Improved Pen Alignment for Bidirectional Printing*

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.

2. Outline • Motivation: why is accurate pen alignment important? • Proposed approach • Imaging analysis tools • Psychophysical experiments • Discussion

3. 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.

4. Motivation • Main focus is on draft print modes (fast, single pass, bidirectional). • Accurate swath-to-swath alignment is essential for good print quality.

5. 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?

6. Background on perception of misalignment: Vernier acuity • Retinal image size is measured by the angle subtended by the object. • 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.

7. Outline • Proposed approach: measuring misalignment and classifying dots. • Psychophysical tests: constant stimuli and signal detection. • Discussion of results.

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.

9. Scanner calibration

10. Measuring misalignment • 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. • Scan printed pattern with the Aztek 8000 drum scanner at 8000 dpi. • Binarize image and find boundaries between rows and colums. • Find centroid of each dot by averaging absorptance distribution inside dot’s cell. • 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

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.

12. 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 Tails and satellites

13. Classification into single and double by principal component analysis • Pick set of training dot image samples 1, 2, … , M whose class is known • Find average image • Find covariance matrix • The k eigenvectors vi, … , vkcorresponding to the k largest eigenvalues of C are the basis of the “feature space” • Any dot image can be approximated as , where • 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 ||

14. Dot Classification - Results

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.

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. Grayscale dot Binary dot Dot outline and fitted ellipse

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.

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.

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

20. Dot attributes across a population of pens The attributes of the printed dot are similar throughout the population of pens.

21. Outline • Proposed approach: measuring misalignment and classifying dots. • Psychophysical tests: constant stimuli and signal detection. • Discussion of results.

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.

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.

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.

25. Psychophysical tests (symmetric Constant Stimuli)

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.

27. Corrected psychometric curves for 45 and 60 ips

28. Outline • Proposed approach: measuring misalignment and classifying dots. • Psychophysical tests: constant stimuli and signal detection. • Discussion of results.

29. Line profiles for misalignment magnitude equal to PSE Swath break

30. Illustration of dot interaction on inter-swath juncture

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

32. Estimated  vs. print speed

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).