1. Modeling the Histogram of the Halftone Image to Determine the Area Fraction of Ink Yat-Ming Wong May 8,1998 Advisor: Dr. Jonathan Arney

2. Background n Drawing useful information from an image is important in various fields that depend upon them n Tools used to interpret an image need to be good enough to give meaningful data

3. Histogram n The histogram is a tool that gives a graphical interpretation of an image n It give us an idea of the make up of the image, such as the amount of ink in its composition

4. Histogram n The image is read pixel by pixel for their reflectance values R 1,9 = 0.1 R 7,10 = 0.9

5. Histogram

6. Histogram of halftone dots Ink Population Paper Population

7. Histogram n Segmentation of the histogram has so far been done by visual approximation n Visual approximation is a highly inaccurate method of measurement in cases where data needs to be in significant figures

8. Threshold Threshold, R T (?)

9. Solution Models to segment histogram computationally: Gaussian Model Straight-Edge Model

10. Gaussian Model Reflectance G1G1 G2G2 G 1 +G 2

11. Gaussian Model +

12. f(i) = F*G 1 (R) + (1-F)*G 2 (R) R1R1 R2R2 11 22 F 1-F REFLECTANCE G 1 +G 2

13. Sum of two gaussians vs. offset lithographic print data PROBLEM REFLECTANCE G 1 +G 2 Data

14. Sum of two gaussians vs. inkjet “stochastic halftone” data REFLECTANCE G 1 +G 2 Data PROBLEM

15. Straight Edge Model Halftone dots are a collection of edges

16. Straight Edge Model Model of the Halftone Reflection Distribution as a Single “Equivalent Edge” H R

17. Model the Halftone “Equivalent Edge Vary F H R

18. Model the Halftone “Equivalent Edge” H Change R min or R max R

19. Model the Halftone “Equivalent Edge” x scan R x 1 1 0 0 where:

20. R x 1 1 0 0 The Model H R 0 1

21. The Noise Model -0.10.1 R S(R) Add A Noise Metric Assume A Reflectance Variation

22. H R 0 1 * S(R) The Noise Model R

23. Straight Edge Model RminRmax  F 1-F a

24. Straight edge model vs. offset lithographic print data H(R) R 00.20.40.6 0 0.02 0.04 0.06 0.08

25. Straight edge model vs. inkjet “stochastic halftone” data 0.10.20.30.40.50.6 0 0.01 0.02 0.03 H(R) R

26. Comparison of models in matching offset lithographic print data Sum of two gaussiansStraight Edge vs.

27. Comparison of models in matching inkjet “stochastic halftone” data Sum of two gaussiansStraight Edge vs.

28. Automated computation n Program written in Visual Basic n Opens up a data file and automatically find the best computational match by looking for the set of variables that yields the lowest RMS deviation value.

29. Problems with the straight edge model H(R) R R 01 0 0.1 Expand

30. Problems with the straight edge model H(R) R R Expand

31. Conclusion n Model fits well for R i and R p close to each other n For R i and R p widely spaced, a single noise metric is inadequate.

32. The End