1. 2.3 Printer-model-based halftoning

2. Outline Halftoning with embedded printer models Electrophotographic
Inkjet
Black-box model

3. Digital marking engine technologies: laser electrophotographic
text
Typical low-end laser electrophotographic printer: HP LaserJet M252dw $ List
Architecture of laser electrophotographic printer
Instability of electrophotographic process

4. Commercial/industrial scale electrophotographic printing
HP Indigo Press ,000 4-color sheets/hr.
HP Indigo Press color sheets/hr.

5. Electrophotographic (EP) print models for halftoning [Baqai and Allebach, 2001; Goyal and Allebach, 2008] Outline
EP print modeling approaches
Print characterization
Equivalent grayscale image
Using equivalent grayscale image in DBS

6. EP print characterization approaches
Hard circular dot overlap model
Early use by Roetling and Holladay (1979), Stucki (1981), and Stevenson and Arce (1985)
Popularized and extended to tabular approach and color by Pappas et al (1991, 1993, 1997)
Simplified center-offset approach developed by Wang et al (1994)
Widely used in color halftoning
Tone compensation
Comparative study (Rosenberg, 1993)
Show examples from Farhan’s work

7. EP print characterization approaches (cont.)
Stochastic models
Micro-grid-based random toner particle models (Lin and Wiseman, 1993; Flohr and Allebach, 1993)
Density-based random toner particle models (Flohr, Allebach, and Bouman, 1994)
Scattering models
Bulk properties-based (Yule and Nielsen)
Point-spread-function-based (Kruse and Gustavson, 1996)

8. Equivalent grayscale image
Image rendered on print
Equivalent grayscale image summarizes effect of dot overlap within each device-addressable cell
Bit Map
Detailed model for rendered halftone

9. Representing the 3x3 Dot Configurations
Weights assigned to binary-valued pixels in computing decimal representation (minus one) 20 21 22 23 24 25 26 27 28 1 1 1 1
………. 1 2 3 4
512

10. Print characterization
Step 1. Print patterns with fudicial marks
Step 2. Segment out fudicials and compute centroids.

11. Print characterization (cont.)
Step 3. Partition cells, segment dot patterns (yellow), stack dot patterns, and compute statistics
Pixel size

12. Sample dot statistics Minimum Variance Pattern
Maximum Variance Pattern
Avg. = 0.76, Std. Dev. = 0.089
Avg. = 0.58, Std. Dev. = 0.480

13. Generating equivalent gray scale image
Halftoning
f[m,n]
Binary halftone pattern
LUT from
Scan Analysis
g[m,n] (Equivalent grayscale image)
Indices of dot configuration

14. Use of equivalent gray-scale image in DBS
Replace binary digital halftone by equivalent grayscale image
Perceived error with printer model
Efficient evaluation of effect of trial changes is still possible, but with greater computational complexity

15. Error metric
Assume that for a fixed bit map , is statistically independent of for
First term is metric for deterministic DBS, based on mean error.
Second term penalizes use of unstable binary patterns.

16. Simulated printer output
Artifact probably due to tone-correction
DBS with no printer model
DBS with hard circular dot model

17. Simulated printer output (cont.)
DBS with no printer model
DBS with hard circular dot model

18. Digital marking engine technologies: inkjet
text
Typical low-end inkjet printer: HP DeskJet 1122 Printer $29.95 List
Characteristics of inkjet printed dots
Architecture of low-end moving carriage inkjet printer
Page-wide array used with HP OfficeJet Pro products
Illustration of print head architecture and print masking concept

19. Commercial/industrial scale inkjet printing
HP T400 color inkjet web press – 800 ft./min.
HP Scitex flatbed press (UV cured ink)

20. Inkjet modeling issues
Most printer model-based halftoning work has focused on EP printers
IJ printers do render dots having a nearly hard, ideal profile, and much more stable than those rendered by EP printers
However, there exist artifacts which are unique to or more significant in inkjet printing process
ink coalescence (firing adjacent nozzles simultaneously)
satellites (firing the nozzle at higher frequency than they can handle)
random dot placement errors (geometrical error in print head)
This slide will explain why we had to develop a model for inkjet printer.
Conventional printer models proposed in the literature have been developed primarily for the EP laser printers.
However, there exist artifacts which are unique to or more significant in inkjet printing process such as
ink coalescence, satellites, and dot displacement errors.
Ink coalescence is caused by firing adjacent nozzles at the same time. Firing nozzle at very high frequency generates satellites. Random dot placement errors are due to the geometric error in print head.
The tabular method may be employed for inkjet printer since there’s no assumption about the printer model.
However, models that represent just what is on the printed page will be limited to predict the complex random nature of the artifact like the random placement errors.
Even if the tabular model can approximate the ink jet printer to some extent, it will require a very large number of measurements

21. Overview of inkjet printing process
Multiple-pass printing and print mask
The pen visits each pixel location more than once
multiple-pass printing is usually used to prevent artifacts such as the ink coalescence and the satellites
print mask provides extra logic control; whether the pen should put a drop in this pass or not
Before going further, let me pause here little bit and explain the basic inkjet printing operations. ….
As the print mask periodically tiled over the media, pen sweeps across the media and marks every other pixel location if there is a data point needed to be marked. Afterwards, the media is advanced half of the pen length and printing resumes.
All entries that are missed by M1 the first time, are picked by M2 during the second visit. The print masks enforce hardware limitations on firing frequency and avoid the consecutive firing of the same nozzle. 1
Pen Sweep
Direction
Media
Advance
Vertical position
of pen for the 1st pass
of pen for the 2nd pass

22. Overview of inkjet printing process (cont.)
Nozzle geometry
cyan
magenta
yellow
Front view
This figures shows the geometry of nozzles.
The print head contains nozzles for three colorants, cyan, magenta, and yellow and each colorant is assigned two columns of nozzles. The drop will travel roughly perpendicular to the nozzle plate at the nozzle.
However, as we you can from the bottom figure, nozzle columns are located on the the curved part of the nozzle plate. Hence the normals to nozzle plate at each nozzle column have a slight inward tilt, causing the drop to travel slightly inward.
This causes the dot placement error.
This artifact has to be compensated by means of halftoning algorithm. Thus in this work, we are focused primarily on the dot placement error.
Intended target
Nozzle
columns
Nozzle
columns
Drop trajectory
Top view
Nozzle plate
Silicon
Ink feed slot
Silicon

23. Modeling specifics Objectives
Development of an inkjet printer model for the target printer
Incorporation of the inkjet printer model into halftoning algorithms
Target printer
HP InkJet 970 Cx printer
Target printing mode
resolution: 600 dpi
printing direction: uni-directional printing mode
printing speed: 10 inch/sec
6-pass printing mode
each of even and odd raster lines is printed with different nozzle column
Our objective is two-fold.
…….. A little later on
We used an HP InkJet 970 Cx as our test vehicle.
And we also used the best mode of the printer as our target mode.
The detail specifications are as follows;
Let’s go back to left the previous slide. ..
This implies that there could be significant mean shift between the lines.

24. Print Characterization
Printout (scanned) +
Segmentation map)
Test pattern (600x600)
even
odd
This is the test image.
We use magenta colorant for the test image
To measure the individual dot statistics, we left some spaces between black pixels. The right image shows the scanned version of the test image where the segmentation map is overlaid. Here the yellow circle is the segmentation mask.
even
odd *

25. Print Characterization (cont.)
Dot profile
Estimate the dot profile based on the measured the absorptance of each segmented cell
Dot displacement
ref. line
After segmentation, we estimate the dot profile based on the measure the absorptance of each segmented cell.
To measure the individual dot displacement, we first need to locate the ideal spot where the center of dot was supposed to be located.
We call it reference line.
To measure the individual sample dot displacement, we first locate the centroid of each dot and compute average centroid of the dots on the same line and use it as a reference line.
Then, the displacement of a dot is gonna be the difference between its centroid and the reference line.
ref. line
* ref. line = averaged centroid
* displacement = centroid - ref. line

26. Printer Characterization (cont.)
This is the mean dot profile. Y axis is the absorptance.
Magenta. Its value is around 0.6.
mean dot profile
std. dev. dot profile

27. Print Characterization (cont.)
This is the mean dot profile. Y axis is the absorptance.
Magenta. Its value is around 0.6.
horizontal dot displacements
for even raster
horizontal dot displacements
for odd raster

28. Print Characterization (cont.)!
vertical dot displacements
for even raster
vertical dot displacements
for odd raster

29. Printer model-based DBS (Conceptual)
– DBS seeks to minimize the statistical average over the ensemble of all possible realization of e
real
printer
EQGS
sampler
HVS
bitmap
Error
original
image
ideal
printer
HVS

30. Error measure
The first term on RHS: deterministic measure based on the mean value of
The second term on RHS: penalizes the random fluctuations between dots
We used two error measures: 1st term only and 1st and 2nd terms

31. Experiments How well DBS can exploit the printer model?
Experimented with simulated printers
How well the model characterizes the printer?
Experimented with the actual printer

32. Simulated printer for testing how DBS can exploit printer model
digital halftone bitmap
low resolution
rendered
bitmap
(high resolution)
rendered
bitmap Up
sampler
Printer
model
Simulated printer
digital halftone
bitmap
low resolution
rendered
bitmap
high resolution
rendered
bitmap

33. Simulated printer: never-centered printer
Dot profile: ideal square dot
Dot displacement: fixed dot placement
even raster: shifted by X/2
odd raster: shifted by -X/2

34. Simulated printer: never-centered printer*
DBS with no printer model
DBS with printer model
*Even raster shifted by X/2; odd raster shifted by -X/2

35. Real printer: sample HP IJ 970 Cx outputs
DBS with no printer model
DBS with printer model
(no covariance term)
DBS with printer model

36. Predicting printed absorptance from the digital halftone: inputs to the black-box model

37. Structure of the black-box model

38. Why We Need to Consider a Larger Neighborhood Than 5x5?
This local influence can be attributed to following facts:
the spot size of the laser write beam is larger than a single printer-addressable pixel
the complex field interactions that are set up by the charge distribution on the photoconductor and in the toner in the gap between the photoconductor and the developer, and how this influences development
the further spreading of toner during the transfer and fusing processes
optical scattering of incident light within the media.

39. Why We Need to Consider a Larger Neighborhood Than 5x5?
Measured central pixel absorptance as a function of neighborhood’s size
Dispersed-dot halftone
generated using DBS algorithm
larger 45x45 neighborhood that is intended to capture the effect of long-path scattering of light between the
point where it is incident on the surface of the printed media and where it finally exits, known as the Yule-Nielsen effect
Conclusion:
Neighborhood larger than 5x5 can strongly influence the central pixel absorptance
We choose 45x45 as the size of neighborhood
We also have verify the influence only depends on the gray level of the neighborhood, not the distribution
Portion of test page

40. How do We Build the Black Box Models?
Print the test pages at dpi
Scan at 2400 dpi
Scanned
image
analysis
Build
printer
model
Design
test
page
The major steps in the print-to-scan procedure that we use to establish the relationship between the digital halftone sent to the printer and the average absorptance of each region corresponding to a single printer-addressable pixel in the scanned printed page. We print a set of specially designed test pages on an HP Indigo Press 5000 at a resolution of dpi, and scan the printed pages using an Epson Expression XL scanner at a resolution of 2400 dpi. We then analyze these scanned images to get the statistics data (mean and std dev of abs), and then generate the parameters for the seven models
Epson Expression 10000XL
HP Indigo Press 5000

41. How do we train the model?5. 1. 2. 3. 4.

42. Scanned Image Analysis
The centroid is calculated based on the spatial distribution of toner absorptance throughout its corresponding mask region
we first perform scanner gray balancing to calibrate the scanned pages to units of absorptance. We then estimate the center
coordinates (here we use the centroid) for each fiducial mark.
The binary mask image is generated using the Otsu’s method
The centroid of each fiducial mark is calculated based on the spatial distribution of toner absorptance throughout its corresponding mask region
this printer-addressable pixel corresponds to a 2400/812.8X2400/812.8 region in the scanned image
we use a sub-scanner-pixel procedure to estimate the average absorptance ˜ g[m,n] corresponding to this printer-addressable pixel.
scanner pixels s[k,l] that overlap either wholly or partially with this region.
weight ωm;n[k; l] is equal to the fractional intersection of the region of the [k; l]-th scanner pixel with the
a 2400/812.8X2400/ region centered at the location of the [m;n]-th printer-addressable pixel
The 0.5 pixel offset shifts the coordinates for each pixel to the center
Calibrated scanned image
Locate the centroid of each fiducial mark
Locate all pixels that have 45x45 surrounding
Estimate absorptance for all pixels within the region of interest
Statistics data for black box models

43. Scanned Image Analysis
Calibrated scanned image
Locate the centroid of each fiducial mark
Locate all pixels that have 45x45 surrounding
Estimate absorptance for all pixels within the region of interest
Statistics data for black box models
we first perform scanner gray balancing to calibrate the scanned pages to units of absorptance. We then estimate the center
coordinates (here we use the centroid) for each fiducial mark.
The binary mask image is generated using the Otsu’s method
The centroid of each fiducial mark is calculated based on the spatial distribution of toner absorptance throughout its corresponding mask region
this printer-addressable pixel corresponds to a 2400/812.8X2400/812.8 region in the scanned image
we use a sub-scanner-pixel procedure to estimate the average absorptance ˜ g[m,n] corresponding to this printer-addressable pixel.
scanner pixels s[k,l] that overlap either wholly or partially with this region.
weight ωm;n[k; l] is equal to the fractional intersection of the region of the [k; l]-th scanner pixel with the
a 2400/812.8X2400/ region centered at the location of the [m;n]-th printer-addressable pixel

44. Experimental results – sample images
Scanned image
ULM5x5 prediction
M45x45 c3b prediction
Digital
an example of the cross-validation model prediction images and prediction error images for mean absorptance using different black-box models. The example irregular, periodic clustered-dot halftone patch has an average gray level 96/255. The size of the image is 57x57 printer-addressable pixels. The prediction error images show the relative magnitude of the errors between the prediction and the measurement by identically scaling all three error images according to the largest magnitude of error observed across the three error images. In keeping
with the units of absorptance in which these images are shown, darker pixels in the prediction error images mean higher error. We can see from the prediction error images that ULM5x5 has the highest prediction error, and M45x45 Class 3b has the minimum prediction error, which is consistent with the statistics in Table and the quality of the visual match between Figures (b) and (e)
ULM5x5 error image
M45x45 c2a error image
M45x45 c3b error image
Gray level 96/255

45. Experimental results – error statistics*
*Absorptance units are on a scale of 0 (white) to 1 (black)