Last Time Color Sensor response is computed from the sensor s response curve and the incoming spectrum Humans have three types of color sensing cones in their eyes The principle of trichromacy says that any spectrum can be matched using three primaries but sometimes you have to subtract a primary A color system consist of primaries and color matching functions that are used to determine how much of each primary is needed to match a spectrum RGB and CIE XYZ are two color systems 1 29 04 University of Wisconsin CS559 Spring 2004 Today Errata from last time Transformations between color systems Limitations of trichromatic color representations 1 29 04 University of Wisconsin CS559 Spring 2004 Errata Primaries Last time I implied a primary was a single wavelength Not true a primary can be a spectrum Single wavelengths are just a special case 3 Primaries 3 Primaries or 400 500 1 29 04 600 700 400 500 University of Wisconsin CS559 Spring 2004 600 700 Errata Color Matching Last time on the board I implied that the matching functions are determined one primary at a time not right First step For a light of unit intensity at each wavelength ask people to match it using some combination of R G and B primaries Gives you r g and b the amount of each primary used for wavelength Defined for all visible wavelengths r g and b are the RGB color matching functions 1 29 04 University of Wisconsin CS559 Spring 2004 Computing the Matching The spectrum function that we are trying to match E gives the amount of energy at each wavelength The RGB matching functions describe how much of each primary is needed to match one unit of energy at each wavelength Hence if means perceptually equal then the match is E rR gG bB r r E d g g E d b b E d 1 29 04 University of Wisconsin CS559 Spring 2004 Going from RGB to XYZ These are linear color spaces related by a linear transformation E xX yY zZ rR gG bB Match each primary for example R xr X yrY zr Z Substitute and equate terms x xr y y r z zr 1 29 04 University of Wisconsin CS559 Spring 2004 xg yg zg xb r yb g zb b Standard RGB XYZ x 0 4124 y 0 2126 z 0 0193 r 3 2410 g 0 9692 b 0 0556 0 3576 0 1805 r 0 7151 0 0721 g 0 1192 0 9505 b 1 5374 0 4986 x 1 8760 0 0416 y 0 2040 1 0570 z Note that each matrix is the inverse of the other Recall Y encodes brightness so the matrix tells us how to go from RGB to grey 1 29 04 University of Wisconsin CS559 Spring 2004 Determining Gamuts XYZ Gamut y G RGB Gamut R B x 1 29 04 Gamut The range of colors that can be represented or reproduced Plot the matching coordinates for each primary eg R G B Region contained in triangle 3 primaries is gamut Really it s a 3D thing with the color cube distorted and embedded in the XYZ gamut University of Wisconsin CS559 Spring 2004 Accurate Color Reproduction High quality graphic design applications and even some monitor software offers accurate color reproduction A color calibration phase is required Fix the lighting conditions under which you will use the monitor Fix the brightness and contrast on the monitor Determine the monitor s Using a standard color card match colors on your monitor to colors on the card This gives you the matrix to convert your monitor s RGB to XYZ Together this information allows you to accurately reproduce a color specified in XYZ format and hence any other standard format 1 29 04 University of Wisconsin CS559 Spring 2004 More linear color spaces Monitor RGB primaries are monitor phosphor colors primaries and color matching functions vary from monitor to monitor sRGB A new color space designed for web graphics YIQ mainly used in television Y is approximately intensity I Q are chromatic properties Linear color space hence there is a matrix that transforms XYZ coords to YIQ coords and another to take RGB to YIQ I and Q can be transmitted with low bandwidth 1 29 04 University of Wisconsin CS559 Spring 2004 HSV Color Space Alvy Ray Smith 1978 Hue the color family red yellow blue Saturation The purity of a color white is totally unsaturated Value The intensity of a color white is intense black isn t Space looks like a cone Parts of the cone can be mapped to RGB space Not a linear space so no linear transform to take RGB to HSV But there is an algorithmic transform 1 29 04 University of Wisconsin CS559 Spring 2004 HSV Color Space HSV Color Cone Program 1 29 04 University of Wisconsin CS559 Spring 2004 Uniform Color Spaces Color spaces in which distance in the space corresponds to perceptual distance Only works for local distances How far is red from green Is it further than red from blue Use MacAdams ellipses to define perceptual distance 1 29 04 University of Wisconsin CS559 Spring 2004 MacAdam Ellipses 1 29 04 Scaled by a factor of 10 and shown on CIE xy color space If you are shown two colors one at the center of the ellipse and the other inside it you cannot tell them apart Only a few ellipses are shown but one can be defined for every point University of Wisconsin CS559 Spring 2004 CIE u v Space CIE u v is a non linear color space where color differences are more uniform Note that now ellipses look more like circles The third coordinate is the original Z from XYZ Violet 1 29 04 u 1 v X 15Y 3Z University of Wisconsin CS559 Spring 2004 4 X 9Y Paint and Ink Paints contain reflective particles Different pigments reflect different colors Combining pigments reflects more colors so additive color Red paint green paint yellow paint Paint covers things Inks contain adsorbing particles You see the color of the paper filtered by the ink Combining inks adsorbs more color so subtractive color White paper red blue green The color and texture of the paper affects the color of the image 1 29 04 University of Wisconsin CS559 Spring 2004 Subtractive mixing Common inks Cyan White Red Magenta White Green Yellow White Blue The colors cyan magenta yellow are how the inks look when printed To make a red mark put down magenta and yellow which removes the green and blue leaving red For a good choice of inks matching is linear C M Y White White Black C M White Red Green Blue Usually require CMY and Black because colored inks are more expensive and registration is hard Registration is the problem of making drops of ink line up 1 29 04 University of Wisconsin CS559 Spring 2004 Calibrating a Printer If the inks think of them as primaries are linear there exists a 3x3 matrix and an offset to take RGB to CMY For example if an RGB of 1 …
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