olor Management of Four-Primary Digital Light Proessing Projetors Journal of Imaging Siene and Tehnology vol. 50, no. 1, Jan./Feb. 2006 David. Wyble and Mithel. osen Shool of Eletrial Engineering and omputer Siene Kyungpook National Univ.
Abstrat Projetor with white primary Inreasing the luminous output possible olor management of four-primary digital light proessing projetor Diffiulty of to W beause of omplexities in the typial olor haraterization New haraterization model Aounting for the relationship digital ounts and resultant projeted olorimetry 2/26
Used projetor Introdution Not DLP inema but DLP data projetor In the offie and leture room Four primary projetor and a supplemental white hannel Treated as display eause of ompliation Unfriendly olor management approah onversion of W 3/26
Forward haraterization A mapping from devie digital oordinates to olorimetry equirement Input LUTs for linearizing the digital input signals 3 3 matrix to omplete the transformation to tristimulus spae Expansion of four primary display Linearization LUT of the fourth hannel 3 4 matrix 4/26
Inverse haraterization onversion from olorimetry to devie digital oordinates Diffiulty of inverse model One-to-many problem of to W Transformation from W bak to 5/26
Four-primary DLP projetion tehnology Four-primary DLP projetor Organization Digital miromirror devie (DMD), optis lens, and filter wheel (W) Fig. 1. Diagram of four-olor DLP projetion system: (a) light soure (b) input optis () filter wheel (e) exit optis and sreen. 6/26
Strategy for white addition Trading with W Eah time the amount of white is inreased, an appropriate amount of is removed Fig. 2. White addition sheme desribed in Kunzman and Pettitt (after Fig. 6 in ef.2). 7/26
haraterization measurements Experimental equipments Optomo EzPro 755 four-primary projetor 1024 768 pixel DMD and 2000 ANSI lumens LMT 1210 olorimeter rightness and ontrast ontrol Eliminating lipping at low or high levels Measurements ed, green, blue, and equip-digit ramp () Measuring every fifth digital ount exept for the ranges 0-10 and 245-255 Verifiation data 10 10 10 matrix of 8/26
175 60 Parameter to the TI to W were based on slightly different projetors Fig. 3. omparison of equal-digit ramp and sum of responses from,, and ramps. Note seondary ordinate axes for the differene plot. Negative areas of the differene plot show digital ounts where the output of the ombined ramps exeeds that of the equal-digit ramp for the same digital ount. Differene indiates plaes where white is mixed into system Above 175 on the equal-digit ramp indiates white addition 9/26
Forward model Proess of forward haraterization glut blut W rlut wlut ( ), ( ), ( ), { min(,, ) } M out in (1) (2) where out is the output olor, are the linearized salars,,,, andw in M is the 3 4 rotation matrix plus a dark orretin making it 3 5. 10 /26
11 /26 K W K W K W M (3) where,, and are measured tristimulus values and the sripts,,, W, and K are for full red, full green, full blue, alulated white, and blak (residual light when 0). in supersript indiates that dark orretion has been applied. K K K ( ) ( ) ( ) + + + + + + W W W 255 255, 255, 255 255, 255, 255 255, 255, (5) (4) Leftover olor that is outside of the range of separations for a given input level
Fig. 4. Forward model lookup tables. 12 /26
Forward model justifiation Primary stability Tristimulus value must not hange Although the linearized salars vary aross their range The substration and ratio of very small tristimulus values results in noisy Primaries vary little and due to this, this is suffiient justifiation Fig. 5. Primary stability. The plot shows D65 10 hromatiity oordinates of the,,, and W ramps. Thin solid line is the spetrum lous. Inset plot are 0.005 units for both axes. o 13 /26
Forward model evaluation Forward model evaluation Using the measured verifiation 10 10 10 matrix of olors Eah hannel ; 0, 32, 64, 96, 128, 170, 180, 190, 200, 210, 220, 230, 240, and 255 Emphasizing the areas of spae above 170 digital ounts where the projetor was potentially adding white 14 /26
Fig. 6. Forward and inverse model data and measurement flow. Fig. 7. Forward model results. For this and the subsequent histograms, the solid line shows umulative perentage on the seondary ordinate axes. 15 /26
16 /26 Inverse model Proess of inverse haraterization (6) (7) W W W K M, request request Not yet invertible
To be white addition At least one of values will be greater than unity theo M theo M 1 Insuffiient for prediting the atual for muh of the gamut theoretial or theo ; that ome from the use of the inverse of M request Part of the gamut where no white addition took plae (8) (9) 17 /26
18 /26 ( ) ( ) ( ) W w j W LUT W rlut rlut rlut request theo 1 1 1, min,,, M (10) (11) (12)
Flow hart Dark orret requested [Eq. (6)] alulate theoretial from dark orreted [Eq. (9)] hek if,, or theoretial is greater than 1. If not, push 1 though rgblut [Eq. (10)] If,, or theoretial is greater than 1,derive the amount of white addition w by pushing min() through LUT j [Eq. (11)] where j is if is minimum, if is minimum and if is minmum Subtrat the white addition from the requested and alulate the that would deliver the new [Eq. (12)] 1 Push the new through rgblut [Eq. (10)]-done 19 /26
Determining LUT of white Proess of LUT w 1. uild a triplet from the new value, ombined with 255 4. alulate theoretial from estimated [Eqs. (6) and (9)] (6) 2. Push through Eq. (1) to W. Maintain the W value 5. Plae the W theo relationship w within LUT 3. Estimate by matrixing as in Eq. (2) W 20 /26
21 /26 Summary of steps 3 and 4 W M M M M M 1 1 1 theo, (13) (14) (15)
Fig. 8. Invert LUTs for determining white addition. In the next, these are referred to w as LUT j 22 /26
Inverse model evaluation Inverse model evaluation (Fig. 6) ase 1 Does the inverse model aurately invert the forward model? Preisely orresponding to ase 2 Similar question When ramdomly seleted (1000) Quantized error ase 3 How well the model performed in a real-world appliation? Errors resulting from measurement and projetor variablility 23 /26
Step1 Step 2 Step 3 Fig. 9, 10, 11. olor differene results for inverse model, step1, step2, and step 3. 24 /26
Table I. olorimetri testing results 25 /26
onlusion Purposed method Forward and inverse olor management for four- primary data projetor based on DLP Inverse haraterization model Aomplished aurately enough for many appliations 26 /26