ࡱ> AC@|7 +bjbjUU "n7|7|#l~,~>2 !!!!!bV#d#4`=b=b=b=b=b=b=$O? oA=Q#!!##='!!='''#!!`='#`='',r6T7! E*[~J%p67D=0>~6A'A7'f4JHYPERLINK "PNG.doc" \l "_CS320_PNG_more"Previous lectureHYPERLINK "..\\JPEG\\Lossy.doc"Next Lecture HYPERLINK "..\\320Syllabus.doc" SyllabusHomeworkColor Representation Problems: The same graphic looks different on different monitors and it looks different when printed. How do we do device independent color? If we want to compress an image that uses thousands of colors to 256 colors, how do we choose the closest color? R G B (Red, Green, Blue) Commonly used for computer monitors that produce light. Colors are additive. When all colors are combined equally, they produce white. [Gonzalez & Woods, plate III] C M Y (Cyan, Magenta, Yellow) Used for printing or painting where the ink absorbs light. Colors are subtractive. Cyan absorbs red light. When all colors are combined equally, they kind of produce black. Depending on the inks used, it may look brownish. Thus a fourth color (black) is usually used. Most printing is in black anyway and it is cheaper to use one ink than three. Y I Q (Luminance and two chrominance channels) This is the NTSC (National Television System Committee) transmission system used for color TV. Most of the bandwidth is devoted to the luminance channel. A similar method (Y Cb Cr) is used for JPEG. H S V (Hue, Saturation, and Value or Brightness) These are the perceptual aspects of color. [Jain 3-10] Color Matching There are three cone types in the human retina, with peak responses at 450 (blue), 525 (green) and 555 (yellow-green) nm. [Levine&Shefner 15-16] Select three primary colors to use in a computer monitor. For example, the CIE standard primary sources are 700 nm (red), 546.1 nm (green) and 435.8 nm (blue). Different colors will be present on different monitors. For the three particular primary colors used by a monitor, we can compute tristimulus curves T1(l), T2(l) and T3(l). These show how the cones will respond to the three primary colors. The amount of each tristimulus value (CIE primary sources) needed to produce a color is denoted X Y Z. [Jain 3-13]. The good news: Any color can be matched by mixing three colored lights. The bad news: For any three practical primary colors, some color matches require negative coefficients. No practical set of three primaries has been found that can reproduce all colors. Laws of Color Matching Any color can be matched by mixing at most three colored lights. The luminance of a color is equal to the sum of the luminance of its components. The human eye cannot resolve the components of a color match. A metameric match is a pair of indistinguishable colors that have different spectra. A color match at one luminance level holds over a wide range of luminances. If two colors match, then their mixtures will match. If two colors match and matching colors are subtracted from each, the remaining colors still match. If C1 matches C2 and C2 matches C3, then C1 matches C3. Color Transformations CIE tristimulus color coordinates are given as X Y Z. If we know the X Y Z values of the 3 primary colors of the monitor on which an image was created, we can compute absolute color coordinates. If we also know the XYZ values for the RGB of the monitor we are using, we can match the original colors. Monitor vendors have XYZ values available but seldom include them in the documentation. Vendors list colors using xyY colorspace, which relates as follows: xyY from XYZXYZ from xyYx = X / (X+Y+Z)X = x * Y/yy = Y / (X+Y+Z)Y = YY = YZ = (1-x-y) Y/y The x,y coordinates give chromaticity and the Y coordinate is used for luminance. Strictly speaking, luminance should be (X+Y+Z) It is also possible to compute the chromaticity z = Z/(X+Y+Z) but this would be redundant since x+y+z = 1. For most monitors, the white point falls on the black body curve 9300K. The coordinates for this white point are: xyY = (0.285, 0.293, 1) XYZ = (0.973, 1, 1.440) [Gonzalez & Woods, plate IV] CIE (Commission Internationale de LEclairage) If you form a triangle on the CIE diagram with the three primary colors at the vertices, the colors inside the triangle are the ones that can be realized. Encoding color as XYZ would require more bits, since it includes colors that cannot be displayed on the RGB for a particular monitor.  HYPERLINK "PNG.doc" \l "Chrm" PNG lets you specify the XYZ coordinates used when the image was created. Confusion potential: Y means two different things: Luminance value (as in YIQ, xyY, XYZ) Yellow (as in CMY) For more on color, see 14. Appendix Color Tutorial on page 89 of the  HYPERLINK "png-1.0-w3c.txt" PNG Standard. Example (see Miano pp. 198-200) Given two monitors with the following specifications (note this is xyY): Monitor 1 Monitor 2xy___xyRed.612.353.625.340Green.293.595.280.595Blue.149.068.155.070White.285.293.285.293How should the following RGB colors on Monitor 1 be matched on Monitor 2? All values are hexadecimal. (c0, 0, 0) (0, c0, 0) (0, 0, c0) (60, ff, ff) (40, 10, 10) To do this, we need to find a matrix that converts between the CIE XYZ space and the RGB for our monitor. In the matrix, the R, G and B values are scaled to be between 0 and 1. For each monitor, we need to find values CR, CG, CB that satisfy  EMBED Equation.3  The z values can be found from z = 1-x-y. Thus we have the values for the first 3x3 matrix from the table. The matrix equation must hold for any values of XYZ and RGB. Thus it will hold for white: RGB = (1,1,1) and XYZ = (0.973, 1.0, 1.440) for the first monitor after we do the transformations from xyY. Thus we can solve by inverting the monitor matrix:  EMBED Equation.3   EMBED Equation.3  For monitor 1, we have CR = 0.660, CG = 1.100, CB = 1.652 [The solution given in Miano, CR = 0.698, CG = 1.094, CB = 1.512 is less accurate.] Once we know these, we can transform between XYZ and RGB by:  EMBED Equation.3  and  EMBED Equation.3  For monitor 1:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 The inverse matrix is:  EMBED Equation.3  EMBED Equation.3   EMBED Equation.3 from which we find CR = 0.660, CG = 1.100, CB = 1.653.  EMBED Equation.3  EMBED Equation.3  We take the given RGB inputs, divide by 255, and plug them into the above equation to get the XYZ colors: Rc0006040G0c00ff10B00c0ff10r0.753000.3760.251g00.75301.0000.063b000.7531.0000.063X0.3040.2430.1850.7210.137Y0.1760.4930.0850.8550.107Z0.0170.0930.9741.4260.095 For monitor 2: EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 The inverse matrix is:  EMBED Equation.3  EMBED Equation.3   EMBED Equation.3 from which we find CR = 0.647, CG = 1.117, CB = 1.649.  EMBED Equation.3  EMBED Equation.3  We take the XYZ colors from monitor 1, put them into the above equations, and get the first three rows in the table below. Values that are less than 0 or greater than 1 cannot be represented exactly on monitor 2. We limit these values to the possible range and multiply by 255, giving the hex answers on rows 4-6 and the decimal answers on rows 7-9. r0.7380.041-0.0260.3890.247g0.0200.7290.0040.9830.068b-0.002-0.0080.7621.0010.062RBCA0633FG5B90FA11B00C2FFFR18810-79963G5186125117B0-219425516 Color Geodesics If we look at the CIE diagram, we find that it is not uniform. [Jain Fig 3.15] The MacAdam ellipses show regions of equivalent colors. Any color on the border of the ellipse is just noticeably different (JND) from the color in the center. Other color coordinate systems have been set up that try to make the distance between two points be equal to the difference in colors. CIE Uniform Chromaticity Scale (UCS) uvY and UVW: u = 4X / (X + 15Y + 3Z) = 4x / (-2x + 12y +3) v = 6Y / (X + 15Y + 3Z) = 6y / (-2x + 12y +3) Chromaticities: u,v; Luminance: Y U = 2X/3 V = Y W = (-X + 3Y + Z) / 2 These are the tristimulus values corresponding to u,v,w. This space is an improvement over xyY, but it is still non-Euclidean. If you want to move between two colors along a path of the smallest changes, you do not follow a straight line. [Jain figure 3.19] Modified UCS system U*V*W* W* = 25 (100 Y) 1/3  17 where 0.01 d" Y d" 1 U* = 13W* (u-u0) V* = 13W* (v-v0) Where u0 and v0 are the chromaticities of the reference white. W* is brightness or contrast. L*, a*, b* system L* = 25 (100 Y/Y0) 1/3  16 where 0.01 d" Y d" 1 a* = 500 [(X/X0)1/3 - (Y/Y0)1/3] b* = 200 [(Y/Y0)1/3 - (Z/Z0)1/3] Where X0, Y0 and Z0 are the tristimulus values of reference white. L* is brightness, a* is red-green content, b* is yellow-blue content. [Jain Table 3.4] There are three CIE color difference formulas. They all use a Euclidean distance but use different color spaces. The 1964 formula is not as good as the other two. 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