Computer Graphics and Imaging UC Berkeley CS184/284A

Lecture 23:

Introduction to Color Science

credit: Science Media Group.

Physical Basis of Color

Ren NgCS184/284A

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 NgCS184/284A

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 NgCS184/284A

Spectral Power Distribution (SPD)

Salient property in measuring light

• The amount of light present at each wavelength

• Units:

• radiometric units / nanometer (e.g. watts / nm)

• Can also be unit-less

• Often use “relative units” scaled to maximum wavelength for comparison across wavelengths when absolute units are not important

Ren NgCS184/284A

Daylight Spectral Power Distributions Vary

Blue sky Solar disk

[Brian Wandell]

Ren NgCS184/284A

Spectral Power Distribution of Light Sources

Describes distribution of energy by wavelength

Figure credit:

Ren NgCS184/284A

Superposition (Linearity) of Spectral Power Distributions[Brian W

andell]

Ren NgCS184/284A

What is Color?

• Color is a phenomenon of human perception; it is not a universal property of light

• Colors are the perceptual sensations that arise from seeing light of different spectral power distributions

• Technically speaking, different wavelengths of light are not “colors”

Biological Basis of Color

Ren NgCS184/284A

Anatomy of The Human Eye

Ren NgCS184/284A

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 NgCS184/284A

Spectral Response of Human Cone CellsThree types of cone cells: S, M, and L (corresponding to peak response at short, medium, and long wavelengths)

Nor

mal

ized

resp

onse

Wavelength (nm)

Ren NgCS184/284A

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 percentage of different cone cell types. (false color image)

Measuring Light

Ren NgCS184/284A

A Simple Model of a Light DetectorCredit: M

arschner

Ren NgCS184/284A

Mathematics of Light Detection

Same math carries over to spectral power distributions

• Light 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 NgCS184/284A

If we think of s and r as discrete, sampled representations (vectors) rather than continuous functions, this integral operation is a dot product:We can also write this in matrix form:

Mathematics of Light Detection

X =⇥

s⇤2

64r

3

75

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Ren NgCS184/284A

Dimensionality Reduction From ∞ to 1

At the detector: • SPD is a function of wavelength (∞ - dimensional signal)

• Detector result is a scalar value (1 - dimensional signal)

Tristimulus Theory of Color

Ren NgCS184/284A

Spectral Response of Human Cone Cells

Instead of one detector as before, now we have three detectors (S, M, L cone cells), each with a different spectral response curve

Nor

mal

ized

resp

onse

Wavelength (nm)

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Ren NgCS184/284A

Spectral Response of Human Cone Cells

Instead of one detector as before, now we have three detectors (S, M, L cone cells), each with a different spectral response curve

Nor

mal

ized

resp

onse

Wavelength (nm)

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rL(�)<latexit sha1_base64="DSBcDilXdsDN8Zn3/L3UUooJZvk=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EXBQwVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPVjpHc</latexit><latexit sha1_base64="DSBcDilXdsDN8Zn3/L3UUooJZvk=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EXBQwVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPVjpHc</latexit><latexit sha1_base64="DSBcDilXdsDN8Zn3/L3UUooJZvk=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EXBQwVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPVjpHc</latexit>

S = rS · sM = rM · sL = rL · s

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Written as vector dot products:

Matrix formulation:2

4SML

3

5 =

2

4rSrMrL

3

5

2

64s

3

75

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Ren NgCS184/284A

Dimensionality Reduction From ∞ to 3

At each position on the human retina: • SPD is a function of wavelength (∞ - dimensional signal)

• 3 types of cones near that position produce three scalar values (3 - dimensional signal)

What about 2D images?

• The dimensionality reduction described above is happening at every 2D position in our visual field

Ren NgCS184/284A

The Human Visual System

• Human eye does not measure and brain does not receive information about each wavelength of light

• Rather, the eye measures three response values only (S, M, L) at each position in visual field, and this is only spectral info available to brain

• This is the result of integrating the incoming spectrum against response functions of S, M, L cones

Kayvon Fatahalian

Metamerism

Ren NgCS184/284A

Metamers

Metameters are two different spectra (∞-dim) that project to the same (S,M,L) (3-dim) response.

• These will appear to have the same color to a human The existence of metamers is critical to color reproduction

• Don’t have to reproduce the full spectrum of a real world scene

• Example: A metamer can reproduce the perceived color of a real-world scene on a display with pixels of only three colors

Ren NgCS184/284A

MetamerismColor matching is an important illusion that is understood quantitatively

Brian Wandell

Ren NgCS184/284A

Metamerism is a Big EffectBrian W

andell

Ren NgCS184/284A

Pseudo-Geometric InterpretationWe are projecting a high dimensional vector (wavelength spectrum function) onto a low-dimensional subspace (SML visual response)

• Differences that are perpendicular to the basis vectors of the low-dimensional space are not detectable

Slide credit: Steve Marschner

Color Reproduction

Ren NgCS184/284A

Additive Color

• Given a set of primary lights, each with its own spectral distribution (e.g. R,G,B display pixels):

• We can adjust the brightness of these lights and add them together to produce a linear subspace of spectral distribution:

• The color is now described by the scalar values:

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RsR(�) +GsG(�) +B sB(�)<latexit sha1_base64="LVQIOiqJL9Q+qlLtKnelhba/mrM=">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</latexit><latexit sha1_base64="LVQIOiqJL9Q+qlLtKnelhba/mrM=">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</latexit><latexit sha1_base64="LVQIOiqJL9Q+qlLtKnelhba/mrM=">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</latexit>

R, G, B<latexit sha1_base64="QByaFQdX/vzs2ihQ1+egrnL8uh0=">AAAB8HicbVBNSwMxEJ31s9avqkcvwSJ4KGVXBPVW9KDeqri22C4lm2bb0CS7JFmhLP0XXjyoePXnePPfmLZ70NYHA4/3ZpiZFyacaeO6387C4tLyymphrbi+sbm1XdrZfdBxqgj1Scxj1QyxppxJ6htmOG0mimIRctoIB5djv/FElWaxvDfDhAYC9ySLGMHGSo93lXblyha66JTKbtWdAM0TLydlyFHvlL7a3ZikgkpDONa65bmJCTKsDCOcjortVNMEkwHu0ZalEguqg2xy8QgdWqWLoljZkgZN1N8TGRZaD0VoOwU2fT3rjcX/vFZqorMgYzJJDZVkuihKOTIxGr+PukxRYvjQEkwUs7ci0scKE2NDKtoQvNmX54l/XD2vurcn5dpNnkYB9uEAjsCDU6jBNdTBBwISnuEV3hztvDjvzse0dcHJZ/bgD5zPH5SVjxs=</latexit><latexit sha1_base64="QByaFQdX/vzs2ihQ1+egrnL8uh0=">AAAB8HicbVBNSwMxEJ31s9avqkcvwSJ4KGVXBPVW9KDeqri22C4lm2bb0CS7JFmhLP0XXjyoePXnePPfmLZ70NYHA4/3ZpiZFyacaeO6387C4tLyymphrbi+sbm1XdrZfdBxqgj1Scxj1QyxppxJ6htmOG0mimIRctoIB5djv/FElWaxvDfDhAYC9ySLGMHGSo93lXblyha66JTKbtWdAM0TLydlyFHvlL7a3ZikgkpDONa65bmJCTKsDCOcjortVNMEkwHu0ZalEguqg2xy8QgdWqWLoljZkgZN1N8TGRZaD0VoOwU2fT3rjcX/vFZqorMgYzJJDZVkuihKOTIxGr+PukxRYvjQEkwUs7ci0scKE2NDKtoQvNmX54l/XD2vurcn5dpNnkYB9uEAjsCDU6jBNdTBBwISnuEV3hztvDjvzse0dcHJZ/bgD5zPH5SVjxs=</latexit><latexit sha1_base64="QByaFQdX/vzs2ihQ1+egrnL8uh0=">AAAB8HicbVBNSwMxEJ31s9avqkcvwSJ4KGVXBPVW9KDeqri22C4lm2bb0CS7JFmhLP0XXjyoePXnePPfmLZ70NYHA4/3ZpiZFyacaeO6387C4tLyymphrbi+sbm1XdrZfdBxqgj1Scxj1QyxppxJ6htmOG0mimIRctoIB5djv/FElWaxvDfDhAYC9ySLGMHGSo93lXblyha66JTKbtWdAM0TLydlyFHvlL7a3ZikgkpDONa65bmJCTKsDCOcjortVNMEkwHu0ZalEguqg2xy8QgdWqWLoljZkgZN1N8TGRZaD0VoOwU2fT3rjcX/vFZqorMgYzJJDZVkuihKOTIxGr+PukxRYvjQEkwUs7ci0scKE2NDKtoQvNmX54l/XD2vurcn5dpNnkYB9uEAjsCDU6jBNdTBBwISnuEV3hztvDjvzse0dcHJZ/bgD5zPH5SVjxs=</latexit>

Ren NgCS184/284A

Recall: Real LCD Screen Pixels (Closeup)

iPhone 6S Galaxy S5iphonearena.com iphonearena.com

Notice R, G, B sub-pixel geometry. Effectively three lights at each (x,y) location.

Ren NgCS184/284A

Color Reproduction Problem

Goal: at each pixel, choose R, G, B values for display so that the output color matches the appearance of the target color in the real world.

Display outputs spectrumTarget real spectrum

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s(�)<latexit sha1_base64="d4GaUWH1wM1bJ2ypPOHpJ6cs7BY=">AAAB8XicbVBNSwMxFHzrZ12/qh69BItQL2UrgnoreNFbBdcWtkvJZrNtaDZZkqxQlv4MLx5UvPpvvPlvTNs9aOtAYJiZR96bKONMG8/7dlZW19Y3Nitb7vbO7t5+9eDwUctcEeoTyaXqRlhTzgT1DTOcdjNFcRpx2olGN1O/80SVZlI8mHFGwxQPBEsYwcZKga67PW7TMT7rV2tew5sBLZNmSWpQot2vfvViSfKUCkM41jpoepkJC6wMI5xO3F6uaYbJCA9oYKnAKdVhMVt5gk6tEqNEKvuEQTP190SBU63HaWSTKTZDvehNxf+8IDfJVVgwkeWGCjL/KMk5MhJN70cxU5QYPrYEE8XsrogMscLE2JZcW0Jz8eRl4p83rhve/UWtdVe2UYFjOIE6NOESWnALbfCBgIRneIU3xzgvzrvzMY+uOOXMEfyB8/kDft2QTQ==</latexit><latexit sha1_base64="d4GaUWH1wM1bJ2ypPOHpJ6cs7BY=">AAAB8XicbVBNSwMxFHzrZ12/qh69BItQL2UrgnoreNFbBdcWtkvJZrNtaDZZkqxQlv4MLx5UvPpvvPlvTNs9aOtAYJiZR96bKONMG8/7dlZW19Y3Nitb7vbO7t5+9eDwUctcEeoTyaXqRlhTzgT1DTOcdjNFcRpx2olGN1O/80SVZlI8mHFGwxQPBEsYwcZKga67PW7TMT7rV2tew5sBLZNmSWpQot2vfvViSfKUCkM41jpoepkJC6wMI5xO3F6uaYbJCA9oYKnAKdVhMVt5gk6tEqNEKvuEQTP190SBU63HaWSTKTZDvehNxf+8IDfJVVgwkeWGCjL/KMk5MhJN70cxU5QYPrYEE8XsrogMscLE2JZcW0Jz8eRl4p83rhve/UWtdVe2UYFjOIE6NOESWnALbfCBgIRneIU3xzgvzrvzMY+uOOXMEfyB8/kDft2QTQ==</latexit><latexit sha1_base64="d4GaUWH1wM1bJ2ypPOHpJ6cs7BY=">AAAB8XicbVBNSwMxFHzrZ12/qh69BItQL2UrgnoreNFbBdcWtkvJZrNtaDZZkqxQlv4MLx5UvPpvvPlvTNs9aOtAYJiZR96bKONMG8/7dlZW19Y3Nitb7vbO7t5+9eDwUctcEeoTyaXqRlhTzgT1DTOcdjNFcRpx2olGN1O/80SVZlI8mHFGwxQPBEsYwcZKga67PW7TMT7rV2tew5sBLZNmSWpQot2vfvViSfKUCkM41jpoepkJC6wMI5xO3F6uaYbJCA9oYKnAKdVhMVt5gk6tEqNEKvuEQTP190SBU63HaWSTKTZDvehNxf+8IDfJVVgwkeWGCjL/KMk5MhJN70cxU5QYPrYEE8XsrogMscLE2JZcW0Jz8eRl4p83rhve/UWtdVe2UYFjOIE6NOESWnALbfCBgIRneIU3xzgvzrvzMY+uOOXMEfyB8/kDft2QTQ==</latexit>

Ren NgCS184/284A

Pseudo-Geometric Interpretation of Color ReproductionSlide credit: Steve M

arschner

• The display can only produce a low-dimensional subspace of all possible (linear combinations of display primaries)

• In color reproduction, for a given spectrum s (high dimensional), we want to choose a spectrum s’ in the display’s low-dimensional subspace, such that s’ and s project to the same response in the low-dimensional subspace of the eye’s SML response

Ren NgCS184/284A

Example Primaries for CRT Display

•Curves determined by phosphor emission propertieswavelength (nm)

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sG(�)<latexit sha1_base64="i5cQkLrONvknzTG3YN57pFHNQWE=">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</latexit><latexit sha1_base64="i5cQkLrONvknzTG3YN57pFHNQWE=">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</latexit><latexit sha1_base64="i5cQkLrONvknzTG3YN57pFHNQWE=">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</latexit>

sR(�)<latexit sha1_base64="cjZfdLKfBX6UB6i6cXFTBjOfzEc=">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</latexit><latexit sha1_base64="cjZfdLKfBX6UB6i6cXFTBjOfzEc=">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</latexit><latexit sha1_base64="cjZfdLKfBX6UB6i6cXFTBjOfzEc=">AAACanicbVHLahRBFL3TvuL4SsxKsmmMQiLYdAeCugu4MbsojglMN8Pt6juZIvVoqm5rxqbBr3Crv+VH+A9Wz8wimXig4HDuOVWXU2WtpOc0/TOIbt2+c/fexv3hg4ePHj/Z3Hr6xdvGCRoJq6w7K9GTkoZGLFnRWe0IdanotLx4389Pv5Lz0prPPK+p0Hhu5FQK5CDlfvJpL1fBXuH+ZHM3TdIF4pskW5Hdo/0f0ONksjU4zisrGk2GhULvx1lac9GiYykUdcO88VSjuMBzGgdqUJMv2sXSXfwyKFU8tS4cw/FCvZoI1zicd9cl7f1clyGskWd+fdaL/5uNG56+LVpp6obJiOXb00bFbOO+lLiSjgSreSAonAzrx2KGDgWH6oa5oW/Cao2metXmoU0u0XVt7hpF49cZXRZtmhzW3LUHySFddt1aYmbd9yuJ3lOsrKtgNwzlZ+tV3ySjg+Rdkn4Mn3AMS2zADjyHPcjgDRzBBziBEQio4Sf8gt+Dv9F29CzaWVqjwSqzDdcQvfgH+TG9Cw==</latexit>

Ren NgCS184/284A

Example Primaries: LCD Display

•Curves determined by backlight and color filters

sB(�)<latexit sha1_base64="vm7FcONLLLs9ErbQboQBc38aXIM=">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</latexit><latexit sha1_base64="vm7FcONLLLs9ErbQboQBc38aXIM=">AAACanicbVHLahRBFL3TvuL4SsxKsmmMQiLYdAeCugu6MbsIjglMN8Pt6juZIvVoqm5rxqbBr3Crv+VH+A9Wz8wimXig4HDuOVWXU2WtpOc0/TOIbt2+c/fexv3hg4ePHj/Z3Hr6xdvGCRoJq6w7K9GTkoZGLFnRWe0IdanotLz40M9Pv5Lz0prPPK+p0Hhu5FQK5CDlfvJ+L1fBXuH+ZHM3TdIF4pskW5Hdo/0f0ONksjU4zisrGk2GhULvx1lac9GiYykUdcO88VSjuMBzGgdqUJMv2sXSXfwyKFU8tS4cw/FCvZoI1zicd9cl7f1clyGskWd+fdaL/5uNG56+LVpp6obJiOXb00bFbOO+lLiSjgSreSAonAzrx2KGDgWH6oa5oW/Cao2metXmoU0u0XVt7hpF49cZXRZtmhzW3LUHySFddt1aYmbd9yuJ3lOsrKtgNwzlZ+tV3ySjg+Rdkn4Kn3AMS2zADjyHPcjgDRzBRziBEQio4Sf8gt+Dv9F29CzaWVqjwSqzDdcQvfgH2PG8+w==</latexit><latexit sha1_base64="vm7FcONLLLs9ErbQboQBc38aXIM=">AAACanicbVHLahRBFL3TvuL4SsxKsmmMQiLYdAeCugu6MbsIjglMN8Pt6juZIvVoqm5rxqbBr3Crv+VH+A9Wz8wimXig4HDuOVWXU2WtpOc0/TOIbt2+c/fexv3hg4ePHj/Z3Hr6xdvGCRoJq6w7K9GTkoZGLFnRWe0IdanotLz40M9Pv5Lz0prPPK+p0Hhu5FQK5CDlfvJ+L1fBXuH+ZHM3TdIF4pskW5Hdo/0f0ONksjU4zisrGk2GhULvx1lac9GiYykUdcO88VSjuMBzGgdqUJMv2sXSXfwyKFU8tS4cw/FCvZoI1zicd9cl7f1clyGskWd+fdaL/5uNG56+LVpp6obJiOXb00bFbOO+lLiSjgSreSAonAzrx2KGDgWH6oa5oW/Cao2metXmoU0u0XVt7hpF49cZXRZtmhzW3LUHySFddt1aYmbd9yuJ3lOsrKtgNwzlZ+tV3ySjg+Rdkn4Kn3AMS2zADjyHPcjgDRzBRziBEQio4Sf8gt+Dv9F29CzaWVqjwSqzDdcQvfgH2PG8+w==</latexit>

sG(�)<latexit sha1_base64="i5cQkLrONvknzTG3YN57pFHNQWE=">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</latexit><latexit sha1_base64="i5cQkLrONvknzTG3YN57pFHNQWE=">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</latexit><latexit sha1_base64="i5cQkLrONvknzTG3YN57pFHNQWE=">AAACanicbVHLahRBFL3TvuL4SsxKsmmMQiLYdAeCugu40OwiOCYw3Qy3q+9kitSjqbqtGZsGv8Kt/pYf4T9YPTOLZOKBgsO551RdTpW1kp7T9M8gunX7zt17G/eHDx4+evxkc+vpF28bJ2gkrLLurERPShoasWRFZ7Uj1KWi0/LifT8//UrOS2s+87ymQuO5kVMpkIOU+8mHvVwFe4X7k83dNEkXiG+SbEV2j/Z/QI+TydbgOK+saDQZFgq9H2dpzUWLjqVQ1A3zxlON4gLPaRyoQU2+aBdLd/HLoFTx1LpwDMcL9WoiXONw3l2XtPdzXYawRp759Vkv/m82bnj6tmilqRsmI5ZvTxsVs437UuJKOhKs5oGgcDKsH4sZOhQcqhvmhr4JqzWa6lWbhza5RNe1uWsUjV9ndFm0aXJYc9ceJId02XVriZl1368kek+xsq6C3TCUn61XfZOMDpJ3SfopfMIxLLEBO/Ac9iCDN3AEH+EERiCghp/wC34P/kbb0bNoZ2mNBqvMNlxD9OIf4wW9AA==</latexit>

sR(�)<latexit sha1_base64="cjZfdLKfBX6UB6i6cXFTBjOfzEc=">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</latexit><latexit sha1_base64="cjZfdLKfBX6UB6i6cXFTBjOfzEc=">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</latexit><latexit sha1_base64="cjZfdLKfBX6UB6i6cXFTBjOfzEc=">AAACanicbVHLahRBFL3TvuL4SsxKsmmMQiLYdAeCugu4MbsojglMN8Pt6juZIvVoqm5rxqbBr3Crv+VH+A9Wz8wimXig4HDuOVWXU2WtpOc0/TOIbt2+c/fexv3hg4ePHj/Z3Hr6xdvGCRoJq6w7K9GTkoZGLFnRWe0IdanotLx4389Pv5Lz0prPPK+p0Hhu5FQK5CDlfvJpL1fBXuH+ZHM3TdIF4pskW5Hdo/0f0ONksjU4zisrGk2GhULvx1lac9GiYykUdcO88VSjuMBzGgdqUJMv2sXSXfwyKFU8tS4cw/FCvZoI1zicd9cl7f1clyGskWd+fdaL/5uNG56+LVpp6obJiOXb00bFbOO+lLiSjgSreSAonAzrx2KGDgWH6oa5oW/Cao2metXmoU0u0XVt7hpF49cZXRZtmhzW3LUHySFddt1aYmbd9yuJ3lOsrKtgNwzlZ+tV3ySjg+Rdkn4Mn3AMS2zADjyHPcjgDRzBBziBEQio4Sf8gt+Dv9F29CzaWVqjwSqzDdcQvfgH+TG9Cw==</latexit>

Ren NgCS184/284A

Color Reproduction as Linear Algebra

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3

5

<latexit sha1_base64="ySbGeev8GB1wVQekFUh7gq+TFEw=">AAADPnicnVJLj9MwEHbCawmvLhy5WFQghESUrFgBB8QKkGBvC6LsSnVUOc60NetHZDvQEuXH8TO4cOWEuHLE6WaBppwYydLnb+abGc84LwW3Lkm+BOGZs+fOX9i6GF26fOXqtcH29XdWV4bBiGmhzVFOLQiuYOS4E3BUGqAyF3CYHz9v/YcfwFiu1Vu3LCGTdKb4lDPqPDUZfCU5zLiqc0md4YsmekPIS0KeERIRUMUf/kmEcT8WeyNzbT7l1OA7+Kk/v68+wf+721pr1fuViX+T84E+jW1b7a4buslgmMTJyvAmSDswRJ0dTLaDfVJoVklQjglq7ThNSpfV1DjOBPjKlYWSsmM6g7GHikqwWb1aRINve6bAU238UQ6v2L8VPo2hy2adktYuZe7Fvum57fta8l++ceWmj7Kaq7JyoNhJ7WklsNO4XTQuuAHmxNIDygz37WM2p4Yy579DRBR8ZFpKqop79en4mpqYSsD4fgqLrE7i3dI19U68C4um6Sm6RZ0q2pisC+2Eq+Gn/VFvgtFO/DhOXj8Y7u13W9hCN9EtdBel6CHaQ6/QARohFrwI3gc2cOHn8Fv4PfxxEhoGneYGWrPw5y9XswY/</latexit><latexit sha1_base64="ySbGeev8GB1wVQekFUh7gq+TFEw=">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</latexit><latexit sha1_base64="ySbGeev8GB1wVQekFUh7gq+TFEw=">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</latexit>

What R, G, B values?Input spectrum s

Ren NgCS184/284A

Color Reproduction as Linear Algebra

Spectrum produced by display given values R,G,B:

sdisp(�) = RsR(�) +GsG(�) +B sB(�)

=)

2

64sdisp

3

75 =

2

64sR sG sB

3

75

2

4RGB

3

5

<latexit sha1_base64="18wLgN673vQKKZCyt4CRfdPEkds=">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</latexit><latexit sha1_base64="18wLgN673vQKKZCyt4CRfdPEkds=">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</latexit><latexit sha1_base64="18wLgN673vQKKZCyt4CRfdPEkds=">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</latexit>

Ren NgCS184/284A

Color Reproduction as Linear Algebra

What color do we perceive when we look at the display?2

4SML

3

5

disp

=

2

4rSrMrL

3

5

2

4sdisp

3

5

=

2

4rSrMrL

3

5

2

4sR sG sB

3

5

2

4RGB

3

5

=

2

4rS · sR rS · sG rS · sBrM · sR rM · sG rM · sBrL · sR rL · sG rL · sB

3

5

2

4RGB

3

5

<latexit sha1_base64="gUtbmUZoR17U/Bu8DCv/rO5/fu4=">AAAFvXic1VRdi9NAFE03Rtf4tdVHXwaLRQRLurioD0KpD3WhhbVr3YVOKJPJtB02mYSZibs15Nf5K/wJvuofcPJV2qRS8M0LIYcz99x75iYzTuhRIS3rR+NAv2XcvnN417x3/8HDR0fNx19EEHFMJjjwAn7pIEE8yshEUumRy5AT5DseuXCuPqTrF18JFzRgn+UqJLaPFozOKUZSUbOmDqFDFpTFjo8kpzeJeQ7hCMIhhCYkzF3zM6jAkvuxS0WYmO33JgBVKVABlwH/5iAO2oDP4vNEvdeUqllPGe1PGW6mpH03jZk7Xag9S5WclRPb3vMWZUa9HAT/y+5SXQk3cdFGzOJxkoJ2CgcZzHE/w6WbPdX2WhpDOICwX/1jikmCv4wynx/EbiCVpfF6oiUzqDH90nE+14p0VJOOdkuHNemwJh3WpP80gtlRy+pYWYA66BagpRVxNms2TqEb4MgnTGIPCTHtWqG0Y8QlxR5RjSNBQoSv0IJMFWTIJ8KOs3sgAc8V44J5wNXDJMjYTYUqw9Eq2aZ8IVa+o8TpGRHVtZTctTaN5PytHVMWRpIwnPeeRx6QAUjvGeBSTrD0VgogzKmyD/AScYSluo1MyMg1DnwfMfdlXP5pSQx55JHpqy65sWOrcxLKJD7unJCbJKkoitNSKtIcu0gthImpht+tjroOJseddx3r0+tW77T4CofaU+2Z9kLram+0nvZRO9MmGta/6z/1X/pvo2fMDc9geepBo9A80bbCuP4DLP/WxA==</latexit><latexit sha1_base64="gUtbmUZoR17U/Bu8DCv/rO5/fu4=">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</latexit><latexit sha1_base64="gUtbmUZoR17U/Bu8DCv/rO5/fu4=">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</latexit>

We want this displayed spectrum to be a metamer for the real-world target spectrum.

Ren NgCS184/284A

Color Reproduction as Linear Algebra

2

4SML

3

5

real

=

2

4rSrMrL

3

5

2

64s

3

75

<latexit sha1_base64="vpwXq4grUl/G2ryr3gQ4FdsVkSE=">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</latexit><latexit sha1_base64="Cgo6Dv3RPA01cjs8LCaOp+n5NJs=">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</latexit><latexit sha1_base64="Cgo6Dv3RPA01cjs8LCaOp+n5NJs=">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</latexit>

Color perceived for real scene spectra, s

How do we reproduce the color of s? Set these lines equal and solve for R,G,B as a function of s!

2

4SML

3

5

disp

=

2

4rSrMrL

3

5

2

64sR sG sB

3

75

2

4RGB

3

5

<latexit sha1_base64="c9XrMfzwWCr0TFZym5LUbsxONJ0=">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</latexit><latexit sha1_base64="Wtc3NRdxUn3t01iGA0VslKbl3WM=">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</latexit><latexit sha1_base64="Wtc3NRdxUn3t01iGA0VslKbl3WM=">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</latexit>

Color perceived for display spectra with values R,G,B

Ren NgCS184/284A

Color Reproduction as Linear Algebra

2

4SML

3

5

real

=

2

4rSrMrL

3

5

2

64s

3

75

<latexit sha1_base64="vpwXq4grUl/G2ryr3gQ4FdsVkSE=">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</latexit><latexit sha1_base64="Cgo6Dv3RPA01cjs8LCaOp+n5NJs=">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</latexit><latexit sha1_base64="Cgo6Dv3RPA01cjs8LCaOp+n5NJs=">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</latexit>

2

4SML

3

5

disp

=

2

4rSrMrL

3

5

2

64sR sG sB

3

75

2

4RGB

3

5

<latexit sha1_base64="c9XrMfzwWCr0TFZym5LUbsxONJ0=">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</latexit><latexit sha1_base64="Wtc3NRdxUn3t01iGA0VslKbl3WM=">AAAD3HichZJdb9MwFIbdhI8SvtYhcQMXFhMTQlqVgqaNC6RpXIxJmzQ2yibVUXAct7WWOJHtQIuVS64Qt9zyG/g53PJLcD5ademkHinqo9fn9Tk9PkEaMalc92/Lsm/cvHW7fce5e+/+g4drnfVPMskEoX2SRIm4CLCkEeO0r5iK6EUqKI6DiJ4Hl++K8/MvVEiW8I9qmlIvxiPOhoxgZSS/09IooCPGdRBjJdgkd84QOkboCCEHUR7OdR8ZGItYh0ymufPWgbDphCbQOBHfAizgJhS+PsvN71wyVy6nHK9OOVpMKeou9uVc24X5y6ryz3GR6zLS16d5AZsFHpRY8X7Js25W3LaypVOEDhDab47U8dc23K5bBlyGXg0be1tPP1u/H/85Mc91iMKEZDHlikRYykHPTZWnsVCMRNRUziRNMbnEIzowyHFMpafLNcnhc6OEcJgI83EFS3XRYa4ReJpflWIpp3FgzMXzy+ZZIV53NsjUcNfTjKeZopxUtYdZBFUCizWEIROUqGhqABPBTPuQjLHARJlldRCnX0kSx5iHL/VszrlGIovoYKtHJ552u9upyvXr7jad5HnDUe/KzFHkeHVqbSyH32uOehn6r7pvuu4H8wiHoIo2eAKegRegB3bAHngPTkAfkNY/q211rHXbt7/bP+yfVarVqj2PwJWwf/0Hssw5Dw==</latexit><latexit sha1_base64="Wtc3NRdxUn3t01iGA0VslKbl3WM=">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</latexit>

Solution:

=)

2

4RGB

3

5 =

0

B@

2

4rSrMrL

3

5

2

64sR sG sB

3

75

1

CA

�1 2

4rSrMrL

3

5

2

64s

3

75

<latexit sha1_base64="dlU4UJyiFCkxP8TewoVADb5Yn24=">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</latexit><latexit sha1_base64="dlU4UJyiFCkxP8TewoVADb5Yn24=">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</latexit><latexit sha1_base64="dlU4UJyiFCkxP8TewoVADb5Yn24=">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</latexit>

Ren NgCS184/284A

Color Reproduction as Linear Algebra

2

4RGB

3

5 =

0

B@

2

4rSrMrL

3

5

2

64sR sG sB

3

75

1

CA

�1 2

4rSrMrL

3

5

2

64s

3

75

<latexit sha1_base64="Wl0252l/Dqwpjl1qZoH92XkycxE=">AAAEeniczVNdb9MwFHWzAiN8rfCEeLGomFbQqgSYgAekaTyMSSCNQdmkOlSOe9tac5zIdqAlirRfwyv8HX4MEk6ajn5M2itXinJyfM+9J9d2mAiujef9rjlr9StXr61fd2/cvHX7zkbj7mcdp4pBh8UiVich1SC4hI7hRsBJooBGoYDj8PRNsX78FZTmsfxkJgkEER1KPuCMGkv1Gs59EsKQyyyMqFF8nLtHhOwTskeIS0D2//GvXSJgYLZcjJcl2AYZxep7SBXexKqXfczt+5yytVZT3l+e8m4+pei7YOhCF/ZfzVR/Dudx1Ub3sqO8AJsF3C/hFO+VeObmkmqrlhQfjkzrS7bt5//tnGb2bSld7HL1uaLrbTS9tlcGXgV+BZq7rTNUxGGvUTsg/ZilEUjDBNW663uJCTKqDGcCbOdUQ0LZKR1C10JJI9BBVh7iHD+yTB8PYmUfaXDJzitsGUUn+SIVaT2JQiu2pkd6ea0gL1rrpmbwMsi4TFIDkk17D1KBTYyLS4L7XAEzYmIBZYpb+5iNqKLM2KvkEgnfWBxFVPYfZ7Px5RlRqYDutg/jIPPaO4nJs2ftHRjn+ZKi2qiZosgJqtRKWA7fXx71Kug8bb9qex/sJhygaayjB+gh2kI+eoF20Vt0iDqIOWfOD+en82vtT71Zb9WfTFOdWqW5hxai/vwvm61qpQ==</latexit><latexit sha1_base64="Wl0252l/Dqwpjl1qZoH92XkycxE=">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</latexit><latexit sha1_base64="Wl0252l/Dqwpjl1qZoH92XkycxE=">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</latexit>

Solution (form #1):

1xNNx33xNNx31x3

1x33x3

RGB = (MSML MRGB)�1MSML s

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Solution (form #2):

1x3 Nx3 3xN Nx3 1xN

Nx3

Ren NgCS184/284A

Color Reproduction as Linear Algebra

2

4RGB

3

5 =

2

4rS · sR rS · sG rS · sBrM · sR rM · sG rM · sBrL · sR rL · sG rL · sB

3

5�1 2

4rSrMrL

3

5

2

4s

3

5

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Solution (form #3):

Nx3

Ren NgCS184/284A

Color Reproduction Issue: No Negative Light

R,G,B values must be positive

• Display primaries can’t emit negative light

• But solution formulas can certainly produce negative R,G,B values

What do negative R,G,B values mean?

• Display can’t physically reproduce the desired color

• Desired color is outside the display’s color gamut (more on this later)

To Be Continued