1. Histograms Analysis of the Microstructure of Halftone Images J.S. Arney & Y.M. Wong Center for Imaging Science, RIT Given by Linh V. Tran ITN, Campus Norrköping, Linköping University In Digital Halftoning Course. Jan. 17, 2003

2. Linh V. Tran - Graduate course in Digital Halftoning 2/36 Outline J.S. Arney & Y.M. Wong. ”Histograms Analysis of the Microstructure of Halftone Images”. 1999 –Problem definition Ideal case More Complicated cases in Reality –Solution: Modeling the bimodal histogram –Experiments MatLab Halftoning Toolbox Developed in University of Texas at Austin, TX, USA Comparison several halftoning methods Done by Michael Bruce deLeon, Stanford, USA

3. Linh V. Tran - Graduate course in Digital Halftoning 3/36 Problem Estimate –The mean reflectance of the paper between the halftone dots, R P –The mean reflectance of the dots, R I and –The halftone dot area fraction, F of a given printed patch.

4. Linh V. Tran - Graduate course in Digital Halftoning 4/36 Paper Ink Perfect ink drops No dot gain Ideal case F 1-F 0 R i R p 1 A perfect frequency occurrence of gray levels of reflectance consists of 2 delta functions.

5. Linh V. Tran - Graduate course in Digital Halftoning 5/36 Microdensitometry CCD Camera Microscope paper CCD Camera: 1000x1000 pixels Can measure also -Resolutions -Granularity -Micro-distribution of color in the image

6. Linh V. Tran - Graduate course in Digital Halftoning 6/36 Experiments Histogram of 65 LPI AM halftone printed by offset lithography, measured at 5 mm field of view (FOV)

7. Linh V. Tran - Graduate course in Digital Halftoning 7/36 More Difficult Histograms at 5mm FOV of error diffusion dot pattern printed by thermal ink jet at 300 dpi with F = 0.5

8. Linh V. Tran - Graduate course in Digital Halftoning 8/36 More and More Difficult Histograms at 5mm FOV of error diffusion dot pattern printed by thermal ink jet at 300 dpi with F = 0.05

9. Linh V. Tran - Graduate course in Digital Halftoning 9/36 Modelling the Bimodal Histogram The edge modeled with R min = 0.3, R max = 0. 7 a = 10, and b = 0.5

10. Linh V. Tran - Graduate course in Digital Halftoning 10/36 Frequency Occurence of R dx

11. Linh V. Tran - Graduate course in Digital Halftoning 11/36 Add Gaussian Noise

12. Linh V. Tran - Graduate course in Digital Halftoning 12/36 Curve Fitting  Five unknowns: R max R min a, b

13. Linh V. Tran - Graduate course in Digital Halftoning 13/36 Inverse Model

14. Linh V. Tran - Graduate course in Digital Halftoning 14/36 Implementation Main results published earlier in Wong’s B.Sc. Thesis: ”Modeling the Halftone Image to Determine the Area Fraction of Ink” CIS, RIT, 1998 www.cis.rit.edu/research/thesis/bs/1998/wong Simulations mainly done in MathCAD

15. Linh V. Tran - Graduate course in Digital Halftoning 15/36 Halftoning MatLab Toolbox Developed in University of Texas at Austin, TX, USA Grayscale halftoning methods –Classical and user-defined screens –Classical error diffusion methods –Edge enhancement error diffusion –Green noise error diffusion –Block error diffusion Figures of merit measures for grayscale halftones –Peak signal-to-noise ratio (PSNR) –Weighted signal-to-noise ratio (WSNR) –Linear distortion measure (LDM) –Universal quality index (UQI)

16. Linh V. Tran - Graduate course in Digital Halftoning 16/36 Figures of Merit PSNR: Peak Signal to Noise Ratio of the output image with respect to the input image in dB

17. Linh V. Tran - Graduate course in Digital Halftoning 17/36 Figures of Merit WSNR: Weighted Signal to Noise Ratio of output image with respect to the input image in dB. A weighting appropriate to the human visual system is used. J. Mannos and D. Sakrison, "The effects of a visual fidelity criterion on the encoding of images", IEEE Trans. Inf. Theory, IT- 20(4), pp. 525-535, July 1974 LDM: Linear Distortion Ratio. UQI: Universal image Quality Index. Zhou Wang and Alan C. Bovik "A Universal Image Quality Index" IEEE Signal Processing Letters, 2001

18. Linh V. Tran - Graduate course in Digital Halftoning 18/36 Halftoning MatLab Toolbox Color halftoning methods –Classical and user-defined (multilevel) screens (separable) –Classical separable error diffusion methods (separable) –Edge enhancement error diffusion (separable) –Green noise error diffusion (separable) –Block error diffusion (separable) –Minimum brightness variation quadruple error diffusion (non- separable design for separable implementation) –Vector error diffusion (non-separable) Figures of merit measures for color –PSNR, WSNR, LDM, UQI as in grayscale halftoning –Noise gain in dB over Floyd-Steinberg error diffusion (specific to Vector Error Diffusion)

19. Linh V. Tran - Graduate course in Digital Halftoning 19/36 Demo http://www.ece.utexas.edu/~bevans/projects/ halftoning/toolbox/

20. Linh V. Tran - Graduate course in Digital Halftoning 20/36 DeLeon’s Comparison Done by Michael Bruce deLeon, Stanford, USA http://ise0.stanford.edu/~mdeleon/ Methods: 1.Bayer Dither Matrix: 8x8 matrix 2.Three Level Dither 3.Error Diffusion: Floyd and Steinberg 4.MBVQ Error Diffusion (Minimum Brightness Variation Quadrants) Test images: Ramps, Trees, Lena, Chart

21. Linh V. Tran - Graduate course in Digital Halftoning 21/36 Original Image Bayer Dither Matrix 3 Level Dither Error Diffusion MBVQ Error Diffusion

22. Linh V. Tran - Graduate course in Digital Halftoning 22/36 Original Image Bayer Dither Matrix 3 Level Dither Error Diffusion MBVQ Error Diffusion

23. Linh V. Tran - Graduate course in Digital Halftoning 23/36 Tree image Original ImageBayer Dither Matrix Three Level DitherError Diffusion

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25. Linh V. Tran - Graduate course in Digital Halftoning 25/36 Tree Image MBQV Error DiffusionBayer Dither Matrix Three Level DitherError Diffusion

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27. Linh V. Tran - Graduate course in Digital Halftoning 27/36 Lena Image Original ImageBayer Dither Matrix Three Level DitherError Diffusion

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29. Linh V. Tran - Graduate course in Digital Halftoning 29/36 Lena Image MBQV Error DiffusionBayer Dither Matrix Three Level DitherError Diffusion

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31. Linh V. Tran - Graduate course in Digital Halftoning 31/36 Chart Image Original ImageBayer Dither Matrix Three Level DitherError Diffusion

32. Linh V. Tran - Graduate course in Digital Halftoning 32/36

33. Linh V. Tran - Graduate course in Digital Halftoning 33/36 Chart Image MBQV Error DiffusionBayer Dither Matrix Three Level DitherError Diffusion

34. Linh V. Tran - Graduate course in Digital Halftoning 34/36

35. Linh V. Tran - Graduate course in Digital Halftoning 35/36 DeLeon’s Conclusions Solid tones seem the most difficult to present smoothly with a halftoning pattern. Thus, simple computer graphics may be more of a challenge for a printer than complex photos. The color error diffusion algorithm can effectively limit the number of colors used for a given region. Its execution time is only marginally longer than that of regular error diffusion. The pattern produced is slightly smoother than the regular error diffusion results, though unless closely examined in these monitor examples, the differences in dot brightness & color is easy to miss. Depending in its use with actual inks, tradeoffs might have to be made between the appearances of colors in grayscale images and this smoothing effect.

36. Linh V. Tran - Graduate course in Digital Halftoning 36/36 DeLeon’s Conclusions Multi-level halftoning seems to offer considerable image quality improvement without expensive algorithms. Although the expenses for realizing this functionality come from other areas (cost of extra inks, complexity of multi-drop or variable drop print head), the results would probably justify the extra overhead. Model-based halftoning seems like an interesting way to make use of our understanding of the human visual system, but the complexity of these algorithms seems to limit their usefulness for the time being.

37. Linh V. Tran - Graduate course in Digital Halftoning 37/36