1. Put the theory into practice. Use the Colour Conversion Matrix of
Equation 6 to convert RGB coordinates
into Y, (R-Y), (B-Y) coordinates.
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

2. +1 Y’ -1 +1 Fig 7 R’-Y’ B’-Y’ -1 +1 Each of the next 9
Black
(0,0,0) 1 +1 Y’ -1 +1
Fig 7
R’-Y’
B’-Y’
Each of the next 9
foils will map one point
of the R’G’B’ unity colour space
into the Luma and colour difference space.
Just ‘play’ the foils by flicking through them with the
‘PageDn’ key on your keyboard and watch how the unity colour
cube is translated into a Luma & colour difference space cube. -1 +1
Luma & Colour Difference
colour space
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

3. Map the WHITE Co-ordinate
(1,1,1)
R’G’B’ White = [1,1,1] +1
Insert the R’G’B’ unit colour space
coordinates into the matrix transform,
here….
……. And then evaluate the
matrix multiplication.
Plot the new coordinates
on the Luma and colour
difference axis -1 +1
R’-Y’
B’-Y’
Fig 8 -1 +1
Y’ R’ [ *R’ *G’ *B’] = Y’601
B’- Y’ = G’ = [ *R’ *G’ *B’] = B’- Y’601
R’- Y’ B’ [ *R’ *G’ *B’] = R’- Y’601
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

4. Map the WHITE Co-ordinate
(1,1,1)
R’G’B’ White = [1,1,1] +1 -1 +1
Fig 9
R’-Y’
B’-Y’
Plot these
co-ordinates -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

5. Map the Black Co-ordinate
R’G’B’ Black = [0,0,0] +1 -1 +1
Fig 10
R’-Y’
B’-Y’
Plot these
co-ordinates -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

6. Map the YELLOW Co-ordinate
Black
(0,0,0)
0.886
R’G’B’ Yellow = [1,1,0] +1 -1 +1
R’-Y’
Fig 11
0.114
B’-Y’
Plot these
co-ordinates -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

7. Map the GREEN Co-ordinate
(0,1,0)
R’G’B’ Green = [0,1,0] +1
0.587 -1 +1
Fig 12
R’-Y’
B’-Y’
Plot these
co-ordinates
-0.587 -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

8. Map the CYAN Co-ordinate
(0,1,1)
R’G’B’ Cyan = [0,1,1] +1 -1
0.701 +1
Fig 13
R’-Y’
B’-Y’
Plot these
co-ordinates
-0.701
0.299 -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

9. Map the BLUE Co-ordinate
R’G’B’ Blue = [0,0,1] +1 -1 +1
Fig 14
R’-Y’
-0.114
B’-Y’
Plot these
co-ordinates
0.114 -1
0.886 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

10. Map the MAGENTA Co-ordinate
(1,0,1)
R’G’B’ Magenta = [1,0,1] +1 -1
0.413 +1
0.587
Fig 15
R’-Y’
B’-Y’
Plot these
co-ordinates
0.587 -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

11. Map the RED Co-ordinate
(1,0,0)
R’G’B’ Red = [1,0,0] +1
0.299 -1 +1
0.701
Fig 16
R’-Y’
-0.299
B’-Y’
Plot these
co-ordinates -1 +1
Y’ [ ]
B’- Y’ = = [ ] =
R’- Y’ [ ]
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

12. The diagram below shows how the (R’G’B’) to (Y’, B’-Y’, R’-Y’) colour space transform re-maps the R’G’B’ unity cube to an area that is 25% of the volume allowed by the maximum excursion of the new axis’. +1
If the colour difference cube was mapped
using 8 bit quantization for each axis,
only 25% of the codes would be legal. -1 +1
Fig 17
R’-Y’
B’-Y’ -1
This introduces the concept
of valid signals (i.e., luma and
color difference signals are found on the
Y and B-Y, R-Y axis, but they may not be legal
because they do not sit inside the 25% of volume that
represents the translated colour space.) +1
Colour legalizers and colour correctors are based on colour space convertors.
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

13. B A F C -1 D E R’-Y’ B’-Y’ G -1 Fig 18 +1 H
…In fact, the remapped colour space occupies
maximum excursions in all three axis that are
not convenient for engineering in either analogue
or digital systems.
To understand this better, let’s project
all the colour points down onto the R-Y
and B-Y axis. A F C -1 D E
R’-Y’
B’-Y’ G -1
Fig 18 +1 H
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14. B A C -1 D R’-Y’ B’-Y’ -1 Fig 19 +1 View the cube via the plane ABCD
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- All Rights Reserved

15. B A C -1 D R’-Y’ B’-Y’ -1 Fig 20 +1 See how the points project
down onto the B-Y and R-Y axis A C -1 D
R’-Y’
B’-Y’ -1
Fig 20 +1
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

16. B A C -1 D R’-Y’ B’-Y’ -1 Fig 21 +1 Now, take away the box and look at
a top-level projection of the axis on
the next foil. A C -1 D
R’-Y’
B’-Y’ -1
Fig 21 +1
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

17. A need to scale the colour difference axis+1 B C
We can see that the maximum excursions of
the colour difference axis are
B’-Y’ = +/
and
R’-Y’ = +/
These are inconvenient for transmission in
practical systems, so the new colour space is
re-scaled (or weighted), to give the colour
difference axis an excursion of +/- 0.5.
0.701
+0.866 -1
B’-Y’ +1
-0.866
-0.701
Fig 22
R’-Y’ A -1 D
Scaling the above B’-Y’ and R’-Y’ axis to give maximum excursions of +/- 0.5 causes some confusion
because of the different nomenclatures used to represent the scaled axis. (Note that the luminance channel
Y’ still has a max excursion of ‘1’ so no scaling is necessary and it is still named Y’).
Scaled B’-Y’, R’-Y’ are sometimes referred to as “weighted colour difference channels” or “± 0.5V colour
difference components” or “PB & PR” .
Whilst there is plenty of scope for confusion in the actual nomenclature, PB & PR are the terms often used to
represent the ± 0.5V analogue outputs on the rear panels of most studio broadcast equipment.
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

18. Create Y’, PB PR From Y,B-Y,R-Y
-0.5
0.5
+0.5 PR A B C D
The vector scope image now looks more symmetrical after the colour difference channels have been scaled to ± 0.5V.
The scaling/weighting factors used to normalise the colour difference channels to unity excursion are : PB
PR = ( R’- Y’601 ) = (R’- Y’601 )
(Equation 7)
PB = (B’- Y’601 ) = (B’- Y’601 )
(Equation 8)
Fig 23
The matrix multiplication below is the definition of Y PBPR. We can see that the matrix multiplication required to convert R’G’B’ signals into Y, PB, PR signals now has the scaling factors of and included to normalise the B-Y and R-Y axis to ± 0.5.
Y’ R’
PB = ( x 0.564) ( x 0.564) (0.886 x 0.564) G’ (Equation 9)
PR (0.701 x 0.713) ( x 0.713) (-0.114x 0.713) B’
Andy Miller © Copyright 2000 Xilinx
- All Rights Reserved

19. Re-Normalize B’-Y’ & R’-Y’ to Create Y’PBPR
Evaluating the bracketed multiplications in the previous matrix equation for Y,PBPR will give numbers that are close to those below. Some rounding has taken place, but the matrix now represents the scaling factors that have to be applied to R’G’B’ data in order to get Y’ PB PR signals.
Y’ R’
PB = G’ (Equation 10)
PR B’
A quick digression…..The Matrix transform for Y’UV
Another set of colour coordinates that are found within the video industry are “YUV.” These are legacy signals from the days of analogue processing and were introduced to ensure that the composite luma & modulated chroma signal were contained within the amplitude limits of the analogue signal processing and recording equipment. The colour difference channels (R-Y’ and B-Y’) were scaled/weighted by the following factors.
U = (B’-Y’601) V = (R’-Y’601)
The matrix for R’G’ B’ to YUV conversion is given by.
(Equation 11)
Which evaluates to the following coefficients.
(Equation 12)
Y’ R’
U = ( x 0.493) ( x 0.493) (0.886 x 0.493) G’
V (0.701 x 0.877) ( x 0.877) (-0.114x 0.877) B’
Y’ R’
U = G’
V B’
(Press your “Page Down”
key to end the presentation.)