(c) University of Wisconsin, CS559 Spring 2002 Color Recap The physical description of color is as a spectrum: the intensity of light at each wavelength Humans have three types of cone – each responds differently to an incoming spectrum Experiments show that humans can match all colors by combining three primary colors The most common computer graphics primaries are Red (645.16nm), Green (526.32nm) and Blue (444.44nm) 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Last Time Digital Images Spatial and Color resolution Color The physics and perception of color Particularly: 3 types of cone, sensor response 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Today More on color Trichromacy Color matching Color Spaces 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Trichromacy Experiment: Show a target color beside a user controlled color User has knobs that add primary sources to their color Ask the user to match the colors By experience, 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

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 suck light into a display device 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 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 with R, G and B primaries Result is three functions, r(), g() and b(), the RGB color matching functions 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

The RGB Color Matching Functions 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

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 the “color” due to E() is E, then the match is: 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 RGB Color Space Color Cube Program 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 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) If you ever need to answer such questions, file rgb.txt under X11 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 CIE x, y Note: This is a representation on a projector with limited range, so the right colors are not being displayed 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

CIE Matching Functions 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

Qualitative features of CIE x, y Linearity implies that colors obtainable by mixing lights with colors A, B lie on line segment with endpoints at A and B Monochromatic colors (spectral colors) run along the “Spectral Locus” Dominant wavelength = Spectral color that can be mixed with white to match Purity = (distance from C to spectral locus)/(distance from white to spectral locus) Wavelength and purity can be used to specify color. Complementary colors=colors that can be mixed with C to get white 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Going from RGB to XYZ These are linear color spaces, related by a linear transformation Match each primary, for example: Substitute and equate terms: 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Determining Gamuts XYZ Gamut Gamut: The range of colors that can be produced Plot the matching coordinates for each primary 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 y RGB Gamut G R B x 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

More linear color spaces Monitor RGB: primaries are monitor phosphor colors, primaries and color matching functions vary from monitor to monitor: Almost all applications assume that RGB is the same as monitor RGB 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Munsell Color Space Problems with linear spaces remain: Hard to specify colors without resorting to matching functions Perceptually non-uniform Munsell: describes surfaces, rather than lights - less relevant for graphics Surfaces must be viewed under fixed comparison light 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Munsell color space 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 HSV Color Space HSV Color Cone Program 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 MacAdam Ellipses Scaled by a factor of 10 and shown on CIE xy color space If you are shown two colors inside the same ellipse, you cannot tell them apart Only a few ellipses are shown, but one can be defined for every point 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 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 01/29/02 (c) University of Wisconsin, CS559 Spring 2002

(c) University of Wisconsin, CS559 Spring 2002 Subtractive mixing Inks subtract light from white, whereas phosphors glow Common inks: Cyan=White−Red, Magenta=White−Green, Yellow=White−Blue For example, 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 For good choice of inks, there is a linear transform between XYZ and CMY 01/29/02 (c) University of Wisconsin, CS559 Spring 2002