Slide No. 1

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. 2

Outline

Motivation: why is accurate pen alignment important?

Proposed approach

1. Imaging analysis tools

2. Psychophysical experiments

Discussion

Slide No. 3

Operation of an inkjet printer

A carriage transports the pen back and forth across the page. The pen fires ink

onto the surface of the page.

Paper is advanced through the printer by a series of rollers driven by a

stepper motor.

Slide No. 4

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. 5

The problemTypical 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

• 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?

Tails and satellites appear more frequently

at higher speeds

Slide No. 6

Background on perception of misalignment: Vernier acuity

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.

Retinal image size is measured by the angle subtended by the object.

______________________

* Regan, David. Human Perception of Objects. 2000.

2D

O=

tanceObject Dis

Size/2Object =)tan( 2

α

Slide No. 7

Outline

Proposed approach: measuring misalignment and

classifying dots.

Psychophysical tests: constant stimuli and signal

detection.

Discussion of results.

Slide No. 8

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. 9

Scanner calibration

Slide No. 10

Measuring misalignment

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.

1 2 3 4

Slide No. 11

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. 12

Dot analysis toolMost 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.

Double dot Tails and satellitesSingle dot

Slide No. 13

Classification into single and double by principal component analysis

1. Pick set of training dot image samples 1, 2, … , M whose class is

known

2. Find average image

3. Find covariance matrix

4. The k eigenvectors vi, … , vk corresponding to the k largest

eigenvalues of C are the basis of the “feature space”

5. Any dot image can be approximated as , where

6. 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 ||

1

1 M

iiM

Ψ Γ

1

1 MT

i iiM

C Γ Ψ Γ Ψ

1

k

i ii

Γ Ψ v

( )Ti i v Γ Ψ

Slide No. 14

Dot Classification - Results

Slide No. 15

Dot bisection Objective is to find a curve that bisects the dot image along the path of lowest

image absorptance: find curve v(s) that minimizes

where Eimage is the absorptance value.

1

0

1( ) ( )

M

image ii

E s E sM

Slide No. 16

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 b2-

4ac<0.

Fitting set of points (xi,yi) equivalent to minimizing subject to

b2-4ac=-1.

Ellipse shape helps estimate dot elongation and orientation.

2( , )i ii

F x y

Grayscale dot Binary dot Dot outline and fitted ellipse

Slide No. 17

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. 18

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. 19

Effect of print speed on dot aspect ratio and on fraction of dots with a tail

MAR

m

Slide No. 20

Dot attributes across a population of pens

The attributes of the printed dot are similar throughout the population of pens.

Slide No. 21

Outline

Proposed approach: measuring misalignment and

classifying dots.

Psychophysical tests: constant stimuli and signal

detection.

Discussion of results.

Slide No. 22

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. 23

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. 24

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. 25

Psychophysical tests (symmetric Constant Stimuli)

Slide No. 26

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. 27

Corrected psychometric curves for 45 and 60 ips

Slide No. 28

Outline

Proposed approach: measuring misalignment and

classifying dots.

Psychophysical tests: constant stimuli and signal

detection.

Discussion of results.

Slide No. 29

Line profiles for misalignment magnitude equal to PSE

Swath break

Slide No. 30

Illustration of dot interaction on inter-swath juncture

Slide No. 31

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:

is estimated as a function of the Hit and False Alarm fractions, and of

the magnitude of the difference of the two alignment values*.

Yes No

Large Hits Misses

Small False

Alarms

Correct

Rejections

_________________* For details, see Detection Theory by Macmillan and Creelman.

Slide No. 32

Estimated vs. print speed

Slide No. 33

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).