spectral components Dielectric Materials: diamonds, lead crystal,
glass Results: colored fringes, rainbow caustics, etc.
[4]
Florescence
Re-emission of photons at different energy levels
Re-emission has at a time delay(typically 10-8 secs.)
[4]
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
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
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
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