Last Time Intensity perception the importance of ratios Dynamic Range what it means and some of the issues Gamma Correction why and how Color Spectra Emission vs adsorption Sensors and response Human color perception Programming tutorial 1 9 14 04 University of Wisconsin CS559 Spring 2004 Today Tri chromacy Color primaries Color Spaces Calibration Homework 1 due Do Programming Tutorial 2 9 14 04 University of Wisconsin CS559 Spring 2004 E Sensitivity Qualitative Response Multiply 500 photons E 400 400 9 14 04 600 700 400 500 600 700 Area under curve Red 500 600 700 Big response University of Wisconsin CS559 Spring 2004 E Sensitivity Qualitative Response Multiply photons E 400 500 600 700 400 500 9 14 04 500 700 Area under curve Blue 400 600 600 700 Tiny response University of Wisconsin CS559 Spring 2004 Recall We re working toward a representation for digital color We have seen that humans have three sensors for color vision Now the implications 9 14 04 University of Wisconsin CS559 Spring 2004 Trichromacy Experiment Show a target color spectrum beside a user controlled color User has knobs that adjust primary sources to set their color Primary sources are just lights with a fixed spectrum and variable intensity Ask the user to match the colors make their light look the same as the target Experiments show that it is possible to match almost all colors using only three primary sources the principle of trichromacy Sometimes have to add light to the target In practical terms this means that if you show someone the right amount of each primary they will perceive the right color This was how experimentalists knew there were 3 types of cones 9 14 04 University of Wisconsin CS559 Spring 2004 Trichromacy means Spectrum Color Matching People think these two spectra look the same monomers 400 500 700 3 Primaries 400 500 9 14 04 600 600 Representing color If you want people to see the continuous spectrum you can just show the three primaries 700 University of Wisconsin CS559 Spring 2004 The Math of Trichromacy Write primaries as R G and B We won t precisely define them yet Many colors can be represented as a mixture of R G B M rR gG bB Additive matching Gives a color description system two people who agree on R G B need only supply r g b to describe a color Some colors can t be matched like this instead write M rR gG bB Subtractive matching Interpret this as r g b Problem for reproducing colors you can t subtract light using a monitor or add it using ink 9 14 04 University of Wisconsin CS559 Spring 2004 Primaries are Spectra Too A primary can be a spectrum Single wavelengths are just a special case 3 Primaries 3 Primaries or 400 500 600 700 400 500 600 700 9 14 04 University of Wisconsin CS559 Spring 2004 Color Matching Given a spectrum how do we determine how much each of R G and B to use to match it 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 9 14 04 University of Wisconsin CS559 Spring 2004 The RGB Color Matching Functions 9 14 04 University of Wisconsin CS559 Spring 2004 Computing the Matching Given a spectrum how do we determine how much each of R G and B to use to match it 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 give one energy unit s worth of response at each wavelength E rR gG bB r r E d g g E d b b E d 9 14 04 University of Wisconsin CS559 Spring 2004 Color Spaces The principle of trichromacy means that the colors displayable are all the linear combination of primaries Taking linear combinations of R G and B defines the RGB color space the range of perceptible colors generated by adding some part each of R G and B If R G and B correspond to a monitor s phosphors monitor RGB then the space is the range of colors displayable on the monitor 9 14 04 University of Wisconsin CS559 Spring 2004 RGB Color Space Color Cube Program 9 14 04 University of Wisconsin CS559 Spring 2004 Problems with RGB Can only a small range of all the colors humans are capable of perceiving particularly for monitor RGB Have you ever seen magenta on a monitor It isn t easy for humans to say how much of RGB to use to make a given color How much R G and B is there in brown Answer 64 16 16 Perceptually non linear Two points a certain distance apart in one part of the space may be perceptually different Two other points the same distance apart in another part of the space may be perceptually the same 9 14 04 University of Wisconsin CS559 Spring 2004 CIE XYZ Color Space Defined in 1931 to describe the full space of perceptible colors Revisions now used by color professionals Color matching functions are everywhere positive Cannot produce the primaries need negative light But can still describe a color by its matching weights Y component intended to correspond to intensity Most frequently set x X X Y Z and y Y X Y Z x y are coordinates on a constant brightness slice 9 14 04 University of Wisconsin CS559 Spring 2004 CIE x y Note This is a representation on a projector with limited range so the correct colors are not being displayed 9 14 04 University of Wisconsin CS559 Spring 2004 CIE Matching Functions 9 14 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 9 14 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 9 14 04 University of Wisconsin CS559 Spring 2004 Determining Gamuts XYZ Gamut y G RGB Gamut R B x 9 14 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 …
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