Conversion Between Colour Systems

Transcription

1 C M C M CM Conversion etween Colour Systems I Q CPSC 553 P

2 Colour Models For Computer raphics colour cube. Transform to CIE and from CIE to iven a monitor whose phosphors have known CIE coordinates it is possible to find the corresponding CIE primaries: Xr, r, Zr etc are the weights applied to red, green and blue phosphors to find X Z : X Z Xr Xg Xb r g b Zr Zg Zb or X Z M M can be calculated for a particular monitor and transformations made for others. CPSC 553 P 2

3 to CIE It is important to be able to convert between systems (, IQ, CM) etc. can be converted to CIE (the standard) and all others to. To convert to CIE we need to find matrix M. A monitor with CIE coordinates for each of the red, green and blue phosphors are given as ed: xr, yr reen: xg, yg lue: xb, yb let Cr Xr + r + Zr by definition the CIE coordinates of the red phosphor are: xr Xr/(Xr + r + Zr) Xr / Cr yr r/(xr + r + Zr) r / Cr zr xr yr Zr/(Xr + r + Zr) Zr / Cr so Xr xrcr so r yrcr so Zr zrcr similarly for green and blue. CPSC 553 P 3

4 to CIE In Matrix form for the red primary: M we have: Xr xrcr r yrcr Zr zrcr X Z Xr Xg Xb r g b Zr Zg Zb substituting for elements of M: X Z x r Cr x g Cg x b C b y r Cr y g Cg y b C b ( x r y r )Cr ( x g y g )Cg ( x b y b )C b To find Cr, Cg, Cb (Method ) We may know the luminances (measurable with a photometer) this means we know the values (see definition of CIE primaries) and the CIE coordinates so: r y r Cr so Cr r /y r C g g /y g Cb b /y b CPSC 553 P 4 F&VD p587

5 Luminance is all in the To find Cr, Cg, Cb (Method 2) We can measure Xw, w, Zw for white when : X Z x r C r x g Cg x b Cb y r C r y g Cg y b C b ( x r y r )Cr ( x g y g )Cg ( x b y b )Cb From above equation and take out the C s into a column vector: X Z x r x g x b y r y g y b ( x r y r ) ( x g y g ) ( x b y b ) Cr Cg Cb CPSC 553 P 5

6 Knowing the CIE coordinates and luminance of white White may be given as xw, yw and the luminance value w but xw Xw/(w+Xw+Zw) and yw w/(w+xw+zw) dividing : xw / yw Xw / w in which case: Xw xww/yw CPSC 553 P 6

7 Converting between other systems C M Cyan subtracts red from white light, ++ + C C M similarly: ++ + M ++ + CM is CM for black for white CPSC 553 P 7

8 IQ System ecording of for transmission efficiency for Television roadcasting. is luminance (as in the CIE primaries) for black and white TV only is shown. Chromaticity encoded in I and Q The IQ mapping is defined as : I Q Matrix based on standard NTSC phosphors ed reen lue x y CPSC 553 P 8

9 Colour Calculation Consider the following phosphor: ed reen lue elative tri chromatic x } amounts of X,, Z in y a given amount of z each phosphor. We wish to compute the brightness required for these phosphors to produce a colour with CIE coordinates x c, y c We also need a target luminance of say Lc Only the primary has any brightness. The y co ordinate expresses the relative brightness (in whatever units). i.e. The relative amounts of X Z primary: x c X c / (X c + c + Zc ) and yc c / (X c + c + Zc ) and x r Xr / (X r + r + Zr ) etc. CPSC 553 P 9

10 Luminance (milli Lamberts) and Tri Chromatic Units (TCU s) In fact we can use whatever units we like, these are known as Tri Chromatic Units (TCU s) ed reen lue x y z Choose TCU of red phosphor is equivalent to 0.345mL in brightness. The y coordinate now represents number of ml for each phosphor (x and z do not carry brightness information.) or ml of ed Phosphor is /0.345 TCU s ml of reen Phosphor is /0.585 TCU s ml of lue Phosphor is /0.066 TCU s TCU s.709 TCU s 5.52 TCU s CPSC 553 P 0

11 rassman s Law When lights are mixed, the X,, Z for the mixture is the sum of the component X,, Z s E.g. lights 2 and 3 exactly match light, so: X X 2 + X Z Z 2 + Z 3 we have x c X c / (X c + c + Zc ) chromaticity coordinates of x c, y c given by: x c (X r + X g + Xb ) (X r + X g + Xb ) + ( r + g + b ) + (Z r + Z g + Zb ) rewrite as: x c ΣX and y c Σ ΣX + Σ + ΣZ ΣX + Σ + ΣZ CPSC 553 P

12 TCU s for a light The total number of TCU s for a light is the sum of X,, Z So for our target light # TCU s X c + c + Zc Also Lc c r + g + b millilamberts since the primary carries luminance information We want to find the luminance of each phosphor, Lr, Lg, Lb To calculate the amount of ΣX primary: 3 contributions, and phosphors ed Contribution: amount of red phosphor emission in ml # of TCU s given by ml Lr * /yr * xr Proportion of TCU s contributing to X similarly for reen and lue CPSC 553 P 2

13 Calculate the contributions to X Z red phosphor green phosphor blue phosphor ΣX Lr * /yr * xr + Lg * /yg * xg + Lb * /yb * xb ΣX Lr * * Lg *.709 * Lb * 5.52*0.55 Lr *.82 + Lg * Lb * Σ Lr * /yr * yr + Lg * /yg * yg + Lb * /yb * yb simplifying gives: Σ Lr + Lg + Lb Lc (no surprise!) ΣZ Lr * /yr * zr + Lg * /yg * zg + Lb * /yb * zb ΣZ Lr * Lg * Lb *.803 x c Lr*.82+Lg*0.586+Lb*2.348 () found from : ΣX Lr*2.898+Lg*.709+Lb*5.5 ΣX + Σ + ΣZ CPSC 553 P 3

14 The final calculation We have x c And y c given by: y c Lr + Lg + Lb (2) Lr*2.898+Lg*.709+Lb*5.5 Suppose we want our target to be equal energy white at 20mL x c y c z c since x c + y c + z c From () we get 0.854Lr + 0.6Lg 2.702Lb 0 From (2) we get 0.034Lr Lg 4.050Lb 0 and we have Lr + Lg + Lb Lc 20 solving these 3 equations gives: Lr 4.54 ml Lg 3.94 ml Lb.52 ml CPSC 553 P 4