lecture 23: introduction to color scienceintroduction to color science. credit: science media group....
TRANSCRIPT
![Page 1: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/1.jpg)
Computer Graphics and Imaging UC Berkeley CS184/284A
Lecture 23:
Introduction to Color Science
![Page 2: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/2.jpg)
credit: Science Media Group.
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Physical Basis of Color
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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
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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
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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
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Ren NgCS184/284A
Daylight Spectral Power Distributions Vary
Blue sky Solar disk
[Brian Wandell]
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Ren NgCS184/284A
Spectral Power Distribution of Light Sources
Describes distribution of energy by wavelength
Figure credit:
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Ren NgCS184/284A
Superposition (Linearity) of Spectral Power Distributions[Brian W
andell]
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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”
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Biological Basis of Color
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Ren NgCS184/284A
Anatomy of The Human Eye
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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
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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)
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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)
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Measuring Light
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Ren NgCS184/284A
A Simple Model of a Light DetectorCredit: M
arschner
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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
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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)
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Tristimulus Theory of Color
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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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rM (�)<latexit sha1_base64="XCKO9LSygpv9mtDU9sdmbxu1vkg=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EUPQgVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPXGpHd</latexit><latexit sha1_base64="XCKO9LSygpv9mtDU9sdmbxu1vkg=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EUPQgVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPXGpHd</latexit><latexit sha1_base64="XCKO9LSygpv9mtDU9sdmbxu1vkg=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EUPQgVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPXGpHd</latexit>
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>
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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)
rS(�)<latexit sha1_base64="qSOhER+8qJVFYltFzk2K/XXWQeM=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EVvFY0tNKFsNpt26WYTdjdCCQV/hRcPKl79Nd78N27aHrR1YGGYmcd7O0HKmdK2/W2V1tY3NrfK25Wd3b39g+rh0YNKMkmoSxKeyF6AFeVMUFczzWkvlRTHAafdYHxV+N1HKhVLxL2epNSP8VCwiBGsjeTJwV3d4yYe4sagWrOb9gxolTgLUms3nqBAZ1D98sKEZDEVmnCsVN+xU+3nWGpGOJ1WvEzRFJMxHtK+oQLHVPn57OYpOjNKiKJEmic0mqm/J3IcKzWJA5OMsR6pZa8Q//P6mY4u/JyJNNNUkPmiKONIJ6goAIVMUqL5xBBMJDO3IjLCEhNtaqqYEpzlL68S97x52bRvTRk3MEcZTuAU6uBAC9pwDR1wgUAKz/AKb1ZmvVjv1sc8WrIWM8fwB9bnD+BikeM=</latexit><latexit sha1_base64="qSOhER+8qJVFYltFzk2K/XXWQeM=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EVvFY0tNKFsNpt26WYTdjdCCQV/hRcPKl79Nd78N27aHrR1YGGYmcd7O0HKmdK2/W2V1tY3NrfK25Wd3b39g+rh0YNKMkmoSxKeyF6AFeVMUFczzWkvlRTHAafdYHxV+N1HKhVLxL2epNSP8VCwiBGsjeTJwV3d4yYe4sagWrOb9gxolTgLUms3nqBAZ1D98sKEZDEVmnCsVN+xU+3nWGpGOJ1WvEzRFJMxHtK+oQLHVPn57OYpOjNKiKJEmic0mqm/J3IcKzWJA5OMsR6pZa8Q//P6mY4u/JyJNNNUkPmiKONIJ6goAIVMUqL5xBBMJDO3IjLCEhNtaqqYEpzlL68S97x52bRvTRk3MEcZTuAU6uBAC9pwDR1wgUAKz/AKb1ZmvVjv1sc8WrIWM8fwB9bnD+BikeM=</latexit><latexit sha1_base64="qSOhER+8qJVFYltFzk2K/XXWQeM=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EVvFY0tNKFsNpt26WYTdjdCCQV/hRcPKl79Nd78N27aHrR1YGGYmcd7O0HKmdK2/W2V1tY3NrfK25Wd3b39g+rh0YNKMkmoSxKeyF6AFeVMUFczzWkvlRTHAafdYHxV+N1HKhVLxL2epNSP8VCwiBGsjeTJwV3d4yYe4sagWrOb9gxolTgLUms3nqBAZ1D98sKEZDEVmnCsVN+xU+3nWGpGOJ1WvEzRFJMxHtK+oQLHVPn57OYpOjNKiKJEmic0mqm/J3IcKzWJA5OMsR6pZa8Q//P6mY4u/JyJNNNUkPmiKONIJ6goAIVMUqL5xBBMJDO3IjLCEhNtaqqYEpzlL68S97x52bRvTRk3MEcZTuAU6uBAC9pwDR1wgUAKz/AKb1ZmvVjv1sc8WrIWM8fwB9bnD+BikeM=</latexit>
rM (�)<latexit sha1_base64="XCKO9LSygpv9mtDU9sdmbxu1vkg=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EUPQgVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPXGpHd</latexit><latexit sha1_base64="XCKO9LSygpv9mtDU9sdmbxu1vkg=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EUPQgVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPXGpHd</latexit><latexit sha1_base64="XCKO9LSygpv9mtDU9sdmbxu1vkg=">AAAB8nicbVBNS8NAFHypX7V+VT16WSxCeymJl+qt4EUPQgVjC00om82mXbrZhN2NUELBX+HFg4pXf403/42btgdtHVgYZubx3k6Qcqa0bX9bpbX1jc2t8nZlZ3dv/6B6ePSgkkwS6pKEJ7IXYEU5E9TVTHPaSyXFccBpNxhfFX73kUrFEnGvJyn1YzwULGIEayN5cnBb97iJh7gxqNbspj0DWiXOgtTajSco0BlUv7wwIVlMhSYcK9V37FT7OZaaEU6nFS9TNMVkjIe0b6jAMVV+Prt5is6MEqIokeYJjWbq74kcx0pN4sAkY6xHatkrxP+8fqajCz9nIs00FWS+KMo40gkqCkAhk5RoPjEEE8nMrYiMsMREm5oqpgRn+curxD1vXjbtO1PGDcxRhhM4hTo40II2XEMHXCCQwjO8wpuVWS/Wu/Uxj5asxcwx/IH1+QPXGpHd</latexit>
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
<latexit sha1_base64="oSCRIM7qSd8zpcJPrPcfNAMIfI0=">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</latexit><latexit sha1_base64="oSCRIM7qSd8zpcJPrPcfNAMIfI0=">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</latexit><latexit sha1_base64="oSCRIM7qSd8zpcJPrPcfNAMIfI0=">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</latexit>
Written as vector dot products:
Matrix formulation:2
4SML
3
5 =
2
4rSrMrL
3
5
2
64s
3
75
<latexit sha1_base64="1o6PSyqM1n+v5KClQcoTxMfmTGA=">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</latexit><latexit sha1_base64="b/GOKbmahNaIWM+WKJxZTQEbAlI=">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</latexit><latexit sha1_base64="b/GOKbmahNaIWM+WKJxZTQEbAlI=">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</latexit>
![Page 24: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/24.jpg)
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
![Page 25: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/25.jpg)
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
![Page 26: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/26.jpg)
Metamerism
![Page 27: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/27.jpg)
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
![Page 28: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/28.jpg)
Ren NgCS184/284A
MetamerismColor matching is an important illusion that is understood quantitatively
Brian Wandell
![Page 29: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/29.jpg)
Ren NgCS184/284A
Metamerism is a Big EffectBrian W
andell
![Page 30: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/30.jpg)
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
![Page 31: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/31.jpg)
Color Reproduction
![Page 32: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/32.jpg)
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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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>
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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.
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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>
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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
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Ren NgCS184/284A
Example Primaries for CRT Display
•Curves determined by phosphor emission propertieswavelength (nm)
Em
issi
on (w
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![Page 37: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/37.jpg)
Ren NgCS184/284A
Example Primaries: LCD Display
•Curves determined by backlight and color filters
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Ren NgCS184/284A
Color Reproduction as Linear Algebra
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3
5
<latexit sha1_base64="ySbGeev8GB1wVQekFUh7gq+TFEw=">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</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
![Page 39: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/39.jpg)
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>
![Page 40: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/40.jpg)
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=">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</latexit><latexit sha1_base64="gUtbmUZoR17U/Bu8DCv/rO5/fu4=">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</latexit><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>
We want this displayed spectrum to be a metamer for the real-world target spectrum.
![Page 41: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/41.jpg)
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=">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>
Color perceived for display spectra with values R,G,B
![Page 42: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/42.jpg)
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=">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</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>
![Page 43: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/43.jpg)
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=">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</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
<latexit sha1_base64="/6n86shPh1lUXOidu5AVGuU3I4U=">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</latexit><latexit sha1_base64="/6n86shPh1lUXOidu5AVGuU3I4U=">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</latexit><latexit sha1_base64="/6n86shPh1lUXOidu5AVGuU3I4U=">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</latexit>
Solution (form #2):
1x3 Nx3 3xN Nx3 1xN
Nx3
![Page 44: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/44.jpg)
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
<latexit sha1_base64="euMO3WCkUi2fUbEyWRl4mlqSPCg=">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</latexit><latexit sha1_base64="euMO3WCkUi2fUbEyWRl4mlqSPCg=">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</latexit><latexit sha1_base64="euMO3WCkUi2fUbEyWRl4mlqSPCg=">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</latexit>
Solution (form #3):
Nx3
![Page 45: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/45.jpg)
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)
![Page 46: Lecture 23: Introduction to Color ScienceIntroduction to Color Science. credit: Science Media Group. Physical Basis of Color. CS184/284A Ren Ng The Fundamental Components of Light](https://reader033.vdocument.in/reader033/viewer/2022052101/603aeed204ba9033981eef77/html5/thumbnails/46.jpg)
To Be Continued