1 (L-cone, M-cone, S-cone) (Luminance, L-M, S-(LM)) CRT ( 2) (a) (b) (c) (d) RGB rgb XYZ LMS DKL (e) 2 RGB ( 3) G 255 B R 3 RGB XYZ xyy

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1 DKL ) DKL (Luminance, L-M, S-(LM)) RGB DKL 2) Brainard 1996 LMS DKL 3) DKL (L-cone, M-cone, S-cone) L-, M-cone parvocellular pathway S-cone koniocellular pathway DKL retinotectal pathway S-cone S-cone (S-cone isolating stimuli) S-cone retinotectal pathway L M S RGC = Lum LM L-M S-Lum = S-(LM) 1 pooneil68@gmail.com 1

2 1 (L-cone, M-cone, S-cone) (Luminance, L-M, S-(LM)) CRT ( 2) (a) (b) (c) (d) RGB rgb XYZ LMS DKL (e) 2 RGB ( 3) G 255 B R 3 RGB XYZ xyy x,y Y luminance CIE xyy ( 4) ( LMS cone excitation LMS retinal ganglion cell DKL ( 5) LGN DKL Derrington AM, Krauskopf J, Lennie P (1984) Chromatic mechanisms in lateral geniculate nucleus of macaque. J Physiol (Lond) 357: DKL MacLeod and Robert M. Boynton (1979) Chromaticity diagram showing cone excitation by stimuli of equal luminance J. Opt. Soc. Am., Vol. 69, No. 8, p MacLeod- Boynton color space 2

3 4 xyy equiluminant plane (Wikimedia Commons) Lum:1 S:-1 L-M:-1 L-M:1 S:1 Lum:-1 5 DKL 1.2 RGB LMS 2 RGB 8bit (0-255) ( 3) linear (gamma 1 ) RGB (255) 1 ( rgb ) ( (a)) Gamma rgb = (RGB 1/γ RGB(0))/RGB(255) lookup table XYZ ( (b)) rgb XYZ 3

4 LMS Spectrometer (e) CRT RGB ([ ], [ ], [ ]) spectrometer RGB L-cone, M-cone, S-cone λ spectrometer bin λ spectrometer C(λ i )( RGB 9 ) L-cone, M-cone, S-cone bin L abs (λ i ) M abs (λ i ) S abs (λ i ) L = M = S = n L abs (λ i )C(λ i ) λ (1) i=1 n M abs (λ i )C(λ i ) λ (2) i=1 n S abs (λ i )C(λ i ) λ (3) i=1 L-cone, M-cone, S-cone Smith, V. C. and Pokorny, J. (1975). Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm. Vision Research, 15, Stockman, A., and Sharpe, L. T. (2000). (4) Spectral sensitivities of the middle- and longwavelength sensitive cones derived from measurements in observers of known genotype. Vision Research, 40, Web site ( human psychophysical validation Spectrometer XYZ LMS (c) L M S = X Y Z (5) RGB [R G B] cone [L M S] Brainard, D. H., Pelli, D.G., and Robson, T. (2002). Display characterization. In the Encylopedia of Imaging Science and Technology. J. Hornak (ed.), Wiley web 4

5 LMS DKL (d) 2 LMS DKL 2.1 LMS DKL Brainard, D. H. (1996). Cone contrast and opponent modulation color spaces. In Kaiser and Boynton, Human Color Vision, 2cd edition, Optical Society of America, Washington, DC. web LMS background ([L 0 ]) = L L 0 M S (6) DKL space background DKL space um LM lum (7) luminance L-M S-(LM)=Sluminance um/k 1 LM/k 2 lum/k 3 = A = w 1 w 2 w 3 w 4 w 5 w 6 w 7 w 8 w 9 (8) w 1 w 9 k 1 k 3 12 k 1 k 3 normalization 2.2 w 1 w 9 w 1 w 9 Lum Lum = k1 (w 1 L w 2 w 3 ) (9) w 1 = 1 w 2 = 1 w 3 = 0 luminance L-cone M-cone S-cone (9) Lum = k 1 (1 L 1 0 ) (10) LM lum 5

6 LM = k 2 (w 4 L w 5 w 6 ) (11) lum = k 3 (w 7 L w 8 w 9 ) (12) LMS background LMS chromaticity LM lum 0 k( 0) L = k L 0 (13) LM = 0 (14) lum = 0 (15) (13) (12) (12) 0 0 = k 2 k (w 4 L 0 w 5 w 6 ) (16) 0 = k 3 k (w 7 L 0 w 8 w 9 ) (17) LM S-cone w 6 = 0 (17) 0 = k 2 k (w 4 L 0 w 5 ) (18) (12) w 5 w 5 = w 4 L0 (19) LM = k 2 k w 4 (1 L L 0 0 ) (20) k 2 k 2 w 4 LM = k 2 (1 L L 0 0 ) (21) lum = 0 (22) Lum = 0 (23) 6

7 lum = 0 (24) (10) 0 = k 1 (1 L 1 ) (25) = 0 (26) L = 0 (27) lum = 0 (28) (12) 0 = k 3 (w 7 L w 8 L) (29) w 7 = w 8 (17) w 8 (12) w 9 0 = k 3 k (w 7 L 0 w 7 w 9 ) (30) w 9 = L 0 w 7 (31) lum = k 3 w 7 (1 L 1 L 0 ) (32) k 3 k 3 1 w 7 lum = k 3 ( 1 L 1 L 0 ) (33) (8) A Lum/k 1 LM/k 2 lum/k 3 = L L 0 L (34) 2.3 k 1 k 3 k 1, k 2, k 3 normalization DKL Brainard 1996 Brainard

8 DKL pooled cone contrast 1 Pooled cone contrast C = ( L L 0 ( ( (35) Cone contrast DKL space DKL space DKL = [1 0 0], [0 1 0], [0 0 1] pooled cone contrast 1 Brainard 1996 A web A 1 1 = L (36) L 0 0 = A 1 um/k 1 LM/k 2 lum/k 3 (37) DKL = [1 0 0], [0 1 0], [0 0 1] pooled cone contrast 1 = A 1 = A 1 = A 1 1/k 1 0/k 2 0/k 3 0/k 1 1/k 2 0/k 3 0/k 1 0/k 2 1/k 3 = 1/k 1 L 0 = 1/k 2 L 0 = 1/k 3 L 0 L (38) (39) (40) pooled cone contrast 1 k 1, k 2, k 3 (38) (35) 1 C = ( L0 /k 1 L 0 L 0 ( M0 /k 1 L 0 ( S0 /k 1 L 0 (41) = 1 3 k 1 L 0 (42) = 1 (43) 8

9 k 1 = 3 L 0 (44) (39) (35) 1 C = ( L0 /k 2 L 0 ( M0 /k 2 L 0 ( 0/k2 L 0 (45) = 1 L 2 0 M0 2/L 0 k 2 L 0 (46) = 1 (47) k 2 = L 2 0 M 2 0 /L 0 L 0 (48) (40) (35) 1 C = ( 0/k3 L 0 ( 0/k3 L 0 ( S0 /k 3 L 0 (49) = 1 1 k 3 L 0 (50) = 1 (51) k 3 = 1 L 0 (52) um LM lum = 1 L L 2 0 M 2 0 /L 0 L 2 0 M 2 0 / L 0 (53) Brainard 1996 LMS [ ] t Background LMS [ ] t LMS = [ ] t (53) L 0,, A (54) Brainard 1996 (A.4.11) 9

10 LMS DKL 2 (b)-(e) PC DKL 5 DKL CRT normalization 1 background L 0 S0 background A DKL (Y/2 ) 3 DKL normalization k 1 k 3 pooled cone contrast normalization Lum. L-M. S perceptual luminance S-cone contrast detection task Brainard 1996 DKL CRT DKL Lumimance 1 Michelson contrast 1 DKL = [1 0 0] t RGB = [ ] t background background S-lum S-lum 1 L-M DKL RGB DKL L-M S 10

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