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Modeling the Histogram of the Halftone Image to Determine the Area Fraction of Ink

Modeling the Histogram of the Halftone Image to Determine the Area Fraction of Ink. Yat-Ming Wong May 8,1998 Advisor: Dr. Jonathan Arney. Background. Drawing useful information from an image is important in various fields that depend upon them

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Modeling the Histogram of the Halftone Image to Determine the Area Fraction of Ink

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

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

  4. Histogram • The image is read pixel by pixel for their reflectance values R1,9 = 0.1 R7,10 = 0.9

  5. Histogram

  6. Histogram of halftone dots Paper Population Ink Population

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

  8. Threshold Threshold, RT (?)

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

  10. Gaussian Model G1 G2 G1+G2 Reflectance

  11. Gaussian Model +

  12. Gaussian Model f(i) = F*G1(R) + (1-F)*G2(R) s1 s2 G1+G2 F 1-F R1 R2 REFLECTANCE

  13. Sum of two gaussians vs. offset lithographic print data G1+G2 Data PROBLEM REFLECTANCE

  14. G1+G2 Data Sum of two gaussians vs. inkjet “stochastic halftone” data PROBLEM REFLECTANCE

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

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

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

  18. Model the Halftone “Equivalent Edge” Change Rmin or Rmax H R

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

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

  21. S(R) -0.1 0.1 R The Noise Model Add A Noise Metric Assume A Reflectance Variation

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

  23. Straight Edge Model s 1-F F a Rmin Rmax

  24. 0.08 0.06 0.04 H(R) 0.02 0 0 0.2 0.4 0.6 R Straight edge model vs. offset lithographic print data

  25. Straight edge model vs. inkjet “stochastic halftone” data 0.03 0.02 H(R) 0.01 0 0.1 0.2 0.3 0.4 0.5 0.6 R

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

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

  28. Automated computation • Program written in Visual Basic • 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. 0.1 H(R) 0 R 0 1 Problems with the straight edge model H(R) R Expand

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

  31. Conclusion • Model fits well for Ri and Rp close to each other • For Ri and Rp widely spaced, a single noise metric is inadequate.

  32. The End

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