CS681 Computational Colorimetry

Transcription

1 9/14/17 CS681 Computational Colorimetry Min H. Kim KAIST School of Computing COLOR (3) 2 1

2 Color matching functions User can indeed succeed in obtaining a match for all visible wavelengths. So color space is 3D. We get so-called color matching functions (CMFs) of k 436, k 546 and k Color matching functions Notice that, at each of the wavelengths 436, 546 and 700, one of the matching functions is set to 1, while the other two are set to 0. In summary, k 436 c(l λ ) = c(l 436 ) c(l 546 ) c(l 700 ) k 546 Color vector Color basis vector k 700 And for mixed beams we get k 436 ldλ Ω c(l) = c(l 436 ) c(l 546 ) c(l 700 ) k 546 ldλ Ω And we can compute the k 700 ldλ Ω mapping from light to color 4 Coordinates 2

3 Bases We can insert any (non singular) 3-by-3 matrix M and its inverse to obtain: c(l) = Color vector = c(l ) c(l ) c(l ( ) M ) 1 M Color basis vector c 1 c2 c3 k 1 ldλ Ω k 2 ldλ Ω k 3 ldλ Ω k 436 ldλ Ω k 546 ldλ Ω k 700 ldλ Ω 5 Coordinates Bases Where the as c i c 1 c2 c3 describe a new color basis defined = c(l436 ) c(l 546 ) c(l 700 ) M 1 The k functions form the new associated matching functions, defined by: k 1 k 436 k 2 = M k 546 k 3 k

4 Basis specification Starting from any fixed basis for color space, such as c(l 436 ) c(l 546 ) c(l 700 ) 1: specify an invertible 3-by-3 matrix M. 2: specify three actual colors Each such c i can be specified by some light beam that generates it. Plug each such light beam into above calculation to obtain its 456 color coordinates, determining the matrix. c i l i 7 Basis specification Directly specify three new matching functions To be valid matching functions, they must arise from a basis change like the above equation, and so each matching function must be some linear combination of k 436, k 546 and k 700 else we will not respect metamerism Some cameras can mess this up 8 4

5 Basis specification 9 LMS revisited The LMS matching functions we saw originally describe a basis for color space. The coordinates of a color are called [L, M,S] t The actual basis is made up of three colors we can call [ c l, c m, c s ] The color c m is a very imaginary color. There is no real light beam with LMS color coordinates [0,1,0] t 10 5

6 Gamut Observe: we cannot find three vectors that both hit the lasso curve and contain the entire curve in their positive span. So if we want a basis where all actual colors have non-negative coordinates, at least one of the basis vectors defining this octant must lie outside of the cone of actual colors. Such a basis vector must be an imaginary color. Conversely, if all of our basis vectors are actual colors, and thus within the color cone, then there must be some actual colors that cannot be written with non-negative coordinates. In this basis, we say that such colors lie outside the gamut of this color space. 11 Remember This Color 6

7 Device Dependent Color Spaces Pros: Simple description of color for the device Natural, easy way to specify color to the user Cons: Cannot compare colors between devices Not perceptually uniform HSV Color Space Math Value: V = M = max(r,g, B). Saturation: m = min(r,g, B), Hue: C = M m, S = C /V, Jacob Rus H = (G B) / C if M = R (B R) / C (R G) / C if M = G if M = B 7

8 Device Independent Color Spaces Pros: Based on human visual perception Color specification independent of device Interchangeable color among devices Comparison, computation of small color differences Cons: CIEXYZ: not uniform CIELAB, CIELUV, CIEXYZ, Munsell: all dependent on the illuminant Perceptual Color Models Opponent primaries Three dimensions: lightness, colorfulness, and hue (L, C, H) Related to processes of human visual perception Meaningful way of describing color 8

9 9/14/17 Munsell System (1915) Five primary hues: Value range: Chroma range: Red Yellow Green Blue Purple RP 4/10 = a specific reddish purple hue of 10RP, a value of 4, and a chroma of 10 CIE Uniform Color Spaces (1976) Originated from Hunter Lab 1948 Perceptually uniform color definition Driven from CIEXYZ L*= a*= b*=

10 CIE LAB Math Simplified cone response (XYZ and a cubic root func.) Color opponent theory for computing chroma and hue Lightness: L * =116 f (Y /Y n ) 16, Color opponents: a * = 500[ f (X / X n ) f (Y /Y n )], b * = 200[ f (Y /Y n ) f (Z / Z n )], f (x) = x 1/3, x > x +16 /116, x Chroma: Hue: C * ab = (a * ) 2 + (b * ) 2, h ab = tan 1 (b * / a * ). Remember This Color 10

11 Color Differences * CIE ΔE ab Conventional Euclidean metric in a perceptually uniform color space (CIELAB) L* b* ΔE * ab = ( ΔL * ) 2 + ( Δa * ) 2 + ( Δb * ) 2 a* How does computation work? Illumination on a surface color (elementby-element product) Reflected color Three CMFs for XYZ Trichromatic response as scalar (sum of energy) 11