Color and compositing

Transcription

1 Color and compositing 2D Computer Graphics: Diego Nehab Summer 208. Radiometry Measurement of radiant energy in terms of absolute power Wave vs. particle Wavelength (λ), frequency (ν = c λ ), and amplitude (A) Energy (E = hν, where h is Planck s constant) and flux (Φ) The electromagnetic spectrum Pure spectral light (monochromatic colors) Prism experiment: visible light (Newton, 666) Infrared light: thermometers (Herschel, 800) Ultraviolet light: silver chloride (Ritter, 80) Spectrum representation As a continuous function of c(λ), c : R >0 R 0, λ A λ As a discrete set of values c(λ i ), c : λ, λ 2,..., λ n } R >0 R 0 λ i A λi Light emitter has a spectrum, material properties modulate the reflected spectrum Fluorescence is something else Black-body radiation B(ν, T ) = 2hν ( hν e c 2 k B T ), where kb is Boltsmann s constant () Measured by a spectrophotometer 2. Photometry How does it work? Measurement light in terms of perceived brightness to human eye Visible light λ [90nm, 700nm] approximately The human visual system Photopic vision: well-lit conditions Cones: Three types of retinal cells with distinct spectral responses Highly concentrated on fovea

2 Response curves S (short λ), M (medium λ), L (long λ) Peaks at λ = 420nm, λ = 54nm, and λ = 564nm Overlap each other Not R, G, and B What about the color-blind? Are there tetrachromats among us? Scotopic vision: low-light conditions Rods: One type of retinal cell Mostly peripheral 20 more numerous, 000 more sensitive than cones Response curve R: peak at λ = 498nm (between S and M) Things look gray-bluish at night Luminosity function Spectral sensitivity of human perception of brightness Different for photopic and scotopic vision Convert radiant flux (W) to luminous flux (lumen) Immense dynamic range : 0 0 from scotopic to photopic (brightness adaptation) Luminance vs. lightness Weber law of just noticeable difference ( ) Y L log (2) Y 0 dl dy Y () Applies only to small differences Power law ( Y L Y 0 ) (4) Modeling color perception st try: measure entire spectral distribution of stimulus and reproduce it Convex combinations of monochromatic colors Could use spectrophotometer to measure c(λ), but how would you reproduce? 2nd try: measure optical nerve response and re-inject to reproduce Remove eye, attach wires to cones: The Matrix Painful, but only values per color rd try: linear algebra Measuring c(λ) is the target color s spectral distribution 2

3 . Color representation l(λ), m(λ), and s(λ) the spectral response curves for the S, M, and L cones Inner-product functions f and g is f, g = f(λ)g(λ)dλ The cone responses to c are S c = c, s, M c = c, m, and L c = c, l Reproduction Assume different stimuli colors r(λ), g(λ), and b(λ) Which stimuli intensities R c, G c and B c produce responses S c, M c, and L c? R c r + G c g + B c b, s = S c S r S g S b R c S c R c r + G c g + B c b, m = M c M r M g M b G c = M c R c r + G c g + B c b, l = L c L r L g L b B c L c Stimuli must be linearly independent Result R c, G c, or B c could be non-convex There is no negative light... Space of visible colors All convex combinations of monochromatic colors Could use entire spectrum Unnecessary (most of the time) due to metamerism Different spectra result in same perceived color [ s m l ] Also, given α > 0, [ αs αm αl ] have same chromaticity, different brightness Similar to RP 2 CIE 9 RGB color matching functions The experiment CIE 9 XYZ color matching functions Linear transformation to R, G, B Visible colors always use non-negative coordinates Y is the photopic luminosity function Equal-energy radiator (constant SPD in visible spectrum, illuminant E) is at [ (Z ended up almost equal to S) Measured by a colorimeter Separation of chromaticity and brightness The CIE xy chromaticity diagram and CIE xyy color space Horseshoe shape Locus of monochromatic colors Locus of black-body colors Line of purples Color gamut Color calibration and matching ]

4 Gamma correction [Poynton, 998] Historically, used to compensate for input-output characteristic of CRT displays Today, it is used for encoding efficiency Lumma Y vs. luminance Y Other color spaces srgb [IEC Project Team 6966, 998] Munsel (HSV and HSL), additive (CMY and CMYK ) TV (YUV, YIQ), perceptual (CIE L a b ) Opponent color models 4. A good reference for color theory is the webpage [MacEvoy, 205] 5. Transparency [Porter and Duff, 984] Imagine semitransparent material with color f on top of opaque material with color b Assume probability of light hitting f is α Reflected color (integrated over small area) is f, α b = αf + ( α)b This is what we call alpha blending or the over operator Now imagine f, α on top of f 2, α 2 on top of b Reflected color is f, α (f 2, α 2 b) = α f + ( α ) ( α 2 f 2 + ( α 2 )b ) Can we combine f, α and f 2, α 2 into a single material f, α? αf + ( α)b = α f + ( α ) ( α 2 f 2 + ( α 2 )b ) (5) = α f + ( α )α 2 f 2 + ( α )( α 2 )b (6) So we have ( α)b = ( α )( α 2 )b αf = α f + ( α )α 2 f 2 α = α + ( α )α 2 αf = α f + ( α )α 2 f 2 (7) Let f = αf, f = α f, f 2 = α 2 f 2 α = α + ( α )α 2 f = f + ( α ) f 2 (8) This is what we call pre-multiplied alpha Blending becomes associative f, α ( f 2, α 2 b) = ( f, α f 2, α 2 ) b Should we blend front-to-back or back-to-front? 4

5 References IEC Project Team Colour measurement and management in multimedia systems and equipment. IEC/4WD , 998. Part 2.: Default RGB colour space srgb. B. MacEvoy. Hardprint: Color vision, 205. URL html. T. Porter and T. Duff. Compositing digital images. Computer Graphics (Proceedings of ACM SIGGRAPH 984), 8():25 259, 984. C. A. Poynton. Rehabilitation of gamma. In Proc. SPIE, volume 299, pages ,