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Understanding Color 2010

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Understanding Color 2010

  1. 1. SC076 Understanding Color Giordano Beretta HP Labs Palo Alto Alexandria, someday 2010 http://www.inventoland.net/imaging/uc/slides.pdf Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 1 / 207
  2. 2. Broad outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 2 / 207
  3. 3. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 3 / 207
  4. 4. Course objectives Develop a systematic understanding of the principles of color perception and encoding Understand the differences between the various methods for color imaging and communication Gain a more realistic expectation from color reproduction Develop an intuition for trade-offs in color reproduction systems interpreting the result of a color measurement Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 4 / 207
  5. 5. What is color? Color is an illusion Colorimetry: the art to predict an illusion from a physical measurement Experience is much more important than knowing facts or theories The physiology of color vision is understood only to a very small degree Physiology: physical stimulus → physiological response Psychophysics: physical stimulus → behavioral response What is essential is invisible to the eye Antoine de Saint-Exupéry (The Little Prince) Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 5 / 207
  6. 6. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 6 / 207
  7. 7. Section Outline 2 Color theories Chronology Color vision is not based on a bitmap Color vision physiology Limited knowledge Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 7 / 207
  8. 8. Color theories over the Millennia Particle theory ca. 945–715 B.C.E.: sun god Horakthy emits light as a flux of colored lilies Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 8 / 207
  9. 9. Color theories 92,000 B.C.E. — Qafzeh Cave, color symbolism 800 B.C.E. — Indian Upanishads there are relations among colors 400 B.C.E. — Hellenic philosophers Democritus: sensations are elicited by atoms Plato: light or fire rays emanate from the eyes Epicurus: replicas of objects enter the eyes 100–170 C.E. — Alexandria’s natural philosophers Claudius Ptolemæus describes additive color based on wheel in section 96 of the second book of Optics First Millennium — Arab school, pure science Abu Ali al-Hasan ibn al-Haytham a.k.a. Alhazen: invents scientific process (observation–hypothesis–experiment) disproves Plato’s emanation theory image is formed within the eye like in a camera obscura describes additive color based on top Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 9 / 207
  10. 10. Opponent colors 15th century — Renaissance, technology Leonardo da Vinci color perception color order system black & white are colors 3 pairs of opponent colors (black–white, red–green, yellow–blue) simultaneous contrast used color filters to determine color mixtures Note: rendered with chiaro-scuro technique Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 10 / 207
  11. 11. Color theories (cont.) 18th century — Enlightenment, physics & chemistry Isaac Newton: spectral dispersion, white can be dispersed in a spectrum by a prism colors of objects relate to their spectral reflectance light is not colored and color perception is elicited in the human visual system 19th century — scientific discovery Thomas Young: trichromatic theory Hermann von Helmholtz: spectral sensitivity curves Ewald Hering: opponent color theory (can explain hues, saturation, and why there is no reddish green or yellowish blue) black and dark gray are not produced by the absence of light but by a lighter surround Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 11 / 207
  12. 12. Color theories (cont.) 20th century — advanced scientific instruments Johannes A. von Kries: chromatic adaptation why is white balance necessary? Georg Elias Müller & Erwin Schrödinger: zone theory physiological evidence for inhibitory mechanisms becomes available in the 1950s molecular biology functional MRI techniques see http://webvision.med.utah.edu/ for the latest progress Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 12 / 207
  13. 13. Section Outline 2 Color theories Chronology Color vision is not based on a bitmap Color vision physiology Limited knowledge Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 13 / 207
  14. 14. Color vision is not based on a bitmap Vision is based on contrast Vision is not hierarchical. The simple model distal event proximal stimulus brain event is very questionable. It is believed that feedback loops exist between all 26 known areas of visual processing In fact, it has been proved that a necessary condition of some activity in even the primary visual cortex is input from “higher” areas Like the other sensory systems, vision is narcissistic Many sensory signals are non-correlational — a given signal does not always indicate the same property or event in the world The “inner eye’s” function is not to understand what the sensory states indicate Example see Science 17 March 2006: Vol. 311. no. 5767, pp. 1606 – 1609 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 14 / 207
  15. 15. Cognitive model for color appearance stimulus detectors early mechanisms pictorial register color edges contour motion depth … context parameters chroma etc. hue Color lexicon lightness chroma internal etc. color space amber hue lightness action color name apparent color representation Reliable color discrimination: 1 week Color-opponent channels: 3 months Color constancy: 4 months Internal color space Color names Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 15 / 207
  16. 16. Memory colors Vision is not hierarchical Delk & Fillenbaum experiment (1965) We tend to see colors of familiar objects as we expect them to be Surround 10º Sky Complexion 2º Adapting field Vegetation Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 16 / 207
  17. 17. Section Outline 2 Color theories Chronology Color vision is not based on a bitmap Color vision physiology Limited knowledge Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 17 / 207
  18. 18. Color vision physiology The retina has a layer of photoreceptors, which grow like hair (10µm per day). They are of two kinds: rods and cones The cones are of three kinds, depending on the pigments they contain. One pigment absorbs reddish light, one absorbs greenish light, and one absorbs bluish light This leads to the method of trichromatic color reproduction, in which we try to stimulate independently the three kinds of cones s ell m ers nc lls ells liu ib lio ls the ef ng cel ell s l ce e c nes epi erv lg a ine rc nta con & co ent tic n ina acr ola orizo d & ds igm op ret am bip h ro ro p stimulus Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 18 / 207
  19. 19. Photoreceptors Credit: Carlos Rozas (CanalWeb, Chile) http://webvision.med.utah.edu/movies/3Drod.mov Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 19 / 207
  20. 20. Photoreceptors Outer segment Credit: Helga Kolb http://webvision.med.utah.edu/movies/discs.mov http://webvision.med.utah.edu/movies/phago4.mov Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 20 / 207
  21. 21. The aging retina Comparative diagrams of 3- and 80-year-old retinal pigment epithelial (RPE) cells in the eye. As the eye ages, the RPE cells deteriorate, making it harder for the brain to receive and register light, leading to blindness. Credit: David Williams, University of Rochester. Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 21 / 207
  22. 22. Evolution From the difference in the amino-acid sequences for the various photoreceptor genes it is clear that the human visual system did not evolve according to a single design Finding Rod and S Mechanisms L and M Mechanisms Anatomy Distribution perifoveal foveal Bipolar circuitry one class (only on) two classes (on and off) Psychophysics Spatial resolution low high Temporal resolution low high Weber fraction high low Wavelength sensitivity short medium Electrophysiology Response function saturates does not saturate Latencies long short ERG-off-effect negative positive Ganglion cell response afterpotential no afterpotential Receptive field large small Vulnerability high low Genetics autosomal sex-linked Source: Eberhart Zrenner, 1983 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 22 / 207
  23. 23. Catching photons Retinal pigments: rhodopsin, cyanolabe, chlorolabe, erythrolabe lysine attaches chromophore to a protein backbone electronic excitation (two-photon catch) initiates a large shift in electron density in less than 10−15 seconds shift activates rotation around two double-bonded carbon atoms in the backbone entire photocycle lasts less than a picosecond (10−12 sec.) photoisomerization induces shift in positive charge perpendicular to membrane sheets containing the protein this generates a photoelectric signal with a less than 5psec. rise time forward reaction is completed in ∼ 50µsec.(10−6 sec.) Quantum efficiency: measure of the probability that the reaction will take place after the absorption of a photon of light 4 pigments sensitized to photons at 4 energy levels (wavelength): L, M, S, and rods Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 23 / 207
  24. 24. Phototransduction Credit: Helga Kolb, http://webvision.med.utah.edu/movies/trasduc.mov Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 24 / 207
  25. 25. Catch probabilities Quantum energy of a photon: hν For each pigment, there is a probability distribution for a reaction, depending on the photon’s wavelength ¯ w(λ)dλ What counts is not the energy of a single photon, but the average ¯ For a spectral power distribution Pλ : S = Pλ w(λ)dλ absorbance S-cone 1.0 M-cone 0.8 L-cone 0.6 Rod 0.4 0.2 nm 0.0 400 450 500 550 600 650 Dartnall, H. J. A., Bowmaker, J. K., & Mollon, J. D. (1983). Human visual pigments: microspectrophotometric results from the eyes of seven persons. Proceedings of the Royal Society of London, B 220, 115–130 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 25 / 207
  26. 26. Retinal mechanisms Surround Center Surround Retinal Amacrine Bipolar Horizontal Receptor ganglion cell cell cell cell Receptors in retina are not like pixels in a CCD sensor Receptive field: area of visual field that activates a retinal ganglion (H.K. Hartline, 1938) Center-surround fields allow for adaptive coding (transmit contrast instead of absolute values) Horizontal cells presumed to inhibit either its bipolar cell or the receptors: opponent response in red–green and yellow–blue potentials (G. Svaetichin, 1956) Balance of red–green channel might be determined by yellow Retinal ganglion can be tonic or phasic: pathway may also be organized by information density or bandwidth Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 26 / 207
  27. 27. Parvocellular and magnocellular pathways P– M– Originating retinal gan- Tonic Phasic glion cells Temporal resolution Slow (sustained responses, low conduction Fast (mostly transient responses, some sus- velocity) tained, high conduction velocity) Modulation dominance Chromatic Luminance Adaptation occurs at high frequencies Adaptation occurs at all frequencies Color Receives mostly opponent type input from Receives mostly combined (broadband) input cones sensitive to short and long wavelengths from M and L cones, both from the center and from the surround of receptive fields Contrast sensitivity Low (threshold > 10%) High (threshold < 2%) LGN cell saturation Linear up to about 64% contrast At 10% Spatial resolution High (small cells) Low (large cells) Spatio-temporal resolu- When fixation is strictly foveal, extraction of Responds to flicker tion high spatial frequency information (test grat- ings), reflecting small color receptive fields Long integration time Short integration time Relation to channels Could be a site for both a lightness channel Might be a site for achromatic channels be- as for opponent-color channels. The role de- cause the spectral sensitivity is similar to Vλ , pends on the spatio-temporal content of the it is more sensitive to flicker, and has only a target used in the experiment weak opponent color component Possible main role in the Sustain the perception of color, texture, shape, Sustain the detection of movement, depth, visual system and fine stereopsis and flicker; reading of text Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 27 / 207
  28. 28. Color constancy Optic tract Lateral Primary Blob geniculate visual Optic cortex body radiations Axons of retinal ganglion cells in optical nerve terminate at LGN and synapse with neurons radiating to striate cortex LGN might generate masking effects; combination with saccadic motion of eye Blobs in area 17 consist mainly of double opponent cells May be site for color constancy Requires input from V4 (Zeki) Why is white balancing necessary in color reproduction? Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 28 / 207
  29. 29. Section Outline 2 Color theories Chronology Color vision is not based on a bitmap Color vision physiology Limited knowledge Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 29 / 207
  30. 30. Limited knowledge Reaction time at rhodopsin level: femtoseconds Reaction time at perceptual level: seconds From photon catches to constant color names We do not know exactly what happens in-between Example simultaneous contrast chromatic induction Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 30 / 207
  31. 31. 1 color appears as 2 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 31 / 207
  32. 32. Appearance mode Three flat objects or picture of a white cube illuminated from the top and right? Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 32 / 207
  33. 33. Our goal We would like to be able to predict the color of a sample by making a measurement Humans can distinguish about 7 to 10 million different colors — just name them and build an instrument that identifies them Task: find good correlates to the subjective color terms Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 33 / 207
  34. 34. Basis for colorimetry Too many unknowns in physiology and cognitive processes Cannot yet build accurate color vision model Unlike auditory system, visual system is not spectral but integrative Advantage of integrative system: metamerism Basis of colorimetry: 1 Instead of a physiological model, build a psychophysical model Physiology: physical stimulus physiological response Psychophysics: physical stimulus behavioral response 2 Assume additivity 3 Keep the viewing conditions constant Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 34 / 207
  35. 35. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 35 / 207
  36. 36. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 36 / 207
  37. 37. The CIE The International Commission on Illumination — also known as the CIE from its French title, the Commission Internationale de l’Éclairage — is devoted to worldwide cooperation and the exchange of information on all matters relating to the science and art of light and lighting, colour and vision, and image technology With strong technical, scientific and cultural foundations, the CIE is an independent, non-profit organisation that serves member countries on a voluntary basis Since its inception in 1913, the CIE has become a professional organization and has been accepted as representing the best authority on the subject and as such is recognized by ISO as an international standardization body Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 37 / 207
  38. 38. CIE definition 845-02-18: (perceived) color Definition (Color) Attribute of a visual perception consisting of any combination of chromatic and achromatic content. This attribute can be described by chromatic color names such as yellow, orange, brown, red, pink, green, blue, purple, etc., or by achromatic color names such as white, gray, black, etc., and qualified by bright, dim, light, dark etc., or by combinations of such names Perceived color depends on the spectral distribution of the color stimulus, on the size, shape, structure and surround of the stimulus area, on the state of adaptation of the observer’s visual system, and on the observer’s experience of the prevailing and similar situations of observation Perceived color may appear in several modes of appearance. The names for various modes of appearance are intended to distinguish among qualitative and geometric differences of color perceptions Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 38 / 207
  39. 39. Colorimetry Definition (Colorimetry) Colorimetry is the branch of color science concerned with specifying numerically the color of a physically defined visual stimulus in such a manner that: 1 when viewed by an observer with normal color vision, under the same observing conditions, stimuli with the same specification look alike, 2 stimuli that look alike have the same specification, and 3 the numbers comprising the specification are functions of the physical parameters defining the spectral radiant power distribution of the stimulus Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 39 / 207
  40. 40. Grassmann’s laws of additive color mixture Definition (Trichromatic generalization) Over a wide range of conditions of observation, many color stimuli can be matched in color completely by additive mixtures of three fixed primary stimuli whose radiant powers have been suitably adjusted (proportionality) In addition, the color stimuli combine linearly, symmetrically, and transitively Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 40 / 207
  41. 41. Color term categories Definition (Subjective color term) A word used to describe a color attribute perceived by a human. Example: the colorfulness of a flower Definition (Objective color term) A word used to describe a physical quantity related to color that can be measured. Example: the energy radiated by a source Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 41 / 207
  42. 42. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 42 / 207
  43. 43. Subjective color terms — Hue Definition (Hue) The attribute of a color perception denoted by blue, green, yellow, red, purple, and so on Definition (Unique hue) A hue that cannot be further described by use of the hue names other than its own. There are four unique hues, each of which shows no perceptual similarity to any of the others: red, green, yellow, and blue Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 43 / 207
  44. 44. Brightness Definition (Brightness) The attribute of a visual sensation according to which a given visual stimulus appears to be more or less intense, or according to which the visual stimulus appears to emit more or less light Objective term: luminance (L) Brightness scales Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 44 / 207
  45. 45. Lightness Definition (Lightness) The attribute of a visual sensation according to which the area in which the visual stimulus is presented appears to emit more or less light in proportion to that emitted by a similarly illuminated area perceived as a “white” stimulus Objective terms: luminance factor (β), CIE lightness (L∗ ) Fact Brightness is absolute, lightness is relative to an area perceived as white Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 45 / 207
  46. 46. Colorfulness Definition (Chromaticness or Colorfulness) The attribute of a visual sensation according to which an area appears to exhibit more or less of its hue. In short: the extent to which a hue is apparent Objective term: CIECAM02 M Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 46 / 207
  47. 47. Colorfulness — Chroma Definition (Chroma) The attribute of a visual sensation which permits a judgement to be made of the degree to which a chromatic stimulus differs from an achromatic stimulus of the same brightness In other words, chroma is an attribute orthogonal to brightness: absolute colorfulness; we perceive a color correctly independently of the illumination level ∗ ∗ Objective term: CIE chroma (Cuv , Cab ) Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 47 / 207
  48. 48. Colorfulness — Saturation Definition (Saturation) The attribute of a visual sensation which permits a judgement to be made of the degree to which a chromatic stimulus differs from an achromatic stimulus regardless of their brightness In other words, it is the colorfulness of an area judged in proportion to its brightness: relative colorfulness; we can judge the uniformity of an object’s color in the presence of shadows and independently of the incident light’s angle Objective term: purity (p), CIE saturation (Suv ) Fact Colorfulness is absolute, chroma is relative to a white area and absolute w.r.t. brightness, saturation is in proportion to brightness Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 48 / 207
  49. 49. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 49 / 207
  50. 50. Spectral curves Quantities we can measure Definition (spectral power curve) The spectral power curve gives at each wavelength the power (in watts), i.e., the rate at which energy is received from the light source Definition (spectral reflectance curve) The spectral reflectance curve gives at each wavelength the percentage of incident light that is reflected 0.40 reflectance 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 400 450 500 550 600 650 700 nm Human complexion Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 50 / 207
  51. 51. Spectral color reproduction Definition (spectral color reproduction) By spectral color reproduction we intend the physically correct reproduction of color, i.e., the duplication of the original object’s spectrum The general reproduction methods (micro-dispersion and Lippmann) are too impractical for normal use For some special applications like painting restoration or illuminant reconstruction, the spectrum may be sampled at a small number of intervals and combined with principal component analysis Fortunately, spectral color reproduction is required only in rare cases, such as paint swatches in catalogs, and in this cases it is often possible to use identical dyes Our aim is to achieve a close effect for a normal viewer under average viewing conditions Mathematically: build a simple model of color vision Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 51 / 207
  52. 52. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 52 / 207
  53. 53. Completing a wardrobe Some observations: If you want to buy a skirt or a pair of slacks to match a jacket, you cannot match the color by memory — you have to take the jacket with you Just matching in the store light is insufficient, you have to match also under the incandescent light in the dressing room and outdoors You always get the opinion of your companion or the store clerk Three fundamental components of measuring color: light sources samples illuminated by them observers Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 53 / 207
  54. 54. Color matching Colors are assessed by matching them with reference colors on a small-field bipartite screen Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 54 / 207
  55. 55. Color-matching functions I Given a monochromatic stimulus Qλ of wavelength λ, it can be written as Qλ = Rλ R + Gλ G + Bλ B where Rλ , Gλ , and Bλ are the spectral tristimulus values of Qλ Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 55 / 207
  56. 56. Color-matching functions II Assume an equal-energy stimulus E whose mono-chromatic constituents are Eλ (equal-energy means Eλ ≡ 1) The equation for a color match involving a mono-chromatic constituent Eλ of E is r ¯ ¯ Eλ = ¯(λ)R + g (λ)G + b(λ)B r ¯ ¯ where ¯(λ), g (λ), and b(λ), are the spectral tristimulus values of Eλ Definition (color-matching functions) r ¯ ¯ The sets of such values ¯(λ), g (λ), and b(λ) are called color-matching functions (CMF) Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 56 / 207
  57. 57. Color-matching functions III 3.0 Stiles-Burch (1955;1959) 2.5 2.0 b(λ) 1.5 g(λ) 1.0 r(λ) 0.5 0.0 nm -0.5 400 500 600 700 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 57 / 207
  58. 58. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 58 / 207
  59. 59. Metameric stimuli Consider two color stimuli Q1 = R1 R + G1 G + B1 B Q2 = R2 R + G2 G + B2 B Definition (metameric stimuli) If Q1 and Q2 have different spectral radiant power distributions, but R1 = R2 and G1 = G2 and B1 = B2 , the two stimuli are called metameric stimuli Fact Color reproduction works because of metamerism Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 59 / 207
  60. 60. Metameric stimuli Metamerism kit 0.6 0.5 reflectance D C 0.4 B A 0.3 0.2 0.1 nm 0.0 400 500 600 700 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 60 / 207
  61. 61. Metameric stimuli Kinds of metamerism Illuminant metamerism example: daylight and a D65 simulation fluorescent lamp Object metamerism example: metameric inks (see metamerism kit) Sensor metamerism example: scanner and human visual system Observer metamerism example: you and your neighbor Complex metamerism example: two inks metameric under two illuminants Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 61 / 207
  62. 62. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 62 / 207
  63. 63. Chromaticity diagrams We can normalize the color-matching functions and thus obtain new quantities r r ¯ ¯ r (λ) = ¯(λ)/[¯(λ) + g (λ) + b(λ)] ¯ r ¯ ¯ g(λ) = g (λ)/[¯(λ) + g (λ) + b(λ)] ¯ ¯ b(λ) = b(λ)/[¯(λ) + g (λ) + b(λ)] r ¯ with r (λ) + g(λ) + b(λ) = 1 Definition (spectrum locus) The locus of chromaticity points for monochromatic colors so determined is called the spectrum locus in the (r , g)-chromaticity diagram Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 63 / 207
  64. 64. (r , g)-chromaticity diagram 2.0 g(m) 1.5 1.0 2° pilot group Stiles-Burch (1955) 0.5 r(m) 0.0 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 -0.5 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 64 / 207
  65. 65. Imaginary color stimuli The fact that the color-matching functions and the chromaticity coordinates can be negative presents a problem when the tristimulus values are computed from a spectral radiant power distribution Because the color-matching space is linear, a linear transformation can be applied to the primary stimuli to obtain new imaginary stimuli that lie outside the chromaticity region bounded by the spectrum locus This ensures that the chromaticity coordinates are never negative Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 65 / 207
  66. 66. (x, y )-chromaticity diagram spectrum locus 2.0 A: ~2856˚K 1.5 Planckian locus D65: ~6504˚K ∞ 1.0 0.5 z2(λ) y2(λ) x2(λ) nm 0.0 400 500 600 700 800 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 66 / 207
  67. 67. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 67 / 207
  68. 68. CIE 1931 standard colorimetric observer We want to build an instrument delivering results valid for the group of normal trichromats (95% of population); since R=k Pλ¯(λ)dλ r G=k ¯ Pλ g (λ)dλ B=k ¯ Pλ b(λ)dλ an ideal observer can be defined by specifying values for the color-matching functions Definition (CIE 1931 standard colorimetric observer) The Commission Internationale de l’Éclairage (CIE) has recommended ¯ ¯ ¯ such tables containing x (λ), y (λ), z (λ) for λ ∈ [360nm, 830nm] in 1nm steps Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 68 / 207
  69. 69. CIE 1931 Observer (cont.) In addition to the color-matching properties, the CIE 1931 Standard Observer is such that it has also the heterochromatic brightness-matching properties. The latter is achieved by ¯ choosing y (λ) to coincide with the photopic luminous efficiency function X and Z are on the alychne, which in the chromaticity diagram is a straight line on which are located the chromaticity points of all stimuli having zero luminance The data is based averaging the results 1 on color matching in a 2◦ field of 17 observers and 2 the relative luminances of the colors of the spectrum, averaged for about 100 observers Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 69 / 207
  70. 70. Section Outline 3 Terminology Basics Subjective color terms Objective color terms Color matching Metamerism Chromaticity diagrams CIE 1931 standard colorimetric observer Tristimulus normalization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 70 / 207
  71. 71. Tristimulus normalization X , Y , and Z are defined up to a common normalization factor. This factor is different for objects and for emissive sources The perfect reflecting diffuser is an ideal isotropic diffuser with a reflectance equal to unity The perfect reflecting diffuser is completely matt and is entirely free from any gloss or sheen. The reflectance is equal to unity at all wavelengths When the tristimulus values are measured with an instrument, YL represents a photometric measure, such as luminance. For object surfaces it is customary to scale X , Y , Z , so that Y = 100 for the perfect diffuser In practice a working standard such as a BaSO4 plate or a ceramic tile is used in lieu of the perfect diffuser For emissive sources there is no illuminant and therefore the perfect diffuser is not relevant. So it is customary to use the photometric measures Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 71 / 207
  72. 72. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 72 / 207
  73. 73. Objective color terms Quantities we can measure Definition (Dominant wavelength) Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions with a specified achromatic stimulus, matches the color stimulus considered [In disuse, replaced by chromaticity] y 520 530 0.8 540 510 550 560 0.6 570 500 580 590 0.4 Planckian locus A: ~2856˚K 600 610 620 490 630 D65: ~6504˚K 700 0.2 ∞ 480 470 0 460 x 45 0 0.2 0.4 0.6 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 73 / 207
  74. 74. Luminance Definition (Luminance) The luminous intensity in a given direction per unit projected area Lv = Km Le,λ V (λ)dλ λ where Km is the maximum photopic luminous efficacy (683lm · W−1 ), Le,λ the radiance, and V (λ) the photopic efficiency Definition (Luminance factor) The ratio of the luminance of a color to that of a perfectly reflecting or transmitting diffuser identically illuminated Symbol: β Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 74 / 207
  75. 75. Section Outline 4 Objective color terms Y and chromaticity Uniformity Color spaces sliced and diced Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 75 / 207
  76. 76. Y Definition (Y stimulus) In the XYZ system the luminance depends entirely on the Y stimulus. The Y values of any two colors are proportional to their luminances. Therefore, Y gives the percentage reflection or transmission directly, where a perfectly reflecting diffuser or transmitting color has a value of Y = 100 Y =V where V is the luminance of the stimulus computed in accordance with the luminous efficiency function V (λ) Called luminosity in some literature Application: conversion of a color image to black and white Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 76 / 207
  77. 77. Excitation purity Definition (Excitation purity) A measure of the proportions of the amounts of the monochromatic stimulus and of the specified achromatic stimulus that, when additively mixed, match the color stimulus considered x − xw y − yw pc = or pc = xb − xw yb − yw where w denotes the achromatic stimulus and b the boundary color stimulus In disuse, replaced by chromaticity y 520 530 0.8 540 510 550 560 0.6 570 500 580 590 0.4 Planckian locus A: ~2856˚K 600 610 620 490 630 D65: ~6504˚K 700 0.2 ∞ 480 470 0 460 x 45 0 0.2 0.4 0.6 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 77 / 207
  78. 78. Chromaticity Definition (Chromaticity) Proportions of the amounts of three color-matching stimuli needed to match a color Relationship between chromaticity coordinates r (λ), g(λ), b(λ) and x(λ), y (λ), z(λ) of a given spectral stimulus of wavelength λ are expressed by the projective transformation 0.49000r (λ) + 0.31000g(λ) + 0.20000b(λ) x(λ) = 0.66697r (λ) + 1.32240g(λ) + 1.20063b(λ) 0.17697r (λ) + 0.81240g(λ) + 0.01063b(λ) y (λ) = 0.66697r (λ) + 1.32240g(λ) + 1.20063b(λ) 0.00000r (λ) + 0.01000g(λ) + 0.99000b(λ) z(λ) = 0.66697r (λ) + 1.32240g(λ) + 1.20063b(λ) Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 78 / 207
  79. 79. Section Outline 4 Objective color terms Y and chromaticity Uniformity Color spaces sliced and diced Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 79 / 207
  80. 80. Uniformity The X , Y , Z tristimulus coordinates allow us to decide if two colors match in a given y context. If there is no match, it 0.8 520 530 does not tell us how large the 510 540 Stiles Line Element 550 Ellipses plotted 3 x perceptual mismatch is. 560 0.6 Consequently, the CIE 1931 500 570 580 chromaticity diagram is not a 590 0.4 perceptually uniform 600 610 620 chromaticity space from which 490 630 700 the perception of chromaticity 0.2 480 can be derived. 470 0 460 x 45 0 0.2 0.4 0.6 x = X /(X + Y + Z ) y = Y /(X + Y + Z ) 1=x +y +z Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 80 / 207
  81. 81. Uniform chromaticity diagram The CIE 1976 UCS (Uniform Chromaticity Scale) chromaticity diagram is perceptually uniform u = 4X /(X + 15Y + 3Z ) = 4x/(−2x + 12y + 3) v = 9Y /(X + 15Y + 3Z ) = 9y /(−2x + 12y + 3) 0.6 v' y 0.8 0.7 0.5 0.6 0.5 0.4 0.3 0.4 0.2 0.1 x 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 v 0.3 0.4 0.3 0.2 0.2 0.1 u 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 u' Original MacAdam data, 10× 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 81 / 207
  82. 82. CIELAB 1976 CIE L a b color space CIE 1976 lightness L A non-linear function to provide a measure that correlates with lightness more uniformly Similar lightness distribution to Munsell Value scale 3 L = 116 · Y /Yn − 16 Tangential near origin — when Y /Yn < 0.001: Y Y Lm = 903.3 for 0.008856 Yn Yn Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 82 / 207
  83. 83. CIELAB (cont.) 1976 CIE L a b color space Two color opponent channels a , b 3 3 a = 500 · X /Xn − Y /Yn 3 3 b = 200 · Y /Yn − Z /Zn Tangential near origin — when X /Xn , Y /Yn , Z /Zn < 0.001 Xn , Yn , Zn : reference white D50 : (96.422, 100.000, 82.521) D65 : (95.047, 100.000, 108.883) von Kries type adaptation Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 83 / 207
  84. 84. Color difference formulæ The CIE has defined two uniform color spaces, 1976 CIE L u v and 1976 CIE L a b in which the difference of two color stimuli can be measured u and v (but not a and b ) are coordinates on a uniform chromaticity diagram. The third dimension is the psychometric lightness 2 2 Cab = a +b hab = arctan(b /a ) 2 2 2 ∆L ∆Cab ∆Hab ∆E94 = + + kL · SL kC · SC kH · S H SL = 1 SC = 1 + 0.045 · Cab SH = 1 + 0.015 · Cab kL = kC = kH = 1 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 84 / 207
  85. 85. Section Outline 4 Objective color terms Y and chromaticity Uniformity Color spaces sliced and diced Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 85 / 207
  86. 86. Color spaces color model operators Device dependent spaces counts received from or sent to a device typically RGB counts or CMYK percentages Device independent spaces human visual system related counts for an idealized device Colorimetric spaces analytically derived from the CIE colorimetry system Uniform spaces Euclidean, with a distance metric Visually scaled spaces Spaces defined by an atlas Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 86 / 207
  87. 87. Colorimetric spaces XYZ + basis for all other CIE color spaces – non-uniform RGB + can be produced by additive devices + linear transformation of XYZ – non-uniform example:      R 0.019710 −0.005494 −0.002974 X G = −0.009537 0.019363 −0.000274 Y  B 0.000638 −0.001295 0.009816 Z matrix elements are the primary colors sRGB + contains non-linearity typical for PC CRTs + easy to implement – non-uniform and non-linear Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 87 / 207
  88. 88. Colorimetric spaces (cont.) CIELAB + most uniform CIE space + widely used in the printing industry – cubic transformation CIELUV + simple transformation of XYZ + uniform + related to YUV (PAL, SECAM) – less uniform than CIELAB YIQ + used for NTSC encoding + black and white compatible – contains gamma correction – non-uniform YES, YCC + linear transformations of XYZ + black and white compatible + opponent color models – less uniform than CIELAB and CIELUV – YCC contains gamma correction – private standards Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 88 / 207
  89. 89. Colorimetric spaces (cont.) L C hab + has perceptual correlates + good for gamut mapping + perceptually uniform – cylindrical – not uniform for compression xvYCC + large gamut for HDTV with LED BLU (backlight unit) + backwards compatible to sRGB Luma Gamut of xvYCC Y 254 Over White 1.0 235 1< R’,G’,B’ 1< R’,G’,B’ BT.709-5 (sRGB) sYCC Extended Region Extended Region 0 < R’,G’,B’ < 1 xvYCC (Gamut of BT.709-5) (sRGB) R’,G’,B’< 0 R’,G’,B’< 0 0.0 16 -0.57 - 0.5 Black +0.5 +0.56 1 128 Cb, Cr 1 16 240 254 Extended Extended Chroma Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 89 / 207
  90. 90. Uniform color spaces Munsell perceptually uniform based on atlas CIELAB colorimetric CIELUV colorimetric OSA perceptually uniform based on atlas Coloroid æstetically uniform based on atlas Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 90 / 207
  91. 91. Visually scaled color spaces Munsell perceptually uniform based on atlas OSA perceptually uniform based on atlas Coloroid æstetically uniform based on atlas NCS atlas with uniform coordinates not perceptually uniform Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 91 / 207
  92. 92. Color spaces defined by an atlas Munsell OSA Coloroid NCS Scandinavian, popular in Europe RAL German, popular in Europe Pantone popular in the U.S.A. Many atlases defined by government agencies, industrial associations, companies Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 92 / 207
  93. 93. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 93 / 207
  94. 94. Illumination The spectral power distribution of the light reflected to the eye by an object is the product, at each wavelength, of the object’s spectral reflectance value by the spectral power distribution of the light source CWF Complexion 400 500 600 700 400 500 600 700 400 500 600 700 Incident SPD x Reflectance curve = Reflected SPD Deluxe Complexion CWF 400 500 600 700 400 500 600 700 400 500 600 700 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 94 / 207
  95. 95. Light sources of interest At the beginning of color perception there is radiant energy Treatment in color science is slightly different from what we learned in high school physics — it can be limited to the visible domain The spectral power distribution of a tungsten filament lamp depends primarily on the temperature at which the filament is operated Typical average daylight has a color temperature of 6504◦ K, which can be achieved also by Artificial Daylight fluorescent lamps, a.k.a. North-light or Color Matching lamps Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 95 / 207
  96. 96. CIE standard illuminants 300 Definition (Illuminant A) 250 CIE standard illuminant A relative radiant power represents light from a full (or 200 D65 blackbody) radiator at 2854◦ K A 150 Definition (Illuminant D65 ) 100 CIE standard illuminant D65 represents a phase of natural 50 daylight with a correlated color wavelength [nm] temperature of 6504◦ K 0 300 350 400 450 500 550 600 650 700 750 800 Fact (Illuminants B, C) CIE standard illuminants B and C were intended to represent direct sunlight with a correlated color temperature of 4874◦ K resp. 6774◦ K. They are being dropped because they are seriously deficient in the UV region (important for fluorescent materials) Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 96 / 207
  97. 97. CIE standard sources Definition (Illuminant) Illuminant refers to a specific spectral radiant power distribution incident to the object viewed by the observer Definition (Source) Source refers to a physical emitter of radiant power, such as a lamp or the sun and sky CIE illuminant A is realized by a gas-filled coiled-tungsten filament lamp operating at a correlated color temperature of 2856◦ K There are no artificial sources for illuminant D65 , due to the jagged spectral power distribution. However, some sources qualify as daylight simulators for colorimetry For more information see http://www.mostlycolor.ch/2007/06/ hot-body-excited-particles-and-north.html Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 97 / 207
  98. 98. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 98 / 207
  99. 99. Measuring color There are no filters that approximate well the color matching functions There are no artificial sources for the popular illuminants D65 and D50 Today’s hardware situation has changed dramatically Embedded processors are inexpensive Holographic gratings are inexpensive Light sources are highly efficient CCD sensors have much less dark noise It is better to perform spectral measurements and let the instrument do the colorimetry Spectroradiometer: determine the reflected SPD Spectrophotometer: determine the reflectance curve Because they are a closed system, spectrophotometers are very reliable Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 99 / 207
  100. 100. Trusting your instrument Sooner or later all users enter a deep trust crisis in their instruments. Some survival tips: Illuminate your work area with a source simulating your target illuminant see what the instrument “sees” Compact spectrophotometers have a very small geometry; perpendicularity between optical axis and sample, as well as distance to the sample are critical maintain an uncluttered work space The instrument’s light source generates heat, which increases dark current noise in the CCD and causes geometric deformations in the grating wait between measurements recalibrate at each session start after each pause after a long series of measurements, when the ambient temperature has changed by more than 5◦ C Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 100 / 207
  101. 101. Calibration White calibration: adjusts computational parameters so the calculated tile’s reflectance curve is the same as the absolute reflectance curve do it often Absolute certification: verifies that the measured color of the tile is within the tolerance (e.g. 0.6∆E units) from the tile’s absolute color important for agreement between laboratories Relative certification: verifies if the measured color of the tile is within the tolerance (e.g. 0.3∆E units) from the initial color of the tile with the same instruments important for reproducibility Collaborative testing: verifies that the entire color measurement procedure is in agreement with outside laboratories Collaborative Testing Services Inc, 21331 Gentry Drive, Sterling, VA 20166, 571–434–1925 http://www.collaborativetesting.com/ Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 101 / 207
  102. 102. Effect of variability A measurement is never perfect The effect of variability of color measurement is reduced by using multiple measurements How many measurements should I make and average? Rule of thumb: 10× for each variability parameter instrument’s variability: measure each spot — 10× sample uniformity: repeat at several locations — 100× sample variability: repeat for several samples — 1000× ... Follow ASTM standard practice E 1345 – 90 to determine how many measurements are necessary in each case ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, 610–832–9585, http://www.astm.org Improve all process aspects to minimize the required number of measurements ISO 9001 Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 102 / 207
  103. 103. Geometries of illumination and viewing On a glossy surface there are mirror-like (specular) reflections There are more reflections in the case of diffuse light sources Since the color of the illuminant is white, specular reflections add white, with the effect of desaturating the color Non-metallic glossy surfaces look more saturated in directional than in diffuse illumination Matte surfaces scatter the light diffusely — matte surfaces usually look less saturated than glossy surfaces Most surfaces are between glossy and matte Diffuse illumination is provided by integrating spheres usually they are provided with gloss traps Instruments with 45◦ /0◦ and 0◦ /45◦ geometry are less critical ASTM recommendation for partly glossy samples: use the geometry that minimizes surface effects (usually the one that gives lowest Y and highest excitation purity) 45◦ /0◦ geometry gives rise to polarization problems Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 103 / 207
  104. 104. Outline 5 Illumination 10 Color image communication 1 Introduction 6 Measuring color 11 Color appearance 2 Color theories modeling 7 Spectral color 3 Terminology 12 Cognitive color 8 Color reproduction 4 Objective color 13 Conclusions terms 9 Milestones in color printing 14 Bibliography Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 104 / 207
  105. 105. Section Outline 7 Spectral color Computational color Metamerism and Matrix R The LabPQR interim connection space Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 105 / 207
  106. 106. Motivation Examples when spectral color methods are required: Metamerism Fluorescence Media and ink characterization Reproduction across illuminants Mapping from one device to another More than 3 colorant hues (e.g., CMYKOGV) Scanner and camera characterization Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 106 / 207
  107. 107. Repetition of Standard Observer R=k Pλ · ¯(λ)dλ r means that the red color coordinate is obtained by integrating the SPD using the red CMF for the measure, where Pλ = E(λ) · S(λ) is the product of the SPD of an illuminant E with the object spectrum S. Usually we are interested in the coordinates of various objects under a fixed illuminant for a standard observer, so we reorder to R=k ¯(λ)E(λ) · S(λ)dλ r Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 107 / 207
  108. 108. Discretization In practice, the CMF are given as a table with 1nm steps, and instruments measure at steps of 1, 4, 10, 20nm etc., so in reality this is a summation [for red R]: R=k ¯(λ)E(λ)S(λ)dλ ≈ k r ¯(λi )E(λi )S(λi )∆λ r The integration resp. summation is over the visible range [380, 780]nm, but in practice it is often over [380, 730]nm for n = 36 samples Instead of doing color science with measure theory, we can do it with simple linear algebra In 1991 H. Joel Trussell has made available a comprehensive MatLab library and several key papers for color scientists Since then, spectral color science is mostly done with linear algebra Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 108 / 207
  109. 109. Formalism We use the vector-space notation WLOG, let k = 1 ¯ ¯ R = (R E)S, G = (G E)S, ¯ B = (B E)S Instead of doing this for each of R, G, B or X , Y , Z , using linear algebra we can write it as a single equation by combining the CMF in an n × 3 matrix A with the CMFs data in the columns: Υ = (A E)S Sometimes we are interested in the color of a fixed object under different illuminants, then we write Υ = A (ES) = A η η corresponds to the Pλ from earlier Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 109 / 207
  110. 110. Matlab, etc. a b c d Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 110 / 207
  111. 111. Section Outline 7 Spectral color Computational color Metamerism and Matrix R The LabPQR interim connection space Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 111 / 207
  112. 112. Fundamental and residual How can we reconcile metamerism and color reproduction technology? In 1953 Günter Wyszecki pointed out that the SPD of stimuli consists of a fundamental color-stimulus function η (λ) intrinsically ´ associated with the tristimulus values, and a residual called the metameric black function κ(λ) κ(λ) is orthogonal to the space of the CMF Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 112 / 207
  113. 113. Matrix R theory How does this translate to the discrete case? In 1982 Jozef Cohen with William Kappauf developed the matrix R theory Use an orthogonal projector to decompose stimuli in fundamental and residual The fundamental is a linear combination of the CMF A The metameric black is the difference between the stimulus and the fundamental For a set of metamers η1 (λ), η2 (λ), . . . , ηm (λ): A η1 = A η2 = · · · = A ηm = Υ Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 113 / 207
  114. 114. Development of matrix R R is defined as the symmetric n × n matrix Definition (matrix R) R := A(A A)−1 A Matrix R is an orthogonal projection A(A A)−1 =: Mf , so R = Mf A (remember: Υ = A η) Because A has 3 independent columns, R has rank 3 It decomposes the stimulus spectrum into fundamental η (λ) and ´ the metameric black κ: η = Rηi ´ κ = ηi − η = ηi − Rηi = (I − R)ηi ´ Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 114 / 207
  115. 115. Corollaries Metameric black has tristimulus value zero A κ = [0, 0, 0] η = Rηi means that any group of metamers has a common ´ fundamental η , but different residuals κ ´ Inversely, a stimulus spectrum can be expressed as ηi = η + κ = Rηi + (I − R)ηi ´ i.e., the stimulus spectrum can be reconstructed if the fundamental metamer and metameric black are known Why is this useful? Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 115 / 207
  116. 116. Section Outline 7 Spectral color Computational color Metamerism and Matrix R The LabPQR interim connection space Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 116 / 207
  117. 117. Reducing the data Storing a multidimensional vector for each pixel is expensive Can we project on a lower-dimensional vector space? Yes, because the spectra are relatively smooth Popular technique: principal component analysis Due to the usually smooth spectra, the dimension can be quite low: between 5 and 8 We have known how to deal with this for decades, it just requires linearly more processing Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 117 / 207
  118. 118. The hard problem We would like to use an ICC type workflow also for spectral imaging Colorimetric workflow: profile connection image 3-hue printer space The killer is the LUT used in the PCS: bands in bands out levels per band size [bytes] 3 6 17 30K 6 6 17 145M 9 6 17 700G 31 6 17 8 · 1027 G Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 118 / 207
  119. 119. Interim Connection Space Proposal by Mitchell Rosen et al. at RIT Introduce a lower-dimensional Interim Connection Space ICS PCS to ICS scene multi-hue printer ICS to counts via low-dim. LUT Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 119 / 207
  120. 120. Choosing the basis vectors Can we deviate from the usual PCA method of choosing the largest eigenvectors and build on some other useful basis? When defining the basis vectors for XYZ, the new basis was chosen so that one vector coincides with luminous efficiency V (λ) compatibility of colorimetry with photometry 1995 proposal by Bernhard Hill et al. at RWTH Aachen: incorporate three colorimetric dimensions compatibility of spectral technology with colorimetry http://www.ite.rwth-aachen.de/Inhalt/Documents/ Hill/AachenMultispecHistory.pdf Giordano Beretta (HP Labs Palo Alto) SC076 Understanding Color Alexandria, someday 2010 120 / 207

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