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

2. Outline 1. Description of NPAC-DBS
2. Experimental results showing effect of different color spaces and HVS models on halftone quality.
3. Example color images halftoned using NPAC-DBS and color PARAWACS based on a DBS screen
(a) A color ramp
(b) The Ruiyi image
(c) The church image

3. Description of NPAC-DBS Imaging pipeline
TRC for target output device (Indigo Press)
Selection matrix/ random selection
Unlinearized NPAC image set
Linearize
with TRC
Linearized NPAC image set
(For printing purpose)
Initial NP images
Unlinearized NPAC image set
(For display purpose)
NPAC image sets
and
NP DBS
Halftoned NP images
NP image
in CMYK/sRGB
Initial NP images
(CMYK image is for print sRGB is gamma corrected for display)

4. Description of NPAC-DBS High level description
For display purposes:
sRGB halftone image
&
CMY halftone description
NPAC image set (non-linearized)
NPAC-DBS
(Does not account for dot gain)
NPAC image set (linearized)
For printing purposes:
CMYK halftone image
(Account for dot gain)
(These halftones are not the same)

5. Description of NPAC-DBS Block Diagram
Random selection NP
YyCxCz
Initial NP image
(GNP )
NPAC image set
eYy ~
GYy
eYy
GYyCxCz - ~
GCx
eCx
eCx ~
eYyCxCz
GNP
GNP’ - E
GCz
eCz ~
eCz -
Accept or reject the swap
Linear trasfor-mation
FYy
FYyCxCz
Here,
FCx
where
FsRGB
is the autocorrelation of HVS point spread function for the i th component of the opponent color space. ,
(original image in linear sRGB color space)
FCz

6. NPAC-DBS block diagram cont’d
After obtaining the final NP halftone, replace NP in each pixel with the corresponding sRGB values to get final halftoned image for display, or replace with the corresponding CMYK values to get halftoned image for printing.
Replace NP on each pixel with sRGB
Halftone in sRGB
(with gamma correct)
Final NP halftone
(generated from non-linearized NPAC image set)
Replace NP on each
pixel with CMYK
Final NP halftone
Halftone in CMYK
(generated from linearized NPAC image set)

7. NPAC image set to initial NP image
Let be the area coverage of the Neugebauer Primaries in an NPAC image, where k denotes the Neugebauer Primary, , and is the location of pixel on the NPAC image, where , and M is the height, N is the width of the image.
Also, let a randomly generated number be , and the Neugebauer Primary being selected for pixel is denoted , where , and satisfy the following condition:
Note:
In theory, can be a very large number, here, can be as large as 255.

8. Delta E calculation
First, calculate the continuous tone image represented in YyCxCz color space according to the halftone image and error.
Where
Next, calculate autocorrelation of point spread function:
Then, calculate correlation between point spread function and perceived error:
Finally,
normalize

9. Outline 1. Description of NPAC-DBS
2. Experimental results showing effect of different color spaces and HVS models on halftone quality.
3. Description of how PARAWACS works
4. Example color images halftoned using NPAC-DBS and color PARAWACS based on a DBS screen
(a) A color ramp
(b) The Ruiyi image
(c) The church image
5. Screens and example images for the CMYK halftones

10. Effect of different color spaces and HVS models on halftone quality
HVS models investigated:
1. Nasenan’s luminance channel HVS model
2. Mullen’s chrominance channel HVS models
3. Wandell’s HVS model
4. Daly’s luminance channel HVS model

11. Nasenan’s Frequency domain Filter
For filtering luminance channel, we chose HVS Nasanen Model, which is given as
where a = 131.6, b = , c = 0.525, d = 3.91, Γ is the average luminance of the light reflected from the print in cd/m2, usually set to 11, and and are the spatial frequency coordinates in cycles/degree subtended at the retina.

12. Nasenan’s spatial domain Filter
Generate HVS point spread function
Windowing p(r) : Circular window size is 6 ( the spread of h(r) )
Where
Normalize p(r) ~
In 2D, , where corresponds to pixel coordinates.
Lee, C. (2008). Hybrid screen design and automatic portrait image enhancement. (Doctoral dissertation)

13. Blue-yellow channel contrast sensitivity function
cycles/degree
Approximation by Kolpatzik and Bouman to experimental data collected by Mullen, which is given as:
where and are the spatial frequency coordinates in cycles/degree subtended at the retina.
Mullen, K T, (1985), The contrast sensitivity of human colour vision to red-green and blue-yellow
chromatic gratings.. The Journal of Physiology, 359 doi: /jphysiol.1985.sp

14. Red-green channel contrast sensitivity function
cycles/degree
Approximation for Red-Green channel contrast sensitivity based on data collected by Mullen:
where and are the spatial frequency coordinates in cycles/degree subtended at the retina.

15. Mullen’s filters in spatial domain
Red-Green and Blue-Yellow channel filters are generated in similar way as Nasenan’s filter.
Generate HVS point spread function
Windowing p(r) : Circular window size is 6 ( the spread of h(r) )
Normalize p(r) ~
Where ,
for Red-Green channel.
for Blue-Yellow channel.
In 2D,

16. Wandell’s HVS filters Wandell’s spatial kernel is: where
The scale factor is chosen so that sums to 1, the scale factor is chosen so that for each color plane, its two-dimensional kernel sums to one.
The parameters for the three color planes are:
Where spread is in degrees of visual angle.
Plane
Weights ωi
Spreads σi
Luminance
0.921
0.0283
0.105
0.133
-0.108
4.336
Red-Green
0.531
0.0392
0.330
0.494
Blue-Yellow
0.488
0.0536
0.371
0.386
Zhang & Wandell (1997). A spatial extension of CIELAB for digital color image
reproduction, SID Journal.

17. Daly’s HVS model Daly HVS model:
Where spatial frequency has unit of cycles/degree, a = 2.2, b = 0.192, c = 0.114, d = 1.1, = 6.6
Daly’s HVS model with respect to spatial frequency in cycles/inch:
Where is

18. Comparison between Wandell, Daly and Nasenan frequency domain models

19. Comparison between Wandell, Daly and Nasenan spatial domain filters

20. YyCxCz and Wandell Color Space halftone results comparison
Luminance: Nasenan’s
Chrominance: Single Mullen
chrominance channel filter
Luminance: Daly’s filter
Chrominance: Single
chrominance channel filter
Wandell O1O2O3 filter ✔
Color Space: YyCxCz
Color Space: Wandell
Color Space: YyCxCz
Normalized Error:
Normalized Error:
Normalized Error:
NPAC set: 40% Yellow, 20% Magenta, 0% Cyan-Magenta, 40% White
Image size: 512 x 512
Filter parameter: S=3000

21. YyCxCz and Wandell Color Space halftone results comparison
Luminance: Nasenan’s
Chrominance: Single Mullen
chrominance channel filter
Luminance: Daly’s filter
Chrominance: Single
chrominance channel filter
Wandell O1O2O3 filter ✔
Color Space: YyCxCz
Color Space: Wandell
Color Space: YyCxCz
Normalized Error:
1.4263
Normalized Error:
5.2454
Normalized Error:
NPAC set: 40% Cyan, 20% Magenta, 0% Cyan-Magenta, 40% White
Image size: 512 x 512
Filter parameter: S=3000

22. YyCxCz and L*a*b* Color Space halftone results comparison
Luminance: Nasenan’s filter
Chrominance: Single chrominance channel filter
Very
similar
Color Space: YyCxCz
Color Space: L*a*b*
Normalized Error:
Normalized Error:
NPAC set: 40% Yellow, 20% Magenta, 0% Cyan-Magenta, 40% White
Image size: 512 x 512
Filter parameter: S=3000

23. YyCxCz and L*a*b* Color Space halftone results comparison
Luminance: Nasenan’s filter
Chrominance: Single chrominance channel filter
Very
similar
Color Space: YyCxCz
Color Space: L*a*b*
Normalized Error:
Normalized Error:
NPAC set: 40% Cyan, 20% Magenta, 0% Cyan-Magenta, 40% White
Image size: 512 x 512
Filter parameter: S=3000

24. Outline 1. Description of NPAC-DBS
2. Experimental results showing effect of different color spaces and HVS models on halftone quality.
4. Example color images halftoned using NPAC-DBS and color PARAWACS based on a DBS screen
(a) A color ramp
(b) The Ruiyi image
(c) The church image

25. Example halftone images
NPAC-DBS
Parawacs selection matrix
Original image

26. Example halftone images
NPAC-DBS
Parawacs selection matrix
Original image

27. Example halftone images
NPAC-DBS
Parawacs selection matrix
Original image

28. Thank you !