1. School of Electrical and
Color Halftoning
Jan Allebach
School of Electrical and
Computer Engineering
Purdue University
West Lafayette, IN

2. Big Picture of Pipeline for NPAC Halftoning
Color Space Transformation
Color Gamut Mapping and Tetrahedral Interpolation
Linearization
Source colors
(sRGB color space)
Tone Correction Curve
XYZ color space
Source sRGB color space in YCxCz coordinates
(8 sRGB NPs: W, C, M, Y, CM, CY, MY, CMY)
Color
mapping +
Table 1: NP area cover (NPAC) and the corresponding YCxCz coordinates when R, G, B changing form 0 to 255
Table 2: YCxCz coordinates of 8 NPs
DBS
Output halftone image
Tetrahedral
interpolation
YCxCz color space
(8 Indigo NPs: W, C, M, Y, CM, CY, MY, CMY)
XYZ color space
Destination color (CMY color space)
Input continuous image

3. Outline Color Management
Step 1: Source and Destination Color Space Transfer
Step 2: Color Gamut Mapping
Step 3: Get the percentage of NPs based on Tetrahedral Interpolation Method
Separation Image

4. Step 1: Color Space Transformation
Source sRGB color space in YCxCz coordinates
(8 sRGB NPs: W, C, M, Y, CM, CY, MY, CMY)
Source colors
(sRGB color space)
XYZ color space
Color
mapping
Getting from reflectance file
YCxCz color space
(8 Indigo NPs: W, C, M, Y, CM, CY, MY, CMY)
Destination color
(CMY color space)
XYZ color space

5. Substep 1: Source Color Transfer
Transfer from sRGB to XYZ color space, which is independent device color space, then to YCxCz color space. or
(R,G,B) in sRGB color space
(X,Y,Z) in XYZ color space
(Y,Cx,Cz) in YCxCz color space
sRGB to XYZ
XYZ to YCxCz

6. Source Gamut in YCxCz Color Space
The source image gamut is distributed in the cube composed by 8 NPs
NPs
YCxCz coordinate Y Cx Cz W
E-14 C M CM
8.3694 CY MY
CMY

7. Substep 2: Destination Color Transfer
1). Get XYZ coordinates based on reflectance spectra
The HP Indigo reflectance can getting from ‘glossydata.txt’.
The illuminant and color matching functions (CMFs) are shown in bottom figures.
D50 Illuminance
Color Matching Function (CMFs)

8. Substep 2: Destination Color Transfer
2). Transform from XYZ to YCxCz
(C,M,Y) in printer color space
(X,Y,Z) in XYZ color space
(Y,Cx,Cz) in YCxCz color space

9. Destination Gamut in YCxCz Color Space
The region spanned by the printed colors in YCxCz is larger than the polyhedron defined by the 8 NPs
The mismatch is caused by printer
Ignore the error caused by the mismatch for now
color
YCxCz coordinate Y Cx Cz W
3.4639E-14
1.3323E-14 C M
3.2936 CM
2.8509
7.8085 CY MY
82.719
CMY
2.176
1.2295

10. Outline Color Gamut Mapping
Step 1: Source and Destination Color Space Transfer
Step 2: Color Gamut Mapping
Step 3: Get the percentage of NPs based on Tetrahedral Interpolation Method
Separation Image

11. Step 2: Color Gamut Mapping
The coordinates of W and CMY NPs are different between source and destination color space

12. Step 2: Color Gamut Mapping
Idea: Only change the lightness and saturation during the mapping, but don’t change the hue of colors
Procedure
Mapping white and black NPs.
Remain the hue unchanged, based on the compression color mapping method to get the corresponding coordinates of all source colors

13. Procedure of Color Gamut Mapping
Step 1: Mapping white and black NPs.
Step 2: Remain the hue unchanged, based on the compression color mapping method to get the corresponding coordinates of all source colors
Step 2
Step 1
Mapping white and black NPs
Color gamut mapping result

14. Color Gamut Mapping Result
Two example of color mapping
Mapping NP: magenta (as indicated by the green arrow)
Mapping NP: yellow (as indicated by the green arrow) o
(33.03,169.47, ) o
(46.46,27.24,-20.16) o
(107.62,-58.85,160.11) o
(71.91,-18.65,69.62)

15. Color Gamut Mapping Result
Do the color mapping for each color in sRGB color space, finally, we can get the mapping color in destination YCxCz color space. As shown in the figure:
Source YCxCz color space
Mapping result

16. Outline Color Gamut Mapping
Step 1: Source and Destination Color Space Transfer
Step 2: Color Gamut Mapping
Step 3: Get the percentage of NPs based on Tetrahedral Interpolation Method
Separation Image

17. Step 3: Tetrahedral Interpolation
Based on the mapping YCxCz coordinate of each source color, we will get the percentage of destination NPs based on tetrahedral interpolation.
The destination color gamut can be divided into several tetrahedrons
tetrahedrons

18. Step 3: Tetrahedral Interpolation
1). Determine which Tetrahedron is P(Y,Cx,Cz) belonging to
Each tetrahedron have four vertexes, we can get three linearly independent vectors
Any point /color in a tetrahedron can be expressed by three vectors
tetrahedron x y z o *
(Y,Cx,Cz)
The coordinate (Y, Cx, Cz) can be expressed by:

19. Step 3: Tetrahedral Interpolation
1). Determine which Tetrahedron P(Y,Cx,Cz) belongs to x y z o *
(Y,Cx,Cz)
P(Y, Cx, Cz) should belong to tetrahedron (W,C,M,CMY), if it satisfies the following constrains:

20. Look Up Table (LUT) of Color Gamut Mapping
Mapping coordinate in destination color gamut
Percentage of NPs
One-to-one correspondence R G B
NP(W)
NP(Y)
NP(C)
NP(CY)
NP(M)
NP(MY)
NP(CM)
NP(CMY) Y Cx Cz 1 …
255
254
RGB
combination in total
Express the destination NPs by sRGB
W(216,216,223)
C(0,79,177)
M(187,1,44)
Y(236,188,0)
CM(6,3,41)
CY(0,67,11)
MY(186,2,2)
CMY(7,4,5)

21. Outline Color Gamut Mapping
Step 1: Source and Destination Color Space Transfer
Step 2: Color Gamut Mapping
Step 3: Get the percentage of NPs based on Tetrahedral Interpolation Method
Separation Image

22. Separation Image
Based on the LUT of color gamut mapping, we can generate the separation image, which each separation image corresponding to a NP
Original Image W C M Y CM CY MY
CMY
Table 1
Getting the percentage of NPs corresponding to each pixel

23. Separation Image 8 Separation images corresponding to 8 NP channels
Black means the percentage of NP almost be 0 W C M Y CM CY MY
CMY