Improved Pen Alignment for
Bidirectional Printing*
Edgar Bernal
Prof. Jan P. Allebach
Prof. Zygmunt Pizlo
Purdue University
* Research supported by the Hewlett-Packard Company.
Slide No. 1
Outline

Motivation: why is accurate pen alignment important?

Proposed approach
1. Imaging analysis tools
2. Psychophysical experiments

Discussion
Slide No. 2
Operation of an inkjet printer
Paper is advanced through the printer
by a series of rollers driven by a
stepper motor.
A carriage transports the pen back and
forth across the page. The pen fires ink
onto the surface of the page.
Slide No. 3
Motivation
•Main focus is on draft print modes (fast, single pass, bidirectional).
•Accurate swath-to-swath alignment is essential for good print quality.
Slide No. 4
The problem
Typical dot shape, 15
ips, right to left swath
Typical dot shape, 45
ips, right to left swath
Typical dot shape, 45
ips, left to right swath
Tails and satellites
appear more frequently
at higher speeds
• Dot shape depends on print speed and print directionality.
• How does the human viewer perceive dot position when
dot shape is asymmetric?
• How does the human viewer perceive alignment when
relationship between main dot/satellite is reversed from
swath to swath?
Slide No. 5
Background on perception of
misalignment: Vernier acuity

Retinal image size is measured by the angle subtended by the object.
tan( α2 ) =
Object Size/2
O
=
Object Dis tance 2D

Vernier acuity, the ability to detect offset between two vertical
or horizontal lines, is in the order of 10 seconds of arc*
(≈10×10-4 in @ 10 in viewing distance).

Want to determine whether Vernier acuity is affected by
changes in dot shape and size.
______________________
* Regan, David. Human Perception of Objects. 2000.
Slide No. 6
Outline

Proposed approach: measuring misalignment and
classifying dots.

Psychophysical tests: constant stimuli and signal
detection.

Discussion of results.
Slide No. 7
Proposed approach

Design tools to measure alignment of printouts.

Analyze the structure of dot formation on the
paper.

Investigate perceptual preferences with respect
to dot alignment and dot characteristics.
Slide No. 8
Scanner calibration
Slide No. 9
Measuring misalignment
1
2
3
4
1.
Print test pattern (square grid of 30x30 dots surrounded by a solid black region) on
the HP DeskJet 6540 inkjet printer. Place upper and lower halves of pattern on
different swaths.
2.
Scan printed pattern with the Aztek 8000 drum scanner at 8000 dpi.
3.
Binarize image and find boundaries between rows and colums.
4.
Find centroid of each dot by averaging absorptance distribution inside dot’s cell.
5.
Misalignment is estimated by calculating offset between average horizontal position of
dots in upper half and average horizontal position of dots in lower half of pattern.
Slide No. 10
Isolating the effects of image skew

Estimate skew of scanned
pattern by performing
orthogonal regression along
rows of dots and finding slope
of line.

Update vertical references by
performing regression along
columns.

Misalignment is calculated by
measuring perpendicular
distances between dots and
new column references to get
rid of effect of skew.
Slide No. 11
Dot analysis tool

Most of the times, single dots are rendered as two
dots when printing at 300 dpi with a pen with 600
dpi resolution.

As print speed increases, tails and satellites appear
more frequently.
Single dot
Double dot
Slide No. 12
Tails and satellites
Classification into single and double
by principal component analysis
1.
2.
3.
Pick set of training dot image samples 1, 2, … , M whose class is
known
1
Find average image Ψ 
M
M
Γ
i 1
Find covariance matrix C  1
i
M
Γ

M
i 1
4.
i
 Ψ  Γi  Ψ 
T
The k eigenvectors vi, … , vk corresponding to the k largest
eigenvalues of C are the basis of the “feature space”
k
5.
Any dot image can be approximated as Γ  Ψ   i v ,i where
i 1
6.
i  vTi (Γ  Ψ)
Let i=[1 ... k]T be the set of coefficients of the i-th training
sample, i . The class to which a new dot  belongs, is the class
corresponding to the i that minimizes ||  - i ||
Slide No. 13
Dot Classification - Results
Slide No. 14
Dot bisection

Objective is to find a curve that bisects the dot image along the path of lowest
1 M 1
image absorptance: find curve v(s) that minimizes E ( s)   Eimage ( si )
M
where Eimage is the absorptance value.
Slide No. 15
i 0
Ellipse fitting

Fit ellipse to points belonging to dot outline via least squares.

Equation of the ellipse is F(x,y)=ax2+bxy+cy2+dx+cy+f=0 subject to b24ac<0.

Fitting set of points (xi,yi) equivalent to minimizing
b2-4ac=-1.

 F(x , y )
i
2
i
subject to
i
Ellipse shape helps estimate dot elongation and orientation.
Grayscale dot
Binary dot
Slide No. 16
Dot outline and fitted ellipse
Tail detection

Similar procedure to dot bisection, except that the initial guess corresponds to
segment of minimum average energy in the direction perpendicular to main axis
of fitted ellipse.
Slide No. 17
Sample output of dot analysis tool
• Output contains information such as: dot type, ellipse
coefficients, location of contour components, location of
centroid of main dot and satellites, etc.
• Tool was used to characterize and classify different pens
according to the characteristics of the dots they produced.
Slide No. 18
Effect of print speed on dot aspect
ratio and on fraction of dots with a tail
M
AR 
m
Slide No. 19
Dot attributes across a population
of pens
The attributes of the printed dot are similar throughout the population of pens.
Slide No. 20
Outline

Proposed approach: measuring misalignment and
classifying dots.

Psychophysical tests: constant stimuli and signal
detection.

Discussion of results.
Slide No. 21
Psychophysical tests (asymmetric
Constant Stimuli)
•Show subject test images printed with different levels of misalignment.
•Record subject’s responses to make inferences about perception of
misalignment.
Slide No. 22
Psychometric curves for 15 and 30 ips
Results for these print modes suggest that point of
perceived perfect alignment coincides with point of
measured perfect alignment.
Slide No. 23
Data points for 45 and 60 ips
Results for these print modes suggest that point of
perceived perfect alignment differs from point of
measured perfect alignment.
Slide No. 24
Psychophysical tests (symmetric
Constant Stimuli)
Slide No. 25
Point of perceived perfect
alignment for 45 and 60 ips
• New constant stimuli test was carried out to estimate the point of
perceived perfect alignment for 45 and 60 ips bidirectional.
• Subjects were asked to respond whether lower segment of a line was
shifted to the left or to the right with respect to upper segment.
• PSE is an estimate of the point of perceived perfect alignment.
Slide No. 26
Corrected psychometric curves
for 45 and 60 ips
Slide No. 27
Outline

Proposed approach: measuring misalignment and
classifying dots.

Psychophysical tests: constant stimuli and signal
detection.

Discussion of results.
Slide No. 28
Line profiles for misalignment
magnitude equal to PSE
Swath break
Slide No. 29
Illustration of dot interaction on
inter-swath juncture
Slide No. 30
Signal detection experiments

Want to measure ability to distinguish between two different alignment
values for each print speed.

Printed 40 test pages at each carriage speed. Half of those pages were
printed with a higher misalignment value than the other half.

Each subject was presented with the test pages and was asked to
classify each of them into one of two groups.

The resulting data was tabulated in a stimulus response matrix:

Yes
No
Large
Hits
Misses
Small
False
Alarms
Correct
Rejections
 is estimated as a function of the Hit and False Alarm fractions, and of
the magnitude of the difference of the two alignment values*.
_________________
* For details, see Detection Theory by Macmillan and Creelman.
Slide No. 31
Estimated  vs. print speed
Slide No. 32
Conclusions

Designed a comprehensive set of image analysis tools to
study formation of dots on paper.

Demonstrated that dot characteristics remain more or less
constant across a wide population of pens.

Alignment judgments are based on dot outline (at a certain
absorptance level) rather than center of mass.

Additional tests showed that sensitivity to changes in
alignment decreases as print speed increases.

Estimated thresholds for perception of alignment are in the
order of the Vernier acuity (5-10 seconds of arc).
Slide No. 33