WideWide ColorColor GamutGamut FiveFive ChannelChannel MultiMulti--PrimaryPrimary DisplayDisplay forfor HDTVHDTV ApplicationApplication

Journal of Imaging Science and Technology, vol. 49, no 6, November/December 2005 Moon Cheol Kim, Yoon-cheol Shin and Jin Sub Um

School of Electrical Engineering and Computer Science Kyungpook National Univ.

1 / 31 AbstractAbstract

‹ Main focus – Inverse display model • Modification of Ajito’s method – Gamut mapping method • Usage of a full range of MPD with a limited color gamut of television signal • Enhancement of the limited color saturation

2 / 31 IntroductionIntroduction

‹ Wide color gamut image system – Prevalence of high saturation color in our life – Selected device • 5-primary MPD – Usage of 120W UHP lamp with a color wheel which has 5 primary spectral band rel. intensity

Wavelength (nm) (a) (b) Fig 1. (a) Relative spectral irradiances of primary colors and the color wheel configuration , and (b) primary color coordinates on CIE-u’v’ color chart. 3 / 31 ColorColor gamutgamut

‹ Property of used device – MPD with 5 colors • Red, green, blue, cyan and orange • Selection by considering the characteristic of UHP lamp – Forward model • Conventional additive model – Linear property of DMD (digital mirror device) and faithful circuits – Negligible black offset = M .CF Where F = (X,Y,Z)T : Tristimulus values = ( C,C,C,C,CC 54321 )T : Linear display control vector (1) ⎛ XXXXX ⎞ ⎜ 54321 ⎟ : 5 primary measured from CS1000 (2) M = ⎜ YYYYY 54321 ⎟ ⎜ ⎟ ⎜ ZZZZZ ⎟ ⎝ 54321 ⎠ 4 / 31 – Comparison of gamut size in CIELab space • Adoption of Hill’ method – Procedure

» Assumption of unit sphere with Δ E ab = 1 (JND) » Filling of each gamut with above spheres and counting – Uncovered color in some region with MPD » Composition of white with 5 time-sequential primary color Colors (Million) uncovered

(a) (b) Fig 2. (a) Perspective view of the MPD gamut in CIELAB76 color space in comparison with the Rec.709 (sRGB) gamut, and (b) gamut volume comparison: distinguishable colors of CRT, MPD and Optimal Color Space(human) for CIE 2° standard observer. 5 / 31 InverseInverse displaydisplay modelmodel

‹ Modified switching model of Ajito – Procedure • Splitting of gamut to several pyramids • Selection of pyramids – Necessity of very big 2D_LUT for searching a involved pyramid • Calculation of control vector v β ,and,, γ with linear equation

U β * γ * −+−+= FFFFF ),13()12(1 F = vU

Where < v < 10

6 / 31 ‹ Modified Procedure

≤ α β γ ≤ 1),,(0

(a) Procedure of Ajito Fig 5. (a) Block diagram of the parallel matrix switching

7 / 31 ‹ Usage of Agito’s model – Composition of pyramid with 4-primares •PP − )2( number pyramids without overlapping (Fig 3(a)) – 5 vertex including common vertex as the black point • Generation of Graphical gamut (Fig 4(a).) – One or zero value for all vertices » Assumption that all primaries are on the gamut surface – PP − + 2)1( surface vertices and PP − )2( pyramids

Fig 3. (a) Color gamut Fig 4. (a) Graphical gamut surface analysis and (b) chromaticity diagram in XYZ space 8 / 31 – Linear equation for computing a control vector

* βα* γ * −+−+= FFFFFF )13()12(1 (3)

Where ≤ α β γ ≤ 1),,(0

F = (X,Y,Z)T : Given parameter • Direct mapping α β γ ),,( to control vector • Simplification of physical constraint condition and existence condition

Fig 3. (b) Vector addition within the pyramid 9 / 31 – Mapping of α β γ ),,( to control values for input F • Exclusive-OR bit-operation(-) between the control values of vertices of a selected pyramid •Example T T T T – CF1 = ) CF 2 = ) CF 3 = ) ,1,1,1,0(,1,1,0,1(,1,1,0,0( and CB = 0,0,0,0( ) – Calculation of the assignment vector

T T α 1-CCA BF == 1,1,0,0( ) ,,0,0( αα) T T β 2-CCA BF == 0,0,0,1( ) β 0,0,0,( ) T T γ 3-CCA BF == 0,0,1,0( ) γ 0,0,,0( )

– Final control vector C = ,,,( ααγβ)T

10 / 31 ‹ Modified Procedure

≤ α β γ ≤ 1),,(0

(a) Fig 5. (a) Block diagram of the parallel matrix switching

11 / 31 – Replacement of color space • YWV color space ⎛ Y ⎞ ⎛ X ⎞ ⎛ 010 ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜W ⎟ T ⋅= ⎜ Y ⎟ with, T ⎜ −−= 643.0187.054.0 ⎟ (3) ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ V ⎠ ⎝ Z ⎠ ⎝ −− 234.0478.1823.1 ⎠

⎛ Y ⎞ ⎛ RL ⎞ ⎛ RL ⎞ ⎛ 072.0715.0213.0 ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ (4) ⎜W ⎟ ⋅= MT 709 ⎜GL ⎟ N ⋅= ⎜GL ⎟ with, N ⎜ −−= 5.0249.025.0 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ V ⎠ ⎝ BL ⎠ ⎝ BL ⎠ ⎝ − 0433.0433.0 ⎠ – For efficient ASIC design –Linear YCbCr – More convenient gamut mapping then in XYZ » Simple computation of chroma and hue

22 ⎡ V ⎤ chroma += VW and H = Arctan ⎥ (5) ⎣⎢W ⎦ – Advantage with a parallel process behind 12 / 31 – Parallel process (in hue plane) • Calculation of hue • Finding m candidate pyramids for the computed hue – Division of hue with the same as 8 pyramid before (Fig 5(b)) – Consistence of two subgroups with overlapping

»~ SS 2421 (non-overlap each plane) with “Ai ” hue line

»~ SS 3431 (non-overlap each plane) with “Bi ” hue line – Determination of m(=P-2) related pyramids for the input » Result from considering HFi (hue field) and Table 1

Table I

13 / 31 – Consist of pyramids on WV-plane

Fig 5(b). example of individual hue field division (HF0~HF7) for 4 primary MPD: S21~S34 indicate the base planes of pyramids – Table to find m related pyramid TABLE I. Hue field regions (HF0~HF7) and the related base planes of pyramids

14 / 31 – Update of M matrix data • For the parallel matrix conversion • Matrix data LUT – All coefficients of conversion matrix from YWV to α β γ ),,( for all pyramids

– Parallel matrix conversion

• Obtaining m candidate control vectors, α β γ 1 α β γ ),,(~),,( m

15 / 31 – Constraint conditions • Physical constraint – ≤ α β γ ≤1),,(0 • Center allocation between two pyramids for given F

Fig 3(c). Case of multiple solution

16 / 31 • Solution of second constraint to get a best single solution – Trigonometrical proportionality » Formulation of proportionality equation * =− α FFFF /1)12/(1 Lmax » Satisfied condition for existence of β − FF )12(* within the pyramid

β − FF )12(* < Lmax » Satisfied condition for existence of γ − FF )12(* α ≥ β, and α ≥ γ

Fig 3(d). Illustration for constraint check 17 / 31 – Obtainment of the final valid vector α β γ ),,( valid • Calculation of assignment vectors α β AA(A γ ),, • Arrangement into appropriate channels

18 / 31 GamutGamut matchingmatching

‹ Best method for gamut matching – Adoption of combining gamut mapping in an intensity linear YWV and in a uniform color space • Combination of simple way and better result way • Method for characteristic of hue constancy and uniformity of hue and chroma – Transformation from XYZ to YWV color space – Rough rescale of W,V axes for human percetion

19 / 31 • Comparison of YWV and CIELab color space – Better hue constancy in YWV » Insufficient hue and chroma uniformity

Fig 6. Upper: equally quantized colors on Y = constant, WV-planes with equidistant hue (11.25° step) and chroma (0.05 step), Lower: their transform into CIE-L*a*b*. 20 / 31 – Comparison of hue constancy with scaling » Better performance in blue region

Fig 7. Hue constancy of YWV in comparison with CIE-LAB (all color scales are quantized by 10 equidistant chroma at constant hue and luminance/ lightness): Hue deviation in blue and red color scale of CIELAB can be observed.

21 / 31 ‹ Best gamut mapping method (future work) – Adaptive gamut mpping • Combination two method – Simple chroma matching at constant lightness and hue » Desaturation in gray region at Fig 8 – Vector mapping for removing desaturation and contouring » Complex computation and time consumming

Fig 8. Gamut comparison in YWV space and mapping concept. 22 / 31 ‹ Conversion of color space from YWV to DIN99d – Disadvantage of YWV color space • Un-uniform space – Difficulty with linear compression or stretching of the chroma

– DIN99d (Lab99d space) • Improvement of uniform color space • Modified contents – Logarithmic chroma compression in radial direction – Logarithmic transformation of lightness • Effective chroma and vector mapping

Fig 9. Gamut comparison in Lab99d pace 23 / 31 – Mapping properties in YWV color space • Chroma mapping – Too much enlargement in cyan colors – Desaturation in red area • Vector mapping – More natural results – Luminance attenuation problem

(a) Chroma mapping (b) Vector mapping Fig 10. Gamut mapping results; (a), (b): mapping in YWV space. A: Chroma streching, B: chroma compression, C: adaptive mapping, and D: vector stretching. 24 / 31 – Mapping properties in Lab99d color space • Similar result with adaptive matching in YWV color space • Better estimation of an appropriate stretching gain • No need to combine chroma matching with vector matching

(a) Chroma mapping (b) Vector mapping Fig 10. Gamut mapping results; (c), (d): mapping in YWV space. A: Chroma streching, B: chroma compression, C: vector mapping, and D: vector stretching.

25 / 31 ImplementationImplementation

‹ Performance of real application – Reproduction of two kind of images •sRGB • Wide color gamut images

Fig 5(a)

Fig 11. Simplified signal flow in FPGA 26 / 31 – First above block

• 32×32 ×32 equidistant linear RGBL signals for Gamut mapping – Simple and low computational intensity • 3D-LUT for gamut mapping – YWV value from PC based mathematical program • Interpolation – Calculation of intermediate YWVint – Tetrahedral interpolation

27 / 31 – Blow block to test wide gamut images

•CIELAB76 signal interface – Usage of conventional television RGB interface in a PC mode • Procedure – Obtaining wide gamut image by Color Aixpert – Gamut mapping for the signal which is out of normal gamut but in of MPD gamut » External program on the PC – Conversion Lab to XYZ and XYZ to YVW

28 / 31 ExperimentsExperiments

‹ Color reproduction error – 3×3×3×3×3 (measured 243) patches for test

• Average error with ΔEab = 35.2

• Max error with ΔEab = 8.5 – Vibrant color reproduction and more details with real life image

29 / 31 ‹ Result images – Not reproducible color with black color

Fig 12. Original MUSP images (Top), reproduced images on MPD (Mid), and reproduced on CRT (Bottom); black marked pixels are colors out of each display gamut.

30 / 31 ConclusionConclusion

‹ Focus – Method for using a full rage of color gamut of MPDs for a given liminted color gamut signal ‹ Success – Real time processing by parallel performance in inverse display model

– Optimization process of mapping in LAB99d ‹ Future work – Noise in dark color by using Ajito’s method – Development of optimal gamut mapping

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