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

2. YCxCz DBS [Agar and Allebach 2005]
Lum. and Chrom.
Spatial Freq. Res.
HVS model to f
[m] Y y C x C z f
[m]
YyCxCz f
YyCxCz ( x) ~
Input R G B +
Continuous-tone
Image e
YyCxCz ( x ) T ~ ~ e
YyCxCz ( x )d
E = - g
YyCxCz ( x ) ~
HVS model C M Y to
Lum. and Chrom. g
[m] Y C C g
[m]
Spatial Freq. Res. y x z
YyCxCz
Initial
Halftone C M Y
under test
accept or reject the trial halftone change
Halftone

3. CMYK halftoning algorithm [Lee and Allebach,
Designed for bi-level CMY printers (or CMYK printers w/ full under color removal).
A colorant-based halftoning algorithm which operates on CMYK colorant space;
can give us explicit control over individual and combined colorant textures.
can directly minimize dot-on-dot printing.
Based on direct binary search (DBS) to enforce exclusion of visually non-homogeneous patterns.
-The target for the proposed halftoning algorithm is bi-level 3 CMY printers, or bi-level CMYK printers with full under color removal.
So I will restrict my discussion to these printers.
As its name implies, the proposed halftoning algorithm is a colorant-based algorithm.
Since it directly operates on CMYK colorant space, it gives us two very important advantages;
First, we can explicitly control the quality of individual and combined colorant textures.
Second, we can minimize dot-on-dot printing which can cause noisy texture and very limited color gamut.
The proposed algorithm uses DBS to enforce exclusion of visually non-homogeneous patterns.
In the next a couple of slides, I’ll explain what is DBS.

4. Proposed halftoning approach
First formulate color design criteria for uniform color textures.
Halftone the image via the DBS technique to meet these criteria.
-In our color halftoning scheme, we first define color design criteria for uniform color textures and use DBS to meet these criteria.

5. Criteria for uniform color texture
We would like ...
the dots of each color (C, M, Y, R, G, B, or K) to be arranged as uniformly as possible.
the overall composite texture consisting of all these colors to be as uniform as possible.
to minimize dot-on-dot printing as much as possible.
-Hear are our three uniform color criteria;
The first criterion is for individual color pattern --- that is the dots of each color must be arranged as uniformly as possible.
The second criterion states that the overall dot patterns must be as uniform as possible.
By overall dot pattern, I mean a kind of ON-and –OFF monochrome dot structures. If there is any color pixel in a given position, we may say that pixel is ON, otherwise it is OFF.
And the last criterion is that we should avoid any dot-on-dot printing as much as possible.

6. Y colorant is much less visible than those of C & M.
Example 1: C 40%, M 20%
Want to have uniform individual C and M dot patterns as well as uniform total dot arrangement.
Y colorant is much less visible than those of C & M.
Total dot coverage: 60% (w/ perfect dot-off-dot printing).
Halftone a 60% fill solid patch with monochrome DBS.
Color dots initially by random threshold.
Iteratively modify C & M pattern with swap-only DBS.
-Now let’s consider in some detail how we actually can design halftone texture for a constant patch which consist of 40% cyan and 20% magenta.
In this example, we exclude yellow components.
In fact, we halftone yellow component totally independently since it is much less visible than cyan and magenta dots.
Any way, for this image, we first set dots for overall dot patterns.
In order to set overall dot pattern, we halftone a 60% fill sold patch with monochrome DBS since the total dot coverage is 60% without any dot-on-dot printing.
We then randomly color this monochrome framework by cyan and magenta like this.
To set individual dot pattern optimally, we iteratively perform swap between C and M until it converges.
Notice that during this swapping, the overall dot pattern is preserved.
Only the individual color pattern is altered.
Set dots for CM
Randomly color dots
Swap between C & M
iteratively

7. Search strategy for swap-only DBS
Perform trial swaps between C and M:
swap1
swap2
-The idea of swap-only DBS is quite similar to the original monochrome DBS.
-We also scan the halftone image in rater order, At each color pixel of halftone image, we try swap between C and M.
-In this example, cyan is the pixel under consideration. So we try swap this pixel with neighboring M pixels.
Here the error measure is the form of weighted sum of C error and M error;
In other words, we accept the trial swap change if it gives us better individual C and M dot patterns.
Halftone
swap3
Accept pattern with the lowest error metric value, which measures the uniformities of C and M dot patterns.

8. Total dot coverage: 130% (introduces 30% B).
Example 2: C 50%, M 80%
Total dot coverage: 130% (introduces 30% B).
C’=100%-M=20%; M’=100%-C=50%.
Halftone a 70% (C’+M’) fill solid patch with monochrome DBS.
Color dots initially by random threshold.
Iteratively modify C & M patterns with swap-only DBS.
Fill holes by B.
Set dots for CM
Randomly color dots
Swap between C & M
iteratively
Fill holes by B
-Before extend our discussion to real images, we will take another example.
-This example is quite similar to the previous example, except that the total dot coverage is greater than 100%.
-Since the the total dot coverage is 130%, at least some portions of C and M have to piled up together introducing the 30% of blue.
-In this case, the percentage of pure cyan, which is denoted by C’ is 1-M, which is 20%. By pure cyan, I mean the Cyan component which do not contribute to Blue.
Similarly, we have 50% of pure magenta here.
Then we halftone a 70% fill patch with monochrome DBS to set overall dot patterns.

9. Extension to real image
Define additional grayscale functions:
-The previous two examples gives us an ideal how to extend our approach to imagery.
We begin by defining the following three gray scale functions.
fC[m] and fm[m] represent intensity of C and M of original image at pixel m.
If their sum is greater than 1, then we extract the blue component from them and we define them as fC’[m] and fm’[m]. Otherwise we don’t change them.
And fCM[m] is the sum of these two grayscale values.
From input CMY image, we compute fCM[m] based on this equation and apply monochrome DBS to set overall dot patterns for cyan and magenta.
Once we set-up the total dot pattern, we apply swap-only DBS to set individual dot pattern optimally.
Again, Y is halftone independently, and the final color halftone is obtained by superposing three halftone images for C,M, and Y.
CM-to-C’M’
conversion
Monochrome
DBS
Swap-only
DBS
CMY
input
Superposition
CMY
halftone
Monochrome
DBS

10. Error metric for Swap-only DBS
Dual error measure
-As I mentioned before, the error measure for swap-only DBS is a dual measure which is the weighted sum of cyan error and magenta error.
And again, each error is total square error between perceived original image and perceived halftone image.
We use equal weights in our experiment.

11. Experimental Results Plane-independent DBS
We compare color halftones from
Plane-independent DBS
HP DeskJet 970 Cx printer driver
Proposed CMYK-DBS
-To test the performance of the proposed halftoning algorithm, we compare color halftones from
Plane-independent DBS, where we apply monochrome DBS to each of color planes independently.
HP DeskJet 970 Cx printer driver, which is based on color error diffusion.
And the proposed CMYK DBS.

12. Experimental Results (a) Plane-independent DBS
-Well, seems like we loose the halftone texture by the projector.
Due to excessive color interference, the result of plane-independent DBS is overall much grainier than those two halftones.
(b) HP DeskJet 970 Cx driver
(c) CMYK DBS

13. Experimental Results Plane-independent (b) HP DeskJet (c) CMYK DBS DBS
970 Cx driver
(c) CMYK DBS

14. Conclusions for model-agnostic approach
The CMYK DBS color halftoning algorithm is based on the CMYK colorant space.
The CMYK halftoning algorithm directly controls the quality of textures corresponding to each colorant, both separately and in combination.
The proposed algorithm yields visually smooth and fine halftone textures. -