lecture 15: introduction to color science...cs184/284a, lecture 15 ren ng, spring 2016 metamers...
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Computer Graphics and Imaging UC Berkeley CS184/284A, Spring 2016
Lecture 15:
Introduction to Color Science
credit: Science Media Group.
Physical Basis of Color
Ren Ng, Spring 2016CS184/284A, Lecture 15
The Fundamental Components of Light
• Newton showed sunlight can be subdivided into a rainbow with a prism • Resulting light cannot be further subdivided with a second prism
Ren Ng, Spring 2016CS184/284A, Lecture 10
Electromagnetic radiation
• Oscillations of different frequencies (wavelengths)
The Visible Spectrum of Light
Image credit: Licensed under CC BY-SA 3.0 via Commons https://commons.wikimedia.org/wiki/File:EM_spectrum.svg#/media/File:EM_spectrum.svg
Visible electromagnetic spectrum
Ren Ng, Spring 2016CS184/284A, Lecture 15
Spectral Power Distribution (SPD)
Salient property in measuring light
• The amount of light present at each wavelength
• Units: watts per nanometer (how much power in a narrow range of wavelengths)
• Often use “relative units” scaled to maximum wavelength for comparison across wavelengths when absolute units are not important
Ren Ng, Spring 2016CS184/284A, Lecture 15
Daylight Spectral Power Distributions Vary
Blue sky Solar disk
[Brian Wandell]
Ren Ng, Spring 2016CS184/284A, Lecture 10
Spectral Power Distribution of Light Sources
Describes distribution of energy by wavelength
Figure credit:
Ren Ng, Spring 2016CS184/284A, Lecture 15
Superposition (Linearity) of Spectral Power Distributions[Brian W
andell]
Ren Ng, Spring 2016CS184/284A, Lecture 15
What is Color?
Colors are the perceptual sensations that arise from seeing light of different wavelengths
• We are sensitive from roughly 380 to 760 nm Color is a phenomenon of human perception; it is not a universal property of light
• Technically speaking, different wavelengths of light are not “colors”
Biological Basis of Color
Ren Ng, Spring 2016CS184/284A, Lecture 15
Anatomy of The Human Eye
Ren Ng, Spring 2016CS184/284A, Lecture 15
Retinal Photoreceptor Cells: Rods and Cones
Rod cells Cone cellsRods are primary receptors in very low light (“scotopic” conditions), e.g. dim moonlight
• ~120 million rods in eye
• Perceive only shades of gray, no color
Cones are primary receptors in typical light levels (“photopic”)
• ~6-7 million cones in eye
• Three types of cones, each with different spectral sensitivity
• Provide sensation of colorhttp://ebooks.bfwpub.com/life.php Figure 45.18
Ren Ng, Spring 2016CS184/284A, Lecture 15
Retinal Photoreceptor Cells: Rods and Cones
http://webvision.med.utah.edu/photo1.html
Rods are primary receptors in very low light (“scotopic” conditions), e.g. dim moonlight
• ~120 million rods in eye
• Perceive only shades of gray, no color
Cones are primary receptors in typical light levels (“photopic”)
• ~6-7 million cones in eye
• Three types of cones, each with different spectral sensitivity
• Provide sensation of color
Ren Ng, Spring 2016CS184/284A, Lecture 15
Spatial Resolution of Rods and Cones in the Retina
• Highest density of cones in fovea (and no rods there)
• “Blind spot” at the optic disc, where optic nerve exits eye
[Roorda 1999]
Ren Ng, Spring 2016CS184/284A, Lecture 15
Fraction of Three Cone Cell Types Varies Widely
Hof
er, H
. et a
l. J.
Neu
rosc
i. 20
05;2
5:96
69-9
679
Distribution of cone cells at edge of fovea in 12 different humans with normal color vision. Note high variability of L/M cone cell percentage. (false color image)
Measuring Light and Color
Ren Ng, Spring 2016CS184/284A, Lecture 15
A Simple Model of a Light DetectorCredit: M
arschner
Ren Ng, Spring 2016CS184/284A, Lecture 15
Mathematics of Light Detection
Same math carries over to power distributions
• Spectrum entering the detector has its spectral power distribution, s(λ)
• Detector has its spectral sensitivity or spectral response, r(λ)
measured signal
input spectrum
detector’s sensitivity
Ren Ng, Spring 2016CS184/284A, Lecture 15
Mathematics of Light Detection
If we think of s and r as vectors, this operation is a dot product (aka inner product) or
• in fact, the computation is done exactly this way, using sampled representations of the spectra.
• let λi be regularly spaced sample points Δλ apart; then:
• this sum is very clearly a dot product
Tristimulus Theory of Color
Ren Ng, Spring 2016CS184/284A, Lecture 15
Spectral Response of Human Cone Cells
Three types of cones: S, M, and L cones (corresponding to peak response at short, medium, and long wavelengths)
Nor
mal
ized
resp
onse
Wavelength (nm)
Ren Ng, Spring 2016CS184/284A, Lecture 15
Response of S,M,L Cones to Monochromatic Light
Figure visualizes cone’s response to monochromatic light (light with energy in a single wavelength) as points in 3D space This is a plot of S, M, L response functions as a point in 3D space.
S
M
L
Marc Levoy
Ren Ng, Spring 2016CS184/284A, Lecture 15
The Human Visual System
• Human eye does not measure and brain does not receive measure of each wavelength of light
• Rather, the eye measures three response values = (S, M, L).
• The result of integrating the incoming spectrum against response functions of S, M, L cones
Kayvon Fatahalian
Ren Ng, Spring 2016CS184/284A, Lecture 15
Metamers
Metameters are two different spectra that integrate to the same (S,M,L) response.
• These will appear to have the same color The existence of metamers is critical to color reproduction
• Don’t have to reproduce the full spectrum of a real world scene
• A metamer can reproduce the perceived appearance of the scene on a monitor, for example
Ren Ng, Spring 2016CS184/284A, Lecture 15
MetamerismColor matching is an important illusion that is understood quantitatively
Brian Wandell
Ren Ng, Spring 2016CS184/284A, Lecture 15
Metamerism is a Big EffectBrian W
andell
Ren Ng, Spring 2016CS184/284A, Lecture 15
Pseudo-Geometric Interpretation
Response of each cone is a dot product (a projection) We are projecting a high dimensional vector (a spectrum) onto three vectors
• Differences that are perpendicular to all 3 vectors are not detectable
For intuition, we can imagine a 3D analog
• 3D stands in for high-D vector of SPD
• 2D stands in for 3D
• Then vision is analogous to projection onto a plane
Slide credit: Steve Marschner
Ren Ng, Spring 2016CS184/284A, Lecture 15
Pseudo-Geometric Interpretation
The information available to the visual system about a spectrum is just three values
• This amounts to aloss of informationanalogous toprojection on a plane
Two spectra thatproduce the sameresponse aremetamers
Slide credit: Steve Marschner
Color Reproduction
Ren Ng, Spring 2016CS184/284A, Lecture 15
Want to match appearance of a spectrum s on an RGB monitor
• Any spectrum that projects to the same point in the visual color space is a good reproduction
Must find a spectrum that the monitor can produce that is a metamer of s
Color Reproduction
r, g, b?
Ren Ng, Spring 2016CS184/284A, Lecture 15
CRT Display Primaries
•Curves determined by phosphor emission propertieswavelength (nm)
Em
issi
on (w
atts
/m2 )
Ren Ng, Spring 2016CS184/284A, Lecture 15
LCD Display Primaries
•Curves determined by (fluorescent) backlight and filters
Ren Ng, Spring 2016CS184/284A, Lecture 15
Pseudo-Geometric Interpretation
In color reproduction, we want to computethe combination ofr, g, b that will projectto the same visualresponse as s. Slide credit: Steve M
arschner
Ren Ng, Spring 2016CS184/284A, Lecture 15
Additive Color Matching Experiment
Show test light spectrum on left Mix “primaries” on right until they match The primaries need not be RGB
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 1
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 1
p1 p2 p3
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 1
p1 p2 p3
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 1
p1 p2 p3
The primary color amounts needed for a match
p1 p2 p3
The primary color amounts needed for a match
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 2
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 2
p1 p2 p3
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 2
p1 p2 p3
Slide from Durand and Freeman 06
Ren Ng, Spring 2016CS184/284A, Lecture 15
Experiment 2
p1 p2 p3 p1 p2 p3
We say a “negative” amount of p2 was needed to make the match, because we added it to the test color’s side.
The primary color amounts needed for a match:
p1 p2 p3
Slide from Durand and Freeman 06
The Color Matching Experiment is Linear
If matches
and matches
matchesthen
Brian Wandell
Ren Ng, Spring 2016CS184/284A, Lecture 15
Additive Color Mixing
• Given three spectral primaries
• We match generic input light with
• Negative light not possible, but can add primary to test light
• Color now described by α, β, γ
p1, p2, p3
� = �p1 + ⇥p2 + ⇤p3
Ren Ng, Spring 2016CS184/284A, Lecture 15
Subtractive Color
Produce desired spectrum by subtracting from white light (usually via absorption by pigments)
Photographic media (slides, prints) work this way
Leads to C, M, Y (cyan, magenta, yellow) as primaries
Approximately, 1 – R, 1 – G, 1 – B
[sou
rce
unkn
own]
Ren Ng, Spring 2016CS184/284A, Lecture 15
Subtractive Color Describes Reflected Spectrum
[Sto
ne 2
003]
CIE RGB Color Matching Experiment
Same setup as additive color matching before, but primaries are monochromatic light (single wavelength) of the following wavelengths defined by CIE standard
The test light is also a monochromatic light
Kayvon Fatahalian
Ren Ng, Spring 2016CS184/284A, Lecture 15
CIE RGB Color Matching Functions
r(�)
g(�)
b(�)
Graph plots how much of each CIE RGB primary light must be combined to match a monochromatic light
Ren Ng, Spring 2016CS184/284A, Lecture 15
Color Reproduction with Matching Functions
r(�)
g(�)
b(�)
For any spectrum s, the perceived color is matched by the following formulas for scaling the CIE RGB primaries
Color Representation
Ren Ng, Spring 2016CS184/284A, Lecture 15
A Universal Color Space: CIE XYZ
Imaginary set of standard color primaries X, Y, Z
Designed such that
• X, Y, Z span all observable colors
• Matching functions are strictly positive
• Y is luminance (brightness absent color)
Imaginary because can only be realized with primaries that are negative at some wavelengths
CIE XYZ color matching functions
Ren Ng, Spring 2016CS184/284A, Lecture 10
Luminance (Lightness)
Integral of radiance scaled by the visual luminous efficiency
Luminous efficiency is a measure of how bright a light at a given wavelength is perceived by a human
https://upload.wikimedia.org/wikipedia/commons/a/a0/Luminosity.png
Dark adapted eye (scotopic)
Daytime adapted eye (photopic)
Y (p,!) =
Z 1
0L(p,!,�)V (�) d�
� (nm)
�v =
Z 1
0�e(�)V (�) d�
Y =
Z�(�)V (�) d�
Ren Ng, Spring 2016CS184/284A, Lecture 15
Separating Luminance, Chromaticity
Luminance: Y Chromaticity: x, y, z, defined as
• since x + y + z = 1, we only need to record two of the three
• usually choose x and y, leading to (x, y, Y) coords
Ren Ng, Spring 2016CS184/284A, Lecture 15
CIE Chromaticity DiagramPure (saturated) spectral colors
around the edge of the plot
Less pure (desaturated) colors
in the interior of the plot
White at the centroid of
the plot (1/3, 1/3)
Ren Ng, Spring 2016CS184/284A, Lecture 15
Gamut
Gamut is the set of chromaticities generated by a set of primaries Because definition of xy is linear, interpolation between chromaticities on a chromaticity plot is also linear So the gamut is the convex hull of the primary chromaticities
Ren Ng, Spring 2016CS184/284A, Lecture 15
Gamut
sRGB is a commoncolor space used throughout theinternet
CIE RGB are the monochromaticprimaries used for color matching tests described earlier
Perceptually Organized Color Spaces
Ren Ng, Spring 2016CS184/284A, Lecture 15
HSV Color Space (Hue-Saturation-Value)
Axes correspond to artistic characteristics of color
Ren Ng, Spring 2016CS184/284A, Lecture 15
Perceptual Non-Uniformity
• In the xy chromaticity diagram at left, MacAdam ellipses show regions of perceptually equivalent color (ellipses enlarged 10x)
• Must non-linearly warp the diagram to achieve uniform perceptual distances
Wikipedia
Ren Ng, Spring 2016CS184/284A, Lecture 15
CIELAB Space (AKA L*a*b*)
A commonly used color space that strives for perceptual uniformity
• L* is lightness
• a* and b* are color-opponent pairs
• a* is red-green, and b* is blue-yellow
• A gamma transform is used for warping because perceived brightness is proportional to scene intensityγ, where γ ≈ 1⁄3
Ren Ng, Spring 2016CS184/284A, Lecture 15
Opponent Color Theory
There’s a good neurological basis for the color space dimensions in CIE LAB
• the brain seems to encode color early on using three axes:
• white — black, red — green, yellow — blue
• the white — black axis is lightness; the others determine hue and saturation
• one piece of evidence: you can have a light green, a dark green, a yellow-green, or a blue-green, but you can’t have a reddish green (just doesn’t make sense)
• thus red is the opponent to green
• another piece of evidence: afterimages (following slides)
slide credit: Steve Marschner
Image Afterimage
Ren Ng, Spring 2016CS184/284A, Lecture 15
Things to Remember
Physics of Light
• Spectral power distribution (SPD)
• Superposition (linearity) Tristimulus theory of color
• Spectral response of human cone cells (S, M, L)
• Metamers - different SPDs with the same perceived color
• Color matching experiment, per-wavelength matching functions
• Color reproduction by integrating color matching functions against input spectrum
Color spaces
• CIE RGB, XYZ, xy chromaticity, LAB, HSV
• Gamut
Art Competition #2 Results
Spring 2016UC Berkeley CS184/284A
Art Competition #2 – Honorable Mention
Allen Zeng
Spring 2016UC Berkeley CS184/284A
Art Competition #2 – Honorable Mention
Annalise Hurst
Spring 2016UC Berkeley CS184/284A
Art Competition #2 – Honorable Mention
Allen Zhao
Spring 2016UC Berkeley CS184/284A
Art Competition #2 – Honorable Mention
Owen Jow
Spring 2016UC Berkeley CS184/284A
Art Competition #2 – Winner
Earth with bump mapping, atmosphere shading and more.Joseph Chen
Ren Ng, Spring 2016CS184/284A, Lecture 15
Acknowledgments
Many thanks and credit for slides to Steve Marschner, Kayvon Fatahalian, Brian Wandell, Marc Levoy, Katherine Breeden and James O’Brien.