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Chi-Cheng Lin, Winona State University CS430 Computer Graphics Color Theory

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2 Topics l Colors l CIE Color Model l RGB Color Model l CMY Color Model l YIQ Color Model l Intuitive Color Concepts l HSV Color Model l HLS Color Model

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3 Colors l Colors zA narrow frequency band within the electromagnetic spectrum

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4 Colors l Visible band zEach frequency corresponds to a distinct color zLow-frequency end (4.3 x Hz): Red zHigh-frequency end (7.5 x Hz): Violet zWavelength = v/f, where v=300,000km/sec zLow frequency High frequency red orange yellow green blue violet Long wavelength Short wavelength 700nm400nm

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5 Colors l Colors of an object zLight source emits white light (all frequencies of light) zObject reflects/absorbs some frequencies zColor = combination of frequencies reflected l Dominant wavelength (or frequency) zHue or color of the light zE.g., pink S( ): spectrum (luminance/intensity of light)

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6 CIE Color Model l Color models zUse three primary colors to produce other colors l Primary colors zColors used in a color model to produce all the other colors in that model. zCannot be made from the other (two) colors defining the model. l CIE color model zX, Y, and Z: nonexistent, super saturated colors yVectors in 3-D additive color space zAny color S = AX + BY + CZ

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7 CIE Color Model l S = AX + BY + CZ can be normalized to zx = A/(A+B+C) zy = B/(A+B+C) zz = C/(A+B+C) s = xX + yY + zZ, where x + y + z = 1 s lies in the plane x + y + z = 1 in 3D =400 =670 x z y

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8 CIE Color Model l CIE chromaticity diagram zs'( ) = (x( ), y( )) zBy viewing the 3D curve in an orthographic projection, looking along the z-axis zhorseshoe shape =400 =670 x z y

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9 CIE Chromaticity Diagram

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10 CIE Chromaticity Diagram

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11 Uses of CIE Chromaticity Diagram

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12 Uses of CIE Chromaticity Diagram l Any colors on the line l between two colors a and b zIs a convex combination of a and b zIs a legitimate color zcan be generated by shining various amounts of a and b onto a screen (like tweening) l Complementary colors zAny two colors on a line passing through white and added up to be white are complementary e.g., e and f zred cyan green magenta blue yellow

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13 Uses of CIE Chromaticity Diagram l Measure dominant wavelength and saturation zColor g: Some combination of h and white zDominant wavelength of g = wavelength at h zSaturation (purity) of g = (g - w) / (h - w) l Color j has no dominant wavelength because k is not a pure color (k lies on the purple line) zRepresented by dominant wavelength of ks complement m, with by a c suffix, e.g., 498 c

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14 Uses of CIE Chromaticity Diagram l Any color within a triangle can be generated by the three vertices of the triangle zAny point inside IJK is a convex combination of points I, J, and K

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15 Uses of CIE Chromaticity Diagram l Define color gamuts zRange of colors that can be produced on a device l CRT monitors gamut is different from printers (See Plate 33 in the textbook) l Any choice of three primaries can never encompass all visible colors l RGB are natural choices for primaries as they can cover the largest part of the horseshoe

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16 Gamut Example

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17 RGB Color Model l Used in light emitting devices zColor CRT monitors l Additive zResult = individual contributions of each primary color added together zC = rR + gG + bB, where r, g, b [0, 1] zR = (1, 0, 0) zG = (0, 1, 0) zB = (0, 0, 1)

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18 RGB Color Model

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19 RGB Color Model l Color Cube zR + G = (1, 0, 0) + (0, 1, 0) = (1, 1, 0) = Y zR + B = (1, 0, 0) + (0, 0, 1) = (1, 0, 1) = M zB + G = (0, 0, 1) + (0, 1, 0) = (0, 1, 1) = C zR + G + B = (1, 1, 1) = W z1 – W = (0, 0, 0) = BLK zGrays = (x, x, x), where x (0, 1)

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20 Color Cube

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21 CMY Color Model l CMY: Complements of RGB l Used in light absorbing devices zHardcopy output devices l Subtractive zColor specified by what is subtracted from white light zCyan absorbs red, magenta absorbs green, and yellow absorbs blue

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22 CMY Color Model

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23 CMY Color Model l W = (0, 0, 0) B = (1, 1, 1) l Conversion from RGB to CMY l Conversion from CMY to RGB

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24 CMYK Color Model l Motivations zDo we get black if paint cyan, magenta and yellow on a white paper? zWhich cartridge is more expensive? l CMYK model zK = greatest gray that can be extracted l Given C, M, and Y zK = min(C, M, Y) zC = C – K zM = M – K zY = Y – K Try some examples…

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25 YIQ Color Model l Used in U.S. commercial color-TV broadcasting zRecoding of RGB for transmission efficiency zBackward compatible with black-and-white TV zTransmitted using NTSC (National Television System Committee) standard

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26 YIQ Color Model l YIQ zY: luminance zI, Q: chromaticity zOnly Y shown in black-and-white TV l RGB YIQ

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27 YIQ Color Model l Humans visual properties zMore sensitive to changes in luminance than in hue or saturation more bits should be used to represent Y than I and Q zLimited color sensation to objects covering extremely small part of our field of view One, rather than two color dimensions would be adequate I or Q can have a lower bandwidth than the others

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28 YIQ Color Model l NTSC encoding of YIQ into broadcast signal zUses humans visual system properties to maximize information transmitted in a fixed bandwidth zY: 4MHz zI: 1.5MHz zQ: 0.6MHz

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29 Intuitive Color Concepts l Terminology Perceptual TermColorimetryComments huedominated wavelength to distinguish colors saturationexcitation purity e.g., red and pink Lightness (reflecting objects) luminance Brightness (self- luminous objects) luminancee.g., Sun, CRT

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30 Intuitive Color Concepts zTint: white pigment added to pure pigment saturation reduced zShade: black pigment added to pure pigment lightness reduced zTone: consequence of adding both white and black pigments to pure pigments tints shades pure color white black grays tones

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31 Intuitive Color Concepts l Tints, shades, and tones different colors of same hue are produced l Grays = black pigments + white pigments l Graphics packages that provide color palettes to users often employ two or more color models

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32 HSV Color Model l HSV = Hue, Saturation, and Value zA.k.a. HSB, where B is Brightness l RGB, CMY, and YIQ: hardware-oriented l HSV and HLS: user-oriented l Cylinder coordinate system zSpace: hexcone zhexagon is obtained from the color cube in isometric projection z(h, s, v), where h [0, 360) and s, v [0, 1] yhue: angle round the hexagon ysaturation: distance from the center yvalue: axis through the center

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33 HSV Color Model Color CubeHexcone

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34 HSV Color Model l W = (-, 0, 1) l B = (-, 0, 0) l R = (0, 1, 1) Y = (60, 1, 1) : M = (300, 1, 1) l Adding white pigments S l Adding black pigments V l Creating tones S and V

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35 HSV Color Model l True color system: 16 million colors l Q: Do we need that many? l Human eyes can distinguish z128 hues z130 tints (saturation levels) z23 shades of yellow colors, 16 of blue colors 128 x 130 x 23 = colors

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36 HLS Color Model l HLS: Hue, Lightness, and Saturation l Cylinder coordinate system zSpace: double cone zbase is from the hexagon as in HSV z(h, l, s), where h [0, 360) and s, v [0, 1] yhue: angle round the base ylightness: axis through the center ysaturation: distance from the center l W = (-, 0, 1) l B = (-, 0, 0) l R = (0, 0.5, 1), Y = (60, 0.5, 1), …

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37 HLS Color Model l Double cones pure color white black h

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