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