Einführung in Visual Computing 186.822 186.822 Color and Color Models Werner Purgathofer Color problem specification light and perception colorimetry l i t device color systems color ordering systems color symbolism 1 Werner Purgathofer 1
Color - Why Do We Care? Computer Graphics is all about the generation and the manipulation of color images proper understanding and handling of color is proper understanding and handling of color is necessary at every step 2 Werner Purgathofer What is Light? “light” = narrow frequency band of electromagnetic spectrum red border: 380 THz ≈ 780 nm violet border: 780 THz ≈ 380 nm visible icrowaves traviolet M radio M radio frared nd TV -rays … … AM FM an inf ult X- m wavelength 10 16 10 14 10 12 10 10 10 8 10 6 10 4 10 2 10 0 10 -2 (nm) frequency 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 (Hz) 3 Werner Purgathofer 2
Light - An Electromagnetic Wave light is electromagnetic energy monochrome light can be described either by frequency f or wavelength q y g c = f (c = speed of light) E t shorter wavelength equals higher frequency frequency red 700 nm violet 400 nm 4 Werner Purgathofer Light – Spectrum normally, a ray of light contains many different waves with individual frequencies the associated distribution of wavelength g intensities per wavelength is referred to as the spectrum of a given ray of a given ray or light source 5 Werner Purgathofer 3
Dominant Wavelength | Frequency energy energy greenish light white light E D wave- wave- E W length length dominant 400 nm 700 nm wavelength dominant wavelength | frequency (hue color) dominant wavelength | frequency (hue, color) brightness (area under the curve) E purity E E D ...dominant energy density D W E W ...white light energy density E D 6 Werner Purgathofer The Human Eye cornea retina contains aqueous [Hornhaut] [Augenkammer] rods: b/w iris [Regen- bogen- bogen cones: color cones: color haut] lens vitreous humor [Glaskörper] optical axis visual axis rods optic disc p [Papille] fovea cones retina [Netzhaut] nerve macula lutea [gelber Fleck] 7 Werner Purgathofer 4
The Human Eye 3 types of cones diff different t fraction of wavelength absorbed light 16% sensitivities: 8% red 4% green green 2% 1% blue λ 400 440 480 520 560 600 640 680 8 Werner Purgathofer Color Blindness red/green blindness red & green cones too similar fraction of absorbed light 16% 8% 4% 2% 1% λ 400 440 480 520 560 600 640 680 9 Werner Purgathofer 5
Color Blindness red/green blindness red & green cones too similar fraction of blue blindness absorbed light 16% no blue cones 8% 4% 2% other other 1% λ cones missing 400 440 480 520 560 600 640 680 cones too similar 10 Werner Purgathofer Color Blindness Tests 5 = normal 2 = red/green weak nothing = red/green blind nothing = normal 11 Werner Purgathofer 6
Color Blindness Tests 8 = normal 8 = red/green blind 3 = red/green weak 12 = blue/yellow blind nothing = r/g blind 182 = normal 12 Werner Purgathofer Color Spaces (CS) Color Metric Spaces (CIE XYZ, L*a*b*) used to measure absolute values and differences - roots in colorimetry Device Color Spaces (RGB, CMY, CMYK) used in conjunction with device Color Ordering Spaces (HSV, HLS) used to find colors according to some criterion the distinction between them is somewhat obscured by the prevalence of multi-purpose RGB in computer graphics 13 Werner Purgathofer 7
What is our Goal? to be able to quantify color in a meaningful, expressive consistent and reproducible way expressive, consistent and reproducible way. problem: color is a perceived quantity , not a direct, physical observable 14 Werner Purgathofer Color - A Visual Sensation light light nerve nerve object eye brain stimulus signal color electromagnetic sensation rays realm of direct realm of psychology observables 15 Werner Purgathofer 8
Colorimetry CM is the branch of color science concerned with numerically specifying the color of a physically defined visual stimulus in such physically defined visual stimulus in such manner that stimuli with the same specification look alike under the same viewing conditions stimuli that look alike have the same specification ifi ti the numbers used are continuous functions of the physical parameters 16 Werner Purgathofer Colorimetry Properties Colorimetry only considers the visual discriminability of physical beams of radiation f for the purposes of Colorimetry a „color“ is an th f C l i t l “ i equivalence class of mutually indiscriminable beams colors in this sense cannot be said to be “red”, “green” or any other “color name” green or any other color name discriminability is decided before the brain - Colorimetry is not psychology 17 Werner Purgathofer 9
Color Matching Experiments observers had to match monochromatic test lights by combining 3 fixed primaries R+G+B test test green 0 1 0 1 0 1 goal: find the unique RGB coordinates for each stimulus 18 Werner Purgathofer Color Matching Experiments observers had to match monochromatic test lights by combining 3 fixed primaries R = 700.0 nm viewer G = 546.1 nm controls independently B = 435.8 nm variable p primary y sources masking viewing screen test screen source 19 Werner Purgathofer 10
Tristimulus Values the values R Q , G Q and B Q R+G+B of a stimulus Q that fulfill test test green Q R Q R G Q G B Q B are called the tristimulus values of Q in the case of a monochromatic stimulus Q , i h f i l h i the values R , G and B are called the spectral tristimulus values 20 Werner Purgathofer Color Matching Procedure (1) test field = 700 nm-red with radiance P ref observer adjusts luminance of R (G=0, B=0) (2) test light wavelength is decreased in (2) test light wavelength is decreased in constant steps (radiance P ref stays the same) observer adjusts R, G, B (3) repeat for entire visible range visible range 350 400 450 500 550 600 650 700 nm Werner Purgathofer 11
Color Matching Result !? 100 no match possible !?!? 0 350 350 400 400 450 450 500 500 550 550 600 600 650 650 700 nm 700 nm observers want to „subtract“ red light from the match side...!? 22 Werner Purgathofer Color Matching Experiment Problem for some colors observers want to reduce red light to negative values…!? but there is no negative light…! g g +G+B test test green t R+ ? 0 1 0 1 0 1 23 Werner Purgathofer 12
“Negative” Light in a Color Matching Exp. if a match using only positive RGB values proved impossible, observers could simulate a subtraction of red from the match side by subtraction of red from the match side by adding it to the test side st + R G+B test green G tes 0 1 0 1 0 1 0 1 24 Werner Purgathofer CIE RGB Color Matching Functions r( λ ) b( λ ) 100 g( λ ) ? 0 350 400 450 500 550 600 650 700 nm 435.8 nm 546.1 nm 700.0 nm 25 Werner Purgathofer 13
CIE XYZ problem solution: XYZ color system tristimulus system derived from RGB based on 3 imaginary primaries b d 3 i i i i all 3 primaries are Y imaginary colors only positive XYZ values can occur! values can occur! 1931 by CIE ( C ommission I nternationale de l’ E clairage) X Z 26 Werner Purgathofer RGB vs. XYZ negative component disappears y( ) is the achromatic luminance sensitivity RGB system XYZ system r( λ ) z( λ ) b( λ ) x( λ ) g( λ ) y( λ ) 1 0 350 400 450 500 550 600 650 700 nm 350 400 450 500 550 600 650 700 nm amounts of RGB primaries amounts of CIE primaries needed needed to display spectral colors to display spectral colors 27 Werner Purgathofer 14
CIE Color Model Formulas XYZ color model C( ) = X X + Y Y + Z Z ( X, Y, Z are primaries) normalized chromaticity values x y normalized chromaticity values x, y X Y x y Y X Y Z X Y Z 1 ( z = 1 – x – y ) complete description of color: x, y, Y X 1 1 Z 28 Werner Purgathofer CIE Chromaticity Diagram identifying complementary spectral colors colors determining dominant wavelength, purity comparing color gamuts spectral color positions are along the boundary purple line curve 29 Werner Purgathofer 15
Properties of CIE Diagram (2) representing p g complementary colors on the chromaticity diagram C 1 C C 2 30 Werner Purgathofer Properties of CIE Diagram (3) determining C s dominant wavelength and purity with the and purity with the C sp chromaticity diagram C 1 → C s C 1 C C 2 → C p ? 2 p → complement C sp C 2 C p 31 Werner Purgathofer 16
Color Spaces (CS) Color Metric Spaces (CIE XYZ, L*a*b) used to measure absolute values and differences - roots in colorimetry y Device Color Spaces (RGB, CMY, CMYK) used in conjunction with device Color Ordering Spaces (HSV, HLS) used to find colors according to some criterion the distinction between them is somewhat obscured by the prevalence of multi-purpose RGB in computer graphics 32 Werner Purgathofer RGB Color Model green (0,1,0) primary colors yellow (1,1,0) red, green, blue cyan cyan white white (0,1,1) (1,1,1) additive color model red (for monitors ) black (1,0,0) (0,0,0) blue (0,0,1) magenta (1,0,1) C( ) = R ) = R R + G + G G + B + B B C( 33 Werner Purgathofer 17
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