Radiometry: Measuring

Radiant power or radiant flux or just flux: Φ = dQ/dt energy per time unit, in joules per sec (= watt (W)) EECS 487: Interactive Spectral Energy Density/ energy Spectral Power Distribution Computer Graphics (or just Energy): • radiant power per unit spectrum interval freq • amount of light present at each wavelength Lecture 22: • W/nm • Light and Intensity (I) is radiant flux per unit solid angle (W/sr) • Color Spaces • solid angle: a 3D angle, in steradians (sr) 4π sr covers the whole area of a unit sphere

RTR3

Photometry Purpose of Computer Graphics? Photometry: quantifying the sensitivity of the average human eye in perceiving the energy of various wavelengths Communication Three levels of realism: (not , which can be affected by many other factors) Human perception 1. Physical realism: • human perception is a non-linear function • fidelity to visual stimulation of scene • deals only with the , wavelength: 380 to 780 nm is the context • highly computationally expensive • CG techniques leverage Radiometry Photometry measures abilities 2. Photo realism: • fidelity to visual response to scene radiant energy (in joules) luminous energy (in talbots) energy Fidelity is a tool, not • takes observer’s visual system into radiant flux (watt) lumen (lm) power (energy/time) account radiant intensity (I, W/sr) candela (cd, lm/sr) power/solid angle (necessarily) the goal • 3. Functional realism: radiant flux density lux (lumens/m2) power/area no apology is required for (watt/m2) (foot-candle, fc) “approximations” • fidelity to visual information of scene • task-oriented info presentation radiance luminance (candela/m2, nit) power/(area*solid angle) • especially for interactive graphics • but not for scientific visualization • takes advantage of observer’s irradiance illuminance integrated radiance and engineering drawing! visual attention to task

Akeley07 Ferweda03 Forsyth Two Types of Light-Sensitive Cell Light Absorbance Short (420) Rods: • highly sensitive, 1000× more The rods and each of the three types of sensitive than cones cone absorb light differently • spread over the retina, but predominate in peripheral vision Given a monochromatic spectrum (λ), • effective in low light, night-vision we denote the response (light Medium (534) • vision: brightness absorbance) of the three cones perception only, no color to λ as s(λ), m(λ), and l(λ)

Cones: • three types, each sensitive to a The response curves S = s(λ), different frequency distribution M = m(λ), and L = l(λ) were

• concentrated in the fovea experimentally determined in the 1980s Long (564) (center of the retina) ⎡ L ⎤ ⎡ 0.3816 0.5785 0.0399 ⎤ ⎡ R ⎤ • less sensitive ⎢ M ⎥ = ⎢ 0.1969 0.7246 0.0785 ⎥ ⎢ G ⎥ • effective in bright light ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ S ⎥ ⎢ 0.0248 0.1248 0.8504 ⎥ ⎢ B ⎥ • give ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ Zhang08

Cones and Rod Sensitivity Tristimulus Response Functions The eye’s response to a unit amount of light with wavelength λ1, r(λ1), is the linear combination s(λ1) + m(λ1) + l(λ1) r(λ2) = s(λ2) + m(λ2) + l(λ2) r(λ1+λ2) = (s(λ1)+s(λ2)) + (m(λ1)+m(λ2)) + (l(λ1)+l(λ2)) .20 G R Let an arbitrary spectrum be the sum of its .18 constituent “monochromatic spectra,” .16 each with radiance Li (λi ) ⇒ ∑i Li (λi ) .14 Assuming linearity, the response of a .12 cone (e.g., s) to an arbitrary spectrum l( ) Rods and cones can is given by a convolution integral: .10 λ2 be thought of as filters r(L, s) =∫ s(λ)L(λ) dλ .08

• rods detect average And the eye’s response to an arbitrary each type of cone by .06 Fraction of light absorbed Fraction m(λ1) intensity across spectrum light is a linear combination of the .04 l( ) m(λ ) responses of the three cones: B λ1 2 .02 s(λ ) s(λ ) r(L) = ∫ (s(λ)+m(λ)+l(λ))L(λ) dλ 1 2 0 ! = ∫ r(λ) L(λ) dλ 400 440 480 520 560600 640 680

Wavelength (nm) Wavelengthλ1 (nm) λ2 Luminous Efficiency of the Eye Luminous Efficiency of the Eye

The eye’s total response to a multitude of illumination our eyes are very sensitive, and we are able to 1 photopicdetect: conditions brighter small di⇥erences in luminance, however our acuity for pattern details and our ability to distinguish colors are wavelengths, all having the same intensity: both poor. This2 is why it is dicult to read a newspaper at 0 cones than 3.4twilight cd/m or to correctly (twilight or brighter, choose a pair of colored socks while dressing at dawn. Conversely, in daylight we have sharp !1 cones effective) color vision, but absolute sensitivity is low and luminance di⇥erences must be great if we are to detect them. This is why it is impossible to see the stars against the sunlit sky. a.k.a. the ACIE Modelphotopic of Visual Adaptation for Realistic Image Synthesis!2 Further, adaptation does not happen instantaneously. scotopic: moonless night or darker, Nearly everyone has experienced the temporary blindness spectral luminous that occurs when you enter2 a dark theatre for a matinee. It !3 James A. Ferwerda Sumanta N. Pattanaikbelow 0.034can Peter sometimes cd/m takeShirley a few, rods effective minutes before you Donald can see well P. Greenberglog Relative Efficiency enough to find an empty seat. Similarly, once you have dark efficiency curve, adapted in the theatre and then go out into the daylight af- !4 (response curve centered around ter the show, the brightness is at first dazzling and you need rods to squint or shield your eyes, but within about a minute, you Program of Computer Graphics,canCornell see normally again. University !5 centered around 555 nm 507 nm) 400 450 500 550 600 650 700 To produce realistic synthetic images that capture the ap- Wavelength (nm) pearance of actual scenes, we need to take adaptation-related • ⇥ spectral sensitivity changes to bluish changes in vision into account. In this paper we develop a Figure 2: Scotopic V and photopic V luminous eciency computational model of visual adaptation and apply it to the functions. After Wyszecki (1982). monochromeproblem of rendering scenes illuminated at vastly di⇥erent levels. The model-6 predicts the -4 visibility of-2 object features 0 2 4 68 Luminance (Y or V): Abstract Luminanceand colors at particular illumination levels, and simulates (logthe cd/m changes2) in visibility and appearance that occur over the the range of 0.01 to 108 cd/m2. At light levels from 0.01 to • time-course of light and dark adaptation. 10 cd/m2 both the rod and cone systems are active. This is the overall magnitude of visual responseIn this paper to a spectrum we develop a computational model of vi- starlight moonlight indooris lighting known as the sunlightmesopic range. Relatively little is known 2 Physiological foundations of adaptation about vision in the mesopic range but this is increasingly a (independent of color, ≈ “brightness/intensity”) sual adaptation for realistic image synthesis based on psy- Range of topic of interest because computer-based oce environments IlluminationThrough adaptation thescotopic visual system functions mesopic over a lumi- with CRT photopic displays and subdued lighting exercise the visual • from radiance to luminance: Ychophysical= 683 lm/W experiments.yL(λ)dλ The model captures the changes nance range of nearly 14 log units, despite the fact that the system’s mesopic range. ∫ Visualindividual neuralno units color that vision make up the system have a re- Thegood rod andcolor cone vision systems are sensitive to light with wave- in threshold visibility, color appearance, visual acuity, and sponse range of only about 1.5 log units (Spillman 1990). lengths from about 400nm to 700nm. The rods have their • 1 Watt of radiant energy at λ = 555 nm equals to 683 lumens functionThrough four distinctpoor acuity adaptation mechanisms, the visual peakgood sensitivity acuity at approximately 505nm. Spectral sensitiv- sensitivity over time that are caused by the visual system’s system moderates the e⇥ects of changing levels of illumi- ity of the composite cone system peaks at approximately 555 nation on visual response to provide sensitivity over a wide nm. The rod and cone systems are not equally sensitive to adaptation mechanisms. We use the model to display the range of ambient light levels. light at all wavelengths. Luminous eciency functions show results of global illumination simulations illuminated at in- Figure 1: The range of luminances inhow the e⇥ective natural light of a particular environ- wavelength is as a visual 2.1 The pupil stimulus. Di⇥erences between the rod and cone systems lead tensities ranging from daylight down to starlight. The re- ment and associated visual parameters.to separate After photopic Hood and scotopic (1986). luminous eciency func- The most obvious mechanism available to regulate the tions that apply to typical daytime and nighttime illumi- sulting images better capture the visual characteristics of amount of light stimulating the visual system is the pupil. nation levels. Figure 2 shows the normalized scotopic and Over a 10 log unit range of luminance, the pupil changes in photopic luminous eciency functions developed by the CIE scenes viewed over a wide range of illumination levels. Be- diameter from approximately 7 mm down to about 2 mm (Wyszecki 1982). (Pugh 1988). This range of variation produces a little more cause the model is based on psychophysical data it can be Verythan a log little unit change work in retinal has illuminance been so pupillary done ac- in computer graphics on tion alone is not sucient to completely account for visual used to predict the visibility and appearance of scene fea- adaptation.adaptation (Spillman Earlier 1990). In work fact, rather has than focused playing primarily on overcom- a significant role in adaptation it is thought that variation 2.3 Bleaching and regeneration of photopigments tures. This allows the model to be used as the basis of ingin the pupil size limits serves to of mitigate conventional the visual consequences CRT of displays and determin- aberrations in the eye’s optical system. At high levels where At high light intensities, the action of light depletes the pho- perceptually-based error metrics for limiting the precisionWhat the of ingthere how is plenty to of best light to see display by, the pupil stopssimulated down to limit environments within the light tosensitive pigmentsreflectance in the rods and cones at a faster rate the e⇥ects of the aberrations. At low levels where catching than chemical processes can restore them. This makes the global illumination computations. limitedenough light dynamic to allow detection range is more available. essential than opti- Tumblinreceptors less and sensitive Rushmeier to light. This process is known as CR Categories and Subject Descriptors: I.3.0 (1993)mizing the introduced resolution of the retinal the image, concept the pupil opens of tonepigment reproduction bleaching. Early theories to of the adaptation were based “Light is not a thing that can Eyes See to allow more light into the eye. the idea that light adaptation was produced by pigment Science of color measurement [Computer Graphics]: General; I.3.6 [Computer Graphics]: computer graphics community and developedbleaching and dark a adaptationtone repro- was produced by pigment 2.2 The rod and cone systems restoration (Hecht 1934). However pigment bleaching can- Methodologybe reproduced, but something and Techniques. duction operator that preserves the apparentnot completely account brightness for adaptation forof two reasons: first, There are somewhere between 75 and 150 million rod and 6 a substantial amount of adaptation takes place in both the Color of an object determine Additionalthat has to be represented with Key Words and Phrases: realistic image sceneto 7 million features. cone photoreceptors Ward in each (1994) retina (Riggs has 1971). takenrod and a cone somewhat systems at ambient di levelser- where little bleach- The rods are extremely sensitive to light and provide achro- ing occurs (Granit 1939); and second, the time courses of synthesis,something else, with colors.” vision, visual perception, adaptation. entmatic approach vision at scotopic andlevels has of illumination developed ranging from a tonethe early reproduction phases of dark and light opera- adaptation are too rapid by reflected (i.e., not absorbed) 106 to 10 cd/m2. The cones are less sensitive than the rods, to be explained by photochemical processes alone (Crawford – Paul Cézanne torbut that provide preserves colorstimulus vision at photopic apparent levels of illumination contrast in and1947). visibility. Spencer wavelengths (1995) has developed a psychophysical model of glare and 1 Introduction has implemented a glare filter that increases the apparent • = all wavelengths or frequencies 250 dynamic range of images. • is 450 nm, 540 nm, red The650 goal nm of realistic image synthesis is to produce im- The model of adaptation presented herein deals with ages that capture the visual appearance of modeled scenes. manycone responses more visual parameters than dynamic range. We Color is not intrinsic in wavelength, Physically-based rendering methods make it possible to ac- develop a model that includes the eects of adaptation curately simulate the distribution of light energy in scenes, on threshold visibility, color appearance, visual acuity,and but related to how a collection of but physical accuracy in rendering does not guarantee that changes in visual sensitivity over time. The algorithm we photons with a spectral distribution the displayed images will have a realistic visual appearance. multiply wavelength derive from our model is based on the psychophysics of adap- There are at least two reasons for this. First, the range of tationby wavelength measured in experimental studies. Therefore, it can is interpreted by our eyes light energy in the scene may be vastly dierent from the be used predictively for illumination engineering work, and range that can be produced by the display device. Second, can be used to develop perceptually-based approaches to ren- the visual states of the scene observer and the display ob- dering andintegrate display. server may be very dierent.

To produce realistic images we need to model notDurand06 only the physical behavior of light propagation, but also the pa- 1.1 Background rameters of perceptual response. This is particularly true of the visual system’s adaptation to the range of light we The range of light energy we experience in the course of a encounter in the natural environment since visual function day is vast. The light of the noonday sun can be as much changes dramatically over the range of environmental illu- as 10 million times more intense than moonlight. Figure 1 mination. shows the range of luminances we encounter in the natural environment and summarizes some visual parameters asso- 580 Frank H. T. Rhodes Hall, Ithaca, NY 14853, USA. ciated with this luminance range. Our visual system copes http://www.graphics.cornell.edu. with this huge range of luminances by adapting to the pre- vailing conditions of illumination. Through adaptation the visual system functions over a luminance range of nearly 14 log units. Adaptation is achieved through the coordinated action of Permission to make digital or hard copies of part or all of this work or mechanical, photochemical, and neural processes in the vi- personal or classroom use is granted without fee provided that copies are sual system. The pupil, the rod and cone systems, bleaching not made or distributed for profit or commercial advantage and that copies and regeneration of receptor photopigments, and changes in bear this notice and the full citation on the first page. To copy otherwise, to neural processing all play a role in visual adaptation. republish, to post on servers, or to redistribute to lists, requires prior Although adaptation provides visual function over a wide specific permission and/or a fee. range of ambient intensities, this does not mean that we see © 1996 ACM-0-89791-746-4/96/008...$3.50 equally well at all intensity levels. For example, under dim

249 Color Classical case: 1 type of cone is missing (e.g., red) Cones do not “see” colors Now project onto a lower- space (2D) • they just respond to intensities of different wavelengths Makes it impossible to distinguish some spectra A physical spectrum is a complex function of wavelengths

An arbitrary spectrum is infinitely dimensional • but our eye-response has only three dimensions How can we encode an infinite dimensional spectrum with just three dimensions? • we can’t: information is lost we’re all color blind! differentiated same responses

Durand06 Schulze08

Color Representation Metamers Our ability to respond to only three primary colors is good news for computers Metamers: when cones give the same response to • only need three values to reproduce the full color spectrum visible to humans! different spectra von Helmholtz 1859 • imagine how much more expensive a display would be if each pixel must encode 6 values

instead of 3, how much more storage, Violet Blue Green Red bandwidth, etc.

Trichromatic Theory: • claims that any color can be represented as a weighted sum of three primary colors Perceived color: red = Perceived color: red • proposed red, green, blue as primaries ReceptorResponses • developed in the 18th, 19th century (before the discovery of photoreceptor cells!) 400 500 600 700 Wavelengths (nm) Durand06 Schulze08 Color Matching Color Matching Experiment

Metamers allows for color matching experiment Result: RGB amounts needed to match all • reproduce the color of any reference light with the wavelengths of the visible spectrum: addition of three given primary • how strong must each of the three primaries be for a certain colors The tristimulus values match? (known as tristimulus weight or value) cannot be were determined reproduced 1920 • if no match can be obtained, add by RGB mixes experimentally c. a primary to reference (negative weight) by the CIE (Commission Internationale de l’Eclairage (Illumination))

Durand06

Grassman’s Laws Color Spaces Color vision is linear and 3D, any based on color matching can be described by a “” with 3 basis For color matches, where u, v, w are colors Lots of different color spaces related by matrix transforms! • symmetry: u = v ⇔ v = u • full spectrum • allows any radiation (visible or invisible) to be described • transitivity: u = v and v = w u = w • usually unnecessary and impractical • proportionality: u = v ⇔ tu = tv • RGB • convenient for display (CRT uses red, green, and blue phosphors) • additivity: if any two of the statements: • not very intuitive u = v, w = x, (u+w) = (v+x) are true, so is the third • HSV • • these are natural laws and they mean an intuitive color space • is cyclic so HSV is a non-linear transformation of RGB matching is linear • CIE XYZ • a linear transform of RGB used by color scientists • Why not use the L, M, S cone responses as the basis? • not discovered until the 1980s … Forsyth&Ponce Additive Primaries: RGB Subtractive Primaries: CMY http://www.jgiesen.de/ColorTheory/RGBColorApplet/rgbcolorapplet.html http://www.jgiesen.de/ColorTheory/CMYColorApplet/cmycolorapplet.html

yellow (1,1,0) red (1,0,0) red yellow (1,0,0) green (1,1,0) (0,1,0) (1,0,1)

white (0,0,0) (1,1,1)

magenta green blue (1,0,1) (0,1,1) (0,1,0) (0,0,1 )

blue (0,0,1) cyan (0,1,1)

Riesenfeld 2006 Riesenfeld 2006

CMY(K) Problems with RGB Typical inks: Cyan, Magenta, Yellow, (blacK) Non-intuitive: how much R, G, and B is there in • the pigments remove parts of the spectrum M Magenta “”? (answer: .64, .16, .16) (0,1,0) Blue pigment absorbs reflects (1,1,0) Black cyan red blue and green Red (1,1,1) (0,1,1) Represent only a small range of human magenta green blue and red Cyan (1,0,0) perceptible colors (not perceptually based) yellow blue red and green C White black all none (0,0,0) Yellow Green Perceptually non-linear (0,0,1) (1,0,1) black ink used to ensure high quality printed black • the perceived difference between two colors is not Y blue • (0,0,1 ) cyan consistently proportional to their separation in the complements of RGB (0,1,1) magenta white color space ⎡ C ⎤ ⎡ 1 ⎤ ⎡ R ⎤ (1,0,1) (1,1,1) ⎢ ⎥ = ⎢ ⎥ − ⎢ ⎥ ⎢ M ⎥ ⎢ 1 ⎥ ⎢ G ⎥ ⎣⎢ Y ⎦⎥ ⎣⎢ 1 ⎦⎥ ⎣⎢ B ⎦⎥ White minus Blue minus Green = Red red yellow (1,0,0) (1,1,0) Hodgins Chenney HSV Color Model HSV: Non-linear Distortion V=1, S=0 V What do we perceive? of the RGB Color Cube 120˚ green yellow • Hue (or ): what color is it? S=1 Top of HSV hexcone corresponds cyan 1.0 white • red vs. green vs. blue red • Saturation (or purity or chroma): to the projection of the RGB color 0˚ how non-gray is it? cube along the principal diagonal blue magenta • vivid red vs. grayish • the main diagonal of RGB space 240˚ • Value (or luminance or intensity): V=0 becomes the V axis of the HSV space how bright is it? The RGB cube has subcubes H • perceived intensity reflected by object black 0.0 S • the term “brightness” is used only for emitters Each plane of constant V in Riesenfeld e.g., light-bulbs Green Yellow HSV space corresponds to Blue Cyan a view of a subcube of RGB White HLS: represented as a double space Cyan Red Magenta White cone with black at the bottom Green and white at the top Blue Magenta Red Yellow Rossignac,Hodgins,Gillies,wikipedia Foley, van Dam 90

Artist’s Color Model

Artists discuss color (hue) in terms of:

Traditional, Artistic: Perceptually Based: • Tint: strength of color RGB XYZ (Tristimulus) • the amount of white added to CMY(K) xyY pure pigment to decrease saturation HSV Hunter-Lab HLS CIE-L*u’v’ • Shade: brightness of color CIE-L*a*b* • the amount of black added to CIE-L*CH° decrease (value) Any set of real lights James07 would need negative • Tone: weighting to cover the • the amount of whole visible light added to a pure pigment (given hue) spectrum

Riesenfeld 2006 CIE XYZ Color Space Recall: Color Matching Experiment Standardized by the International Commission on Certain visible colors cannot Illumination (Commission Internationale de l’Éclairage) be reproduced by RGB mixes • defines three “imaginary” primary lights (X, Y, Z) representing an imaginary basis that does not correspond to human perception of color • color c = X X + Y Y + Z Z • all visible colors can be matched with positive X, Y, and Z they are in the positive octant of the XYZ space • provides a standard for sharing color information between disciplines, e.g., All visible colors can be matched computer graphics and fabric design with positive X, Y, and Z

RTR3 Durand06

2D Visualization of CIE Color Space 2D Visualization of CIE Color Space

Given a color c = X X + Y Y + Z Z Then map it to a 2D chromaticity diagram It’s cumbersome to visualize it in 3D by dropping the z coordinate Want a 2D representation: First map it to a triangle in 3D: X Y Z x = ; y = ; z = X +Y + Z X +Y + Z X +Y + Z x + y + z = 1 and x, y, z ≥ 0, i.e., x, y, and z are coefficients of a FvD convex combination and the point is in the (X + Y + Z = 1) plane RTR3 CIE Chromaticity Color Diagram The color gamut of a device is the convex hull defined The horseshoe region ideal green by the convex combinations of its primary colors 520 nm represents all visible 540 nm • a device can only produce chromaticity values 510 nm colors within its color gamut green 560 nm • all perceivable colors • different devices have with the same different color 500 nm 580 nm chromaticity but different • to match gamuts between yellow devices can be difficult luminance map into the 600 nm same point within this region cyan white • points outside a gamut red 700 nm • shaded area: color 490 nm correspond to negative found in nature blue weights of the primaries magenta

FvD ideal blue 400 nm ideal red

Riesenfeld,TP3

Energy

HSV ↔ CIE XYZ ED RGB ↔ CIE XYZ Hue (chromaticity) E • the /frequency, W RGB color model identified by drawing a line from • additive primaries cλ = R R + G G + B B c (white) to spectral color Red f Violet D • is contained within the CIE XYZ color space • c6 cs Frequency Y • c7 is nonspectral, cannot be identified with a dominant wavelength, instead the dominant 520 Spectral Colors c wavelength is the complement of cc c c cs Saturation (chroma) cc blue cyan (0,0,1) • “purity” of the color, distance from c (white) Green Yellow (0,1,1) to spectral color magenta c6 (1,0,1) white • c4 very pure (1,1,1) Red • c6 not so pure c gray c4 Value (brightness/lightness) White 700 black green c7 (0,0,0) • perceived luminance (intensity) c Blue c (Red) (0,1,0) • lightness: reflecting objects c Magenta red yellow Watt 2002 • brightness: emitting objects (1,0,0) (1,1,0) • not represented (not representable) in 2D 400 (Violet) X Riesenfeld 2006 RGB Color Gamut sRGB ↔ CIE XYZ Transforms 520 G RGB sRGB: RGB with standard conversion to CIE XYZ 510 540 Color Gamut ⎡ X ⎤ ⎡ 0.4124 0.3576 0.1805 ⎤ ⎡ R ⎤ 560 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ Y ⎥ = ⎢ 0.2126 0.7151 0.0721 ⎥ ⎢ G ⎥ 500 ⎣⎢ Z ⎦⎥ ⎣⎢ 0.0193 0.1192 0.9505 ⎦⎥ ⎣⎢ B ⎦⎥ 580

600 ⎡ R ⎤ ⎡ 3.2410 −1.5374 −0.4986 ⎤ ⎡ X ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ G ⎥ = ⎢ −0.9692 1.8760 0.0416 ⎥ ⎢ Y ⎥ 490 700 ⎣⎢ B ⎦⎥ ⎣⎢ 0.0556 −0.2040 1.0570 ⎦⎥ ⎣⎢ Z ⎦⎥

RTR3 R • each matrix is the inverse of the other B • Y encodes luminance; to go from color to gray: 400 Riesenfeld Y = 0.213 R + 0.712 G + 0.072 B RGB chromaticity coordinates: • grayscale intensity (Y) is not equal parts RGB because to R = (0.735, 0.265) the eye, the intensity of red and green contribute more G = (0.274, 0.717) B = (0.167, 0.009) than that of blue to overall perceived brightness Chenney

Pyschophysics YIQ Color Model

Humans are Luminous Efficiency Curve For NTSC color TV • not so sensitivity to low Separate luminance from frequencies • we perceive brightness ranges • more sensitive to medium better than color ranges, so give to high frequencies it more bandwidth (samples): Y: 4.5 MHz, I: 1.5 MHz, Q: 0.6 MHz Separate intensity from • backward compatibility: the color of a pixel: B&W TV displays only • reduce the contrast the Y component of low frequencies • two colors on B&W with • but keep the color different luminance show up as different grades of gray Merrell08

Freeman&Durand06 RGB ↔ YIQ xyY Coordinate

The chromaticity diagram brightness ⎡ Y ⎤ ⎡ 0.299 0.587 0.144 ⎤ ⎡ R ⎤ 1.0 Y ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Spectral Colors does not represent a I = 0.596 −0.275 −0.321 G 0.9 color ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 520 Q 0.8 540 complete color palette: ⎣⎢ ⎦⎥ ⎣⎢ 0.212 −0.528 0.311 ⎦⎥ ⎣⎢ B ⎦⎥ 510 • doesn’t account for color 0.7 green 560 ⎡ ⎤ ⎡ ⎤ ⎡ R ⎤ 1 0.9563 0.6210 Y 0.6 changes due to luminance ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 580 • brown, which is orange-red with G = 1 −0.2721 −0.6474 I 0.5 500 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ yellow low luminance, is not represented ⎣⎢ B ⎦⎥ ⎣⎢ 1 −1.1070 1.7046 ⎦⎥ ⎣⎢ Q ⎦⎥ 0.4 cyan 600 • to recover full palette add 0.3 490 white • for modern CRT and HDTV: red 700 blue back luminance: (x,y,Y) Y = 0.2125 R + 0.7154 G + 0.0721 B 0.2 magenta x (1− x − y) 0.1 X = Y, Y = Y, Z = Y comparable to sRGB: 400 X y y Y = 0.213 R + 0.712 G + 0.072 B 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Riesenfeld 2006

Characteristics of Color Spaces Perceptual Non-linearity

Perceptually Perceptually Device MacAdam ellipses: Color Space Intuitive? based? linear? independent? regions in CIE xy color HSV ✔ ✗ ✗ ✗ space that are perceived RGB ✗ ✗ ✗ ✗ as the same color (based CMY ✗ ✗ ✗ ✗ on a 1942 experiment) • in perceptually uniform color CIE XYZ ✗ ✔ ✗ ✔ space, the ellipses should be CIE L*u’v’ ✗ ✔ ✔ ✔ circles CIE L*a*b* ✗ ✔ ✔ ✔ TP3

Schulze,Schubert Perceptually Uniform Color Spaces CIE L*a*b* Two major color spaces standardized by the CIE

• designed so that equal steps in coordinates produce equally Perceptually uniform -a visible differences in color color space: • L*u’v’: non-linear color space that gives perceptual linearity: • L*: luminance MacAdam ellipses now look more like circles • a*: red-green • b*: blue-yellow ⎡ u′ ⎤ 1 ⎡ 4X ⎤ ⎢ ⎥ = ⎢ ⎥ • the ‘*’s are to differentiate it from v X + 15Y + 3Z 9Y ⎣ ′ ⎦ ⎣ ⎦ Hunter-Lab color space . . . • L*a*b*: more complex but more uniform Non-linear conversion • both separate luminance between CIE XYZ and (L*) from chromaticity CIE L*a*b*

James,Chenney,Schubert

Opponent Opponent Color Theory Since the cones respond to overlapping The brain seems to encode color using three axes: wavelengths, the visual system can more efficiently white – black, red – green, yellow – blue record the differences between total cone responses, • the white – black axis determines luminance instead of individual cone’s responses (V or Y), the others determine chromaticity • first proposed in the 19th century, physiological 0th 1st 2nd The , , derivatives of a Gaussian weighting evidence in the 1950s function of the wavelengths are similar to the luminance, blue-yellow, and red-green weighting You can have light green, dark green, functions found in the human visual system yellow-green (), or a blue-green (), but not reddish green red is the opponent to green

James,Schulze,Bratkova et al., Adelson&Bergen James,Schulze,Bratkova et al., Adelson&Bergen