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Color

Color. ECE 847: Digital Image Processing. Stan Birchfield Clemson University. How it all began. S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847. An aside. Tyrannosaurus. Titanosaurus. 50 feet (L). 65 feet (L). Height: 45 feet. Allosaurus. (of course,

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Color

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  1. Color ECE 847:Digital Image Processing Stan Birchfield Clemson University

  2. How it all began S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  3. An aside Tyrannosaurus Titanosaurus 50 feet (L) 65 feet (L) Height: 45 feet Allosaurus (of course, juveniles are much smaller) 40 feet (L) American football field: 300 feet x 160 feet Ark: 450 feet x 75 feet http://www.kickoffzone.com/articles/images/ClemsonMemorialStadium02.jpg http://dinodictionary.com S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  4. Dragons and dinosaurs • 1500 BC: Behemoth has tail like a cedar of Lebanon (Job 40) http://www.biblegateway.com/passage/?search=Job+40%3A15-24&version=KJV • 255 BC: During First Punic War, Roman General Marcus Atilius Regulus had to kill 120-foot serpent when trying to cross River Bagrada. Its skin was displayed in Rome for 100 years. http://dragon.falbepublishing.com/carthagianserpent.html • 1st cent. AD: Dragons in India are always fighting with the elephants. Pliny the Elder, History of Nature, Book 8, Ch. 11 http://penelope.uchicago.edu/holland/pliny8.html • 7th cent. AD: The dragon is the largest animal on earth, found in Ethiopia and India. Isidore of Seville, Etymologies, Book 12, 4:4-5 http://pot-pourri.fltr.ucl.ac.be/files/AClassftp/TEXTES/ISIDORUS/Etymologie/B1N8PWGetQy.pdf • Soft tissues (proteins) are still present in dinosaur bones http://www.smithsonianmag.com/science-nature/dinosaur.html S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  5. A brief look at ancient history According to the Bible, • 8 people were preserved in the ark (Noah, his 3 sons, and their wives) • They left the ark in approx. 4004 – 1657 = 2347 B.C. • “Estimation of absolute dates becomes possible in the 2nd half of the 3rd millennium BC.” (c. 2500 B.C.) http://en.wikipedia.org/wiki/Short_chronology • Sumerian king list: 385,000 years of kings, “Then the Flood swept over.” Then list of kings dating back to c. 2300 B.C. http://www.livius.org/k/kinglist/sumerian.html • Assyrian king list goes back to c. 1800 B.C. http://www.livius.org/k/kinglist/assyrian.html • The Babylonian chronicle, “After the Flood had swept over and caused the destruction of the earth,” list of kings http://www.livius.org/cg-cm/chronicles/cm/lagash.html • Uruk chronicle goes back to c. 2100 B.C. http://www.livius.org/cg-cm/chronicles/cm/uruk.html • Xia Dynasty of China (first dynasty described in ancient historical records) from c. 2100 B.C. http://en.wikipedia.org/wiki/History_of_China • Indus Valley Civilization goes back to c. 2600 B.C. (mature period) http://en.wikipedia.org/wiki/Indus_Valley_Civilization (Gomer) (Tubal) (Madai) JAPHETH (Javan) (Asshur) (Canaan) SHEM (Elam) HAM Chinese word for “boat”: (Mizraim) eight vessel (Cush) people S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  6. Now back to color...

  7. Outline • Physics and psychology of color • Trichromacy • Physiology: Spectral Sensitivity Functions (SSFs) • Psychology: Color Matching Functions (CMFs) • Linear color space transformations • Color spaces • Primary colors

  8. Physics of color • Spectral power distribution (SPD) – amount of power in each wavelength of light • Measured by spectroradiometer, typically every 5 to 20 nm • To make it concrete, we will consider 31 numbers capturing the values in 10 nm bands from 400 – 700 nm (visible spectrum) nanometer The relative SPD of two light sources http://en.wikipedia.org/wiki/Spectral_power_distribution S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  9. Absorption and reflection of light • The color of a surface is the light reflected • Reflection is additive(the more reflected light the brighter) • Absorption is subtractive(the more pigments the darker) http://www.specialchem4coatings.com/tc/color-handbook/?id=object S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  10. Physics of color (cont.) Illumination spectra Reflectance spectra blue skylight tungsten bulb Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Forsyth, 2002

  11. Visible spectrum Physically, the colors are linear: 720 nm 380 nm electromagnetic (EM) spectrum S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  12. Question • Why then does violet look like red mixed with blue? • Red and blue are at extreme ends of the spectrum • Should have the least in common 720 nm 380 nm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  13. Psychology of color Psychologically, the colors are circular: Newton chose 7 colors (ROYGBIV) because 7 is a perfect number 6 colors fits the data better (what is indigo anyway?) This is the famous color wheel S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  14. Color in music De Clario’s color music code http://home.vicnet.net.au/~colmusic/clario1.htm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  15. Color and moods intense attention royal, wealthy happy, optimistic calm, natural peaceful, depressing Goethe’s color triangle http://www.infoplease.com/spot/colors1.html http://www.cs.brown.edu/courses/cs092/VA10/HTML/GoethesTriangleExplanation.html S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  16. Outline • Color: Physics vs. Psychology • Trichromacy • Physiology: Spectral Sensitivity Functions (SSFs) • Psychology: Color Matching Functions (CMFs) • Linear color space transformations • Color spaces • Primary colors

  17. Trichromacy“three colors” Physiology Psychology Color perception in human visual system based on 3 primary colors • Color sensation in human retina is result of 3 different photoreceptors SSFs CMFs

  18. Rods and cones • Young-Helmholtz theory (early 1800s): Color vision is the result of three different photoreceptors • Experimentally confirmed (1960s) by measuring the cone response functions (absorption spectra) • Three photoreceptors: • S-cones • M-cones • L-cones • (It is better not to callthem red-, green-, and • blue-cones) SSFs http://en.wikipedia.org/wiki/Trichromatic_color_vision S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  19. Tetrachromacy • At low light levels, rod cells may contribute to color vision • Studies suggest that some people may have four cones • Some animals have many more than four cones (some shrimp have 11!) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  20. Tetrachromacy in action? Sharp’s LE810 television, the first to use RGB-Y quadpixel technology(2010) http://www.technewsdaily.com/addition-of-yellow-pixels-designed-to-make-tvs-better-0230/ S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  21. Color matching experiment In the human visual system, every color can be obtained as the linear combination of three independent primary colors Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

  22. Color matching experiment 1 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  23. The primary color amounts needed for a match Color matching experiment 1 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  24. The primary color amounts needed for a match Color matching experiment 1 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  25. The primary color amounts needed for a match Color matching experiment 1 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  26. Color matching experiment 2 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  27. Color matching experiment 2 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  28. Color matching experiment 2 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  29. p1 p2 p3 Color matching experiment 2 The primary color amounts needed for a match: We say a “negative” amount of p2 was needed to make the match, because we added it to the test color’s side. p1 p2 p3 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  30. Metamer Two colors are metamers if they have • different spectral distributions • same visual appearance http://escience.anu.edu.au/lecture/cg/Color/Image/metamer.gif

  31. Color matching functions • Select 3 primary lights • For each wavelength l, find the amounts e1, e2, e3 of the primaries needed to match spectral signal t(l) • These yield thecolor matchingfunctions (CMFs)for those primaries • Store in 3x31 matrix CMFs Note the negative dip S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  32. Color matching functions • CMFs allow us to transform between color spaces (more later) • Why is this important? • Want to paint a logo on a product with the correct shade of color • Want color to look the same no matter which monitor, inkjet printer, laser printer, etc. S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  33. Grassman’s Laws • Color matching is (approximately) linear • Principle of superposition:Ifthen • This makes math much simpler (later) • But not true at extreme ends of measurements S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  34. Do two people see the same color? • Yes! • In the following sense:They will choose the same weights for the three primaries to match the color (Modulo color-blindness) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  35. Luminous efficiency • Another color matching experiment • Whether one color is brighter or darker than another • Goal • Obtain a luminous efficiency function (LEF) • Experimental environment • photopic vision:Daytime (high intensity levels), cones dominate • scotopic vision:Nighttime (low-light situation), rods dominate S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  36. Luminous efficiency (cont.) • Photopic LEF (solid black) • M-cone SSF (solid green) • Combination of the cone SSFs (green circles) • 1931 CIE XYZ space (dashed magenta) Scotopic Photopic Purkinje shift S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  37. Luminous efficiency (cont.) weights The photopic LEF The cone SSFs • The photopic LEF a weighted combination of the cone SSFs • M-cones dominate S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  38. Outline • Color: Physics vs. Psychology • Trichromacy • Physiology: Spectral Sensitivity Functions (SSFs) • Psychology: Color Matching Functions (CMFs) • Linear color space transformations • Color spaces • Primary colors

  39. Sensing light wavelength SSF of the sensor (“spectral sensitivity function”) SPD of the incidentirradiance (“spectral power distribution”) Output of a single photoreceptor: S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  40. Sensing light (cont.) v = sTt SSF of the sensor (“spectral sensitivity function”) SPD of the incidentirradiance (“spectral power distribution”) 31×1 vector 31×1 vector (wavelength is used to index the elements of the vectors) Recall: 31 numbers capture the values in 10 nm bands from 400 – 700 nm (visible spectrum) Discrete approximation: S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  41. Sensing three colors cone SSFs Projection from a point in a 31D space to a 3D space 31×1 vector 3×31 matrix • Three cone types: • S-cones (“blue”) • M-cones (“green”) • L-cones (“red”) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  42. Color matching Grassman’s Laws:  Three primaries(independent) Test light ( ) “the colors match” = “the SPDs are metamers”  Color matching is (approximately) linear! S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  43. Color matching (cont.) is the SPD of the test light Intensities of the three primaries The rows are the color matching functions (CMFs) of the three primaries Do not confuse the CMF C with the SSF Sv = Stare the cone values; e = Ctare the primary intensities The linear function for modeling color matching S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  44. Color matching functions (CMFs) Overlaid circles obtained by a 3x3 linear transform of cone SSFs (close agreement) CMFs using RGB primaries (solid lines) CMFs using 1931 CIE XYZ primaries Related exactly by a 3 x 3 transform S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  45. Transforming between color spaces Test light 31 x 1 Intensities of the three primaries 3 x 1 CMFs 3 x 31 set of primaries 31 x 3 (each column is SPD of a primary light) Recall: Match the same test light using two different sets of primaries: The resulting SPDs are and S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  46. Transforming between color spaces (could use C or C’ here – does not matter) } (since prev eqn is true for all t) } 3x3 transform between color spaces or (by substituting from above) • From previous slide: • For both cases, the resulting SPD looks identical to the test light These are metamers   S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  47. Transforming between color spaces One color space Another color space 3×3 transformation matrix between two color spaces CMFs differ according to the primaries used http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt

  48. Transforming between color spaces • Given two sets of primaries, P and P’ • Measure color matching functions C and C’ • Solve C=FC’ for the 3x3 matrix F=CP’ • F now converts between tristimulus values: e = Fe’ Note that we don’t need P and P’ once we have C and C’ S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

  49. Outline • Color: Physics vs. Psychology • Trichromacy • Physiology: Spectral Sensitivity Functions (SSFs) • Psychology: Color Matching Functions (CMFs) • Color space transformations • Color spaces • Primary colors

  50. CIE color space • The most important color space of all • CIE XYZ tristimulus coordinate system proposed in 1931 • Advantages • Non-negative everywhere • The middle coordinate (Y) approximates the photopic luminous efficiency function (LEF) • Note that the CIE XYZ primaries are not physically realizable S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

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