2D Computer Graphics Diego Nehab Summer 2020 IMPA 1
Color and compositing
The prism experiment 2
Infrared light: thermometers (Herschel, 1800) Ultraviolet light: silver chloride (Ritter, 1801) More than visible light Visible light: prism experiment (Newton, 1666) 3
Ultraviolet light: silver chloride (Ritter, 1801) More than visible light Visible light: prism experiment (Newton, 1666) Infrared light: thermometers (Herschel, 1800) 3
More than visible light Visible light: prism experiment (Newton, 1666) Infrared light: thermometers (Herschel, 1800) Ultraviolet light: silver chloride (Ritter, 1801) 3
Full electromagnetic spectrum 4
Wave vs. particle c ), and amplitude ( A ) • Wavelength ( ), frequency ( • Energy ( E h , where h is Planck’s constant) and fmux ( ) Pure spectral light (monochromatic colors) Spectrometer Radiometry Measurement of radiant energy in terms of absolute power 5
Pure spectral light (monochromatic colors) Spectrometer Radiometry Measurement of radiant energy in terms of absolute power Wave vs. particle • Wavelength ( λ ), frequency ( ν = c λ ), and amplitude ( A ) • Energy ( E = h ν , where h is Planck’s constant) and fmux ( Φ ) 5
Spectrometer Radiometry Measurement of radiant energy in terms of absolute power Wave vs. particle • Wavelength ( λ ), frequency ( ν = c λ ), and amplitude ( A ) • Energy ( E = h ν , where h is Planck’s constant) and fmux ( Φ ) Pure spectral light (monochromatic colors) 5
Radiometry Measurement of radiant energy in terms of absolute power Wave vs. particle • Wavelength ( λ ), frequency ( ν = c λ ), and amplitude ( A ) • Energy ( E = h ν , where h is Planck’s constant) and fmux ( Φ ) Pure spectral light (monochromatic colors) Spectrometer 5
Colors are spectral distributions 6
As a discrete set of values c i c R R A 1 2 n 0 0 i i Light emitter has a spectrum, material properties modulate the refmected spectrum (Fluorescence is something else) Spectral representation As a continuous function of c ( λ ) c : R > 0 → R ≥ 0 , λ �→ A λ 7
Light emitter has a spectrum, material properties modulate the refmected spectrum (Fluorescence is something else) Spectral representation As a continuous function of c ( λ ) c : R > 0 → R ≥ 0 , λ �→ A λ As a discrete set of values c ( λ i ) c : { λ 1 , λ 2 , . . . , λ n } ⊂ R > 0 → R ≥ 0 λ i �→ A λ i 7
Spectral representation As a continuous function of c ( λ ) c : R > 0 → R ≥ 0 , λ �→ A λ As a discrete set of values c ( λ i ) c : { λ 1 , λ 2 , . . . , λ n } ⊂ R > 0 → R ≥ 0 λ i �→ A λ i Light emitter has a spectrum, material properties modulate the refmected spectrum (Fluorescence is something else) 7
Black-body radiation B ( ν, T ) = 2 h ν 3 h ν � − 1 , kBT − 1 e where k B is Boltsmann’s constant � c 2 5500K 8E+11 Spectral energy density / kJ/m 3 nm 6E+11 5000K 4E+11 4500K 2E+11 4000K 3500K 0 0 500 1000 1500 2000 Wavelength / nm 8
Visible light 390 nm 700 nm approximately Photometry Measurement light in terms of perceived brightness to human eye 9
Photometry Measurement light in terms of perceived brightness to human eye Visible light λ ∈ [ 390 nm , 700 nm ] approximately 9
Photometry Measurement light in terms of perceived brightness to human eye Visible light λ ∈ [ 390 nm , 700 nm ] approximately Prism Aperture Viewfinder Film or sensor 9 Lenses Mirror
Cones: Three types of retinal cells with distinct spectral responses Highly concentrated on fovea Response curves S (short ), M (medium ), L (long ) • Peaks at 420 nm , 534 nm , and 564 nm • Overlap each other • Not R, G, and B What about the color-blind? Are there tetrachromats among us? Photopic vision Well-lit conditions 10
Highly concentrated on fovea Response curves S (short ), M (medium ), L (long ) • Peaks at 420 nm , 534 nm , and 564 nm • Overlap each other • Not R, G, and B What about the color-blind? Are there tetrachromats among us? Photopic vision Well-lit conditions Cones: Three types of retinal cells with distinct spectral responses 10
Response curves S (short ), M (medium ), L (long ) • Peaks at 420 nm , 534 nm , and 564 nm • Overlap each other • Not R, G, and B What about the color-blind? Are there tetrachromats among us? Photopic vision Well-lit conditions Cones: Three types of retinal cells with distinct spectral responses Highly concentrated on fovea 10
What about the color-blind? Are there tetrachromats among us? Photopic vision Well-lit conditions Cones: Three types of retinal cells with distinct spectral responses Highly concentrated on fovea Response curves S (short λ ), M (medium λ ), L (long λ ) • Peaks at λ = 420 nm , λ = 534 nm , and λ = 564 nm • Overlap each other • Not R, G, and B 10
Are there tetrachromats among us? Photopic vision Well-lit conditions Cones: Three types of retinal cells with distinct spectral responses Highly concentrated on fovea Response curves S (short λ ), M (medium λ ), L (long λ ) • Peaks at λ = 420 nm , λ = 534 nm , and λ = 564 nm • Overlap each other • Not R, G, and B What about the color-blind? 10
Photopic vision Well-lit conditions Cones: Three types of retinal cells with distinct spectral responses Highly concentrated on fovea Response curves S (short λ ), M (medium λ ), L (long λ ) • Peaks at λ = 420 nm , λ = 534 nm , and λ = 564 nm • Overlap each other • Not R, G, and B What about the color-blind? Are there tetrachromats among us? 10
Rods: One type of retinal cell Mostly peripheral 20 more numerous, 1000 more sensitive than cones Response curve • R: peak at 498 nm (between S and M) Things look “gray-bluish” at night Scotopic vision Low-light conditions 11
Mostly peripheral 20 more numerous, 1000 more sensitive than cones Response curve • R: peak at 498 nm (between S and M) Things look “gray-bluish” at night Scotopic vision Low-light conditions Rods: One type of retinal cell 11
20 more numerous, 1000 more sensitive than cones Response curve • R: peak at 498 nm (between S and M) Things look “gray-bluish” at night Scotopic vision Low-light conditions Rods: One type of retinal cell Mostly peripheral 11
Response curve • R: peak at 498 nm (between S and M) Things look “gray-bluish” at night Scotopic vision Low-light conditions Rods: One type of retinal cell Mostly peripheral 20 × more numerous, 1000 × more sensitive than cones 11
Things look “gray-bluish” at night Scotopic vision Low-light conditions Rods: One type of retinal cell Mostly peripheral 20 × more numerous, 1000 × more sensitive than cones Response curve • R: peak at λ = 498 nm (between S and M) 11
Scotopic vision Low-light conditions Rods: One type of retinal cell Mostly peripheral 20 × more numerous, 1000 × more sensitive than cones Response curve • R: peak at λ = 498 nm (between S and M) Things look “gray-bluish” at night 11
Human photoreceptor distribution Receptor density (mm − 2 × 10 3 ) 160 140 120 Optic disk 100 Rods Rods 80 60 40 20 Cones Cones 0 80 60 40 20 0 20 40 60 80 Temporal Eccentricity (degrees) Nasal 12
Different for photopic and scotopic vision 10 10 (brightness adaptation) Immense dynamic range 1 Convert radiant intensity (W/sr) to luminous intensity (cd) v c c V d Luminous efficiency function Spectral sensitivity V ( λ ) of human perception of brightness 13
10 10 (brightness adaptation) Immense dynamic range 1 Convert radiant intensity (W/sr) to luminous intensity (cd) v c c V d Luminous efficiency function Spectral sensitivity V ( λ ) of human perception of brightness Different for photopic and scotopic vision 13
Convert radiant intensity (W/sr) to luminous intensity (cd) v c c V d Luminous efficiency function Spectral sensitivity V ( λ ) of human perception of brightness Different for photopic and scotopic vision Immense dynamic range 1 : 10 10 (brightness adaptation) 13
Luminous efficiency function Spectral sensitivity V ( λ ) of human perception of brightness Different for photopic and scotopic vision Immense dynamic range 1 : 10 10 (brightness adaptation) Convert radiant intensity (W/sr) to luminous intensity (cd) � v ( c ) = c ( λ ) V ( λ ) d λ λ 13
Photopic luminous efficiency function 14
Power law 1 116 Y 3 L 0 16 100 Y 0 Weber law of just noticeable difference Y L 100 Lightness Nonlinear perceptual response to brightness 15
Weber law of just noticeable difference Y L 100 Lightness Nonlinear perceptual response to brightness Power law � Y � 1 L ∗ ≈ 116 3 − 0 . 16 100 Y 0 15
Lightness Nonlinear perceptual response to brightness Power law � Y � 1 L ∗ ≈ 116 3 − 0 . 16 100 Y 0 Weber law of just noticeable difference Y ∆ L ∗ ≈ 100 15
Today, due to remarkable coincidence, it is used for encoding effjciency Gamma correction Created to compensate for input-output characteristic of CRT displays Y = V 2 . 5 = V γ 16
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