Introduction to Color Science (Cont)
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1 Lecture 24: Introduction to Color Science (Cont) Computer Graphics and Imaging UC Berkeley
2 Empirical Color Matching Experiment
3 Additive Color Matching Experiment Show test light spectrum on left Mix primaries on right until they match The primaries need not be RGB
4 Example Experiment Slide from Durand and Freeman 06
5 Example Experiment p 1 p 2 p 3 Slide from Durand and Freeman 06
6 Example Experiment p 1 p 2 p 3 Slide from Durand and Freeman 06
7 Example Experiment The primary color amounts needed for a match p 1 p 2 p 3 Slide from Durand and Freeman 06
8 Experiment 2: Out of Gamut Slide from Durand and Freeman 06, Lecture 15, Spring 2016
9 Experiment 2: Out of Gamut p 1 p 2 p 3 Slide from Durand and Freeman 06, Lecture 15, Spring 2016
10 Experiment 2: Out of Gamut p 1 p 2 p 3 Slide from Durand and Freeman 06, Lecture 15, Spring 2016
11 Experiment 2: Out of Gamut We say a negative amount of p 2 was needed to make the match, because we added it to the test color s side. The primary color amounts needed for a match: p 1 p 2 p 3 p 1 p 2 p 3 p 1 p 2 p 3 Slide from Durand and Freeman 06, Lecture 15, Spring 2016
12 The Color Matching Experiment is Linear If matches and matches then matches Brian Wandell
13 CIE RGB Color Matching Experiment Same setup as additive color matching before, but primaries are monochromatic light (single wavelength) of the following wavelengths defined by CIE RGB standard Kayvon Fatahalian The test light is also a monochromatic light
14 <latexit sha1_base64="wl0252l/dqwpjl1qzoh92xkycxe=">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</latexit> Color Matching Functions Recall our analysis of color reproduction as linear algebra R 4G5 = 4 r S r M 5 6 4s R s G s B 7 5 C A 4 r S r M s5 B r L r L 3 5 = 2 4 r S s R r S s G r S s B r M s R r M s G r M s B r S r M s5 r L s R r L s G r L s B r L Nx3 This Nx3 matrix contains, as row vectors, color matching functions associated with the primary lights s R, s G, s B.
15 CIE RGB Color Matching Functions Graph plots how much of each CIE RGB primary light must be combined to match a monochromatic light of wavelength given on x-axis b( ) r( ) ḡ( ) Careful: these are not response curves or primary spectra!
16 <latexit sha1_base64="wnhan9lzt/jfuzulh/+lt/gltj4=">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</latexit> Color Reproduction with Matching Functions For any spectrum s, the perceived color is matched by the following formulas for scaling the CIE RGB primaries Z b( ) r( ) R CIE RGB = s( ) r( ) d ḡ( ) Z G CIE RGB = s( )ḡ( ) d Z B CIE RGB = s( ) b( ) d Careful: these are not response curves or primary spectra!
17 <latexit sha1_base64="i3w7wh3g9ubstmq/imisowjhi08=">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</latexit> sha1_base64="boayurrhvpywsz4mpojj5r2to+s=">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</latexit> Color Reproduction with Matching Functions For any spectrum s, the perceived color is matched by the following formulas for scaling the CIE RGB primaries Written as vector dot products: R CIE RGB = s r b( ) r( ) G CIE RGB = s ḡ ḡ( ) B CIE RGB = s b <latexit sha1_base64="kkmo15mvvnwqcaptewldkm+vtuq=">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</latexit> <latexit sha1_base64="kkmo15mvvnwqcaptewldkm+vtuq=">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</latexit> <latexit sha1_base64="kkmo15mvvnwqcaptewldkm+vtuq=">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</latexit> Matrix formulation: R 4G5 = 4 r ḡ b s5 B CIE RGB Careful: these are not response curves or primary spectra!
18 Color Representation
19 Color Spaces Need three numbers to specify a color but what three numbers? a color space is an answer to this question Common example: display color space define colors by what R, G, B scalar values will produce them on your monitor (in math, s = rr + gg + bb for some spectra r, g, b) device dependent (depends on gamma, phosphors, gains, ) therefore if I choose R,G,B by looking at my display and send it to you, you may not see the same color also leaves out some colors (limited gamut), e.g. vivid yellow
20 Standard Color Spaces Standardized RGB (srgb) makes a particular monitor RGB standard other color devices simulate that monitor by calibration srgb is usable as an interchange space; widely adopted today gamut is still limited
21 A Universal Color Space: CIE XYZ Imaginary set of standard color primaries X, Y, Z Designed such that CIE XYZ color matching functions X, Y, Z span all observable colors Matching functions are strictly positive Y is luminance (brightness absent color) Imaginary because can only be realized with primaries that are negative at some wavelengths
22 Luminance (Lightness) Integral of radiance scaled by the visual luminous efficiency Z Dark adapted eye (scotopic) Daytime adapted eye (photopic) Y = ( ) V ( )d V ( ) Luminous efficiency )V ( ) is a measure of how bright a light at a given wavelength is perceived by a human (nm)
23 Separating Luminance, Chromaticity Luminance: Y Chromaticity: x, y, z, defined as since x + y + z = 1, we only need to record two of the three usually choose x and y, leading to (x, y, Y) coords
24 CIE Chromaticity Diagram Pure (saturated) spectral colors around the edge of the plot Less pure (desaturated) colors in the interior of the plot White at the centroid of the plot (1/3, 1/3)
25 Gamut Gamut is the set of chromaticities generated by a set of primaries Because definition of xy is linear, interpolation between chromaticities on a chromaticity plot is also linear So the gamut is the convex hull of the primary chromaticities
26 Gamut srgb is a common color space used throughout the internet CIE RGB are the monochromatic primaries used for color matching tests described earlier
27 Perceptually Organized Color Spaces
28 HSV Color Space (Hue-Saturation-Value) Axes correspond to artistic characteristics of color
29 Perceptual Dimensions of Color Hue the kind of color, regardless of attributes colorimetric correlate: dominant wavelength artist s correlate: the chosen pigment color Saturation the colorfulness colorimetric correlate: purity artist s correlate: fraction of paint from the colored tube Lightness (or value) the overall amount of light colorimetric correlate: luminance artist s correlate: tints are lighter, shades are darker
30 Perceptual Non-Uniformity In the xy chromaticity diagram at left, MacAdam ellipses show regions of perceptually equivalent color (ellipses enlarged 10x) Must non-linearly warp the diagram to achieve uniform perceptual distances Wikipedia
31 CIELAB Space (AKA L*a*b*) A commonly used color space that strives for perceptual uniformity L* is lightness a* and b* are color-opponent pairs a* is red-green, and b* is blue-yellow A gamma transform is used for warping because perceived brightness is proportional to scene intensity γ, where γ 1 3
32 Opponent Color Theory There s a good neurological basis for the color space dimensions in CIE LAB the brain seems to encode color early on using three axes: white black, red green, yellow blue the white black axis is lightness; the others determine hue and saturation one piece of evidence: you can have a light green, a dark green, a yellow-green, or a blue-green, but you can t have a reddish green (just doesn t make sense) thus red is the opponent to green another piece of evidence: afterimages (following slides) slide credit: Steve Marschner
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37 Image Afterimage
38 Adapt
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40 Even simple judgments such as lightness - depend on brain processing (Anderson and Winawer, Nature, 2005)
41 Everything is Relative
42 Everything is Relative
43 Everything is Relative
44 Everything is Relative
45 Everything is Relative
46 Everything is Relative
47 Everything is Relative
48 Everything is Relative
49 Things to Remember Physics of Light Spectral power distribution (SPD) Superposition (linearity) Tristimulus theory of color Spectral response of human cone cells (S, M, L) Metamers - different SPDs with the same perceived color Color reproduction mathematics Color matching experiment, per-wavelength matching functions Color spaces CIE RGB, XYZ, xy chromaticity, LAB, HSV Gamut
50 Acknowledgments Many thanks and credit for slides to Steve Marschner, Kayvon Fatahalian, Brian Wandell, Marc Levoy, Katherine Breeden and James O Brien.
51
52 Extras
53 Response of S,M,L Cones to Monochromatic Light Visualization of human cone S cells response to monochromatic light (light with energy in a single wavelength) as points in 3D space. This is a plot of the S, M, L response functions as a point in 3D space. Space of all possible responses are linear combinations of points on this curve. L M Marc Levoy
54 Subtractive Color Produce desired spectrum by subtracting from white light (usually via absorption by pigments) Photographic media (slides, prints) work this way Leads to C, M, Y (cyan, magenta, yellow) as primaries Approximately, 1 R, 1 G, 1 B [source unknown]
55 Subtractive Color Describes Reflected Spectrum [Stone 2003]
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