1. DIGITAL HALFTONING
Sasan Gooran

2. Digital Images Pixel based
They consist of a number of square image elements, which are called pixels. Each pixel has a position in the image and a value that describes its tone value in that position.
The number of pixels per inch is called resolution. (ppi = pixels / inch)
Another way of mentioning resolution is to say how many pixels an image totally consists of. Ex x 768 pixels.
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Digital Halftoning

3. Digital Images Pixel based
Bit depth: Number of bits that are used in order to represent the tone value in computer. Commonly we use 256 levels of tone, i.e. Bit depth = 8.
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Digital Halftoning

4. Digital Images How much memory?
bit/pixel
Line tones
Grayscale tones
Indexed color colors
RGB *8= ^3=16.7 millions colors
CMYK *8= ^4=4.3 billions colors
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Digital Halftoning

5. Halftoning
Because printing is generally not able to reproduce different tones of a color, the original image has to be transformed to a binary image. This is called halftoning.
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Digital Halftoning

6. Halftoning Prepress Halftoning Print Con-tone Image Halftoned
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Digital Halftoning

7. Halftone cell Halftone cell Halftone dot
The fractional area of the cell
covered with ink is decided by
the pixel value. (Or by the mean
of the pixel values if the small
square shown in the image to
the left consists of more than
one pixel).
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Digital Halftoning

8. Line screen frequency
In conventional halftoning the distance between the centers of two neighboring dots is constant.
Number of halftone dots per inch is called line screen frequency. It is denoted by lpi (lines per inch).
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Digital Halftoning

9. Line screen frequency & Resolution
Micro dot
Resolution: number of
micro dots per inch (dpi)
Halftone cell
In this case:
17 levels of gray
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Digital Halftoning

10. Levels of gray Ex, 600 dpi and 100 lpi gives 37 levels of gray
Which one to choose????
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Digital Halftoning

11. lpi & ppi
When scanning an image, for practical reasons and for better reproduction, you normally choose a ppi that is twice as high as lpi.
A sampling factor of 1.5 is acceptable in most cases.
A sampling factor higher than 2 is unnecessary.
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Digital Halftoning

12. Lpi & ppi Ex. If your original image is (24 x 36 mm) and you want
the printed image to be (80 x 120) mm when lpi = 133,
you should choose a ppi around 887 lines/inch.
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Digital Halftoning

13. AM and FM Halftoning AM (Amplitude Modulated) Halftoning
The size of the dots varies while their frequency is kept constant. The darker the gray tone the bigger the dot.
FM (Frequency Modulated) Halftoning
The size of the dots is constant. Their frequency (number) is changed. The darker the gray tone the more the number of micro dots.
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Digital Halftoning

14. AM and FM Halftoning
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Digital Halftoning

15. AM and FM Halftoning
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Digital Halftoning

16. AM and FM Halftoning AM FM
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17. Thresholding This threshold matrix represents 10 levels of gray.
0.6 1
0.1
0.3
0.2
Original Image
Threshold matrix
Halftoned Image
This threshold matrix represents 10 levels of gray.
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18. Threshold matrix Example: Line
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19. Threshold Matrix Example: spiral
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20. Threshold Matrix Example: spiral
Line
Spiral
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21. Error Diffusion FM Original Image Halftoned Image 0.3 Threshold 0.5
0.7
Threshold
0.5
Original Image
Halftoned Image
0.3
Error Filter 7
(*1/16) 3 5 1
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22. Error Diffusion FM
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23. Hybrid Halftoning Example 1
AM+FM
Homogeneous parts by AM
Details by FM
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24. Hybrid Halftoning Example 1
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25. Hybrid Halftoning Example 2
Some printing methods are not able to produce the dots sufficiently small.
Ex. Flexography.
5.2%
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Digital Halftoning

26. Hybrid Halftoning Example 2
Utilize a FM method for the highlights and shadows using the smallest possible dot.
Use an AM method for the rest of the image.
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Digital Halftoning

27. Hybrid halftoning Example 2
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Digital Halftoning

28. Hybrid Halftoning Example 2
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29. Hybrid Halftoning AM
Hybrid
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30. Hybrid Halftoning Hybrid, The FM method is Error diffusion
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Digital Halftoning

31. Color Mixing (Additive)
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32. Color Mixing (Subtractive)
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33. Color Mixing Three primary colors CYAN (C) MAGENTA (M) YELLOW (Y)
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34. Color Mixing Three secondary colors RED (R, MY) GREEN (G, CY)
BLUE (B, CM)
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35. Color Mixing
And Black
BLACK (K, CMY)
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36. 3-Color Print
Original
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37. Konventionellt raster
AM Halftone
Konventionellt raster
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38. FM Halftone
FM- raster
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39. AM Halftone, same angle for C, M, Y & K
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40. AM Halftone, same angle for C & M Miss-registration
Correct registration
Position error
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41. AM Halftone, same angle for C & M Miss-registration
Correct registration
Angle error
Moiré pattern
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Digital Halftoning

42. AM Halftone, different angles for C, M,Y & K 15, 75, 0 and 45 degrees
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Digital Halftoning

43. Rosette Pattern
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44. Rosette Pattern
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45. FM (Stochastic) Halftone, 4-color print
“Moiré pattern” and “Rosette pattern” disappear
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Digital Halftoning

46. NUEGEBAUER’S Equations
X, Y, Z are the tristimulus values for the average color
of a surface
ai is the fractional area covered by color Xi, Yi, Zi
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Digital Halftoning

47. Demichel’s Equations (3-color print)
Aw =(1-ac)(1-am)(1-ay)
Ac =ac(1-am)(1-ay)
Am =am(1-ac)(1-ay)
Ay =ay(1-ac)(1-am)
Ar =amay(1-ac)
Ag =acay(1-am)
Ab =acam(1-ay)
Ak=acamay
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