Transcript No Slide Title

DIGITAL HALFTONING
Sasan Gooran
Digital Images
Pixel based
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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.
1024 x 768 pixels.
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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 Images
How much memory?
bit/pixel
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Line
1
Grayscale
8
Indexed color 8
RGB
3*8=24
CMYK
4*8=32
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2 tones
256 tones
256 colors
256^3=16.7 millions colors
256^4=4.3 billions colors
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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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Halftoning
Con-tone
Prepress
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Image
Halftoned
Halftoning
Image
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Print
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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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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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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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Levels of gray
 dpi 

  1  levelsOFgray
 lpi 
2
Ex, 600 dpi and 100 lpi gives 37 levels of gray
Ex, 600 dpi and 75 lpi gives 65 levels of gray
Ex, 600 dpi and 50 lpi gives 145 levels of gray
Which one to choose????
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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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Lpi & ppi
pr int_ size
* 2 * lpi  ppi
original _ size
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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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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AM and FM Halftoning
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AM and FM Halftoning
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AM and FM Halftoning
FM
AM
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Thresholding
0.6
1
0.1
0.3
0.2
Original Image
0
Threshold matrix
Halftoned Image
This threshold matrix represents 10 levels of gray.
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Threshold matrix
Example: Line
1 2
5 6
9 10
13 14
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3 4
7 8
11 12
15 16
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Threshold Matrix
Example: spiral
1
12
11
10
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2
13
16
9
3 4
14 5
15 6
8 7
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Threshold Matrix
Example: spiral
Line
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Spiral
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Error Diffusion
FM
0.3
Threshold
0.5
0.7
Error Filter
Original Image
Halftoned Image
7
(*1/16)
3
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5
1
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Error Diffusion
FM
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Hybrid Halftoning
Example 1

AM+FM
– Homogeneous parts by AM
– Details by FM
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Hybrid Halftoning
Example 1
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Hybrid Halftoning
Example 2
Some printing methods are not able to
produce the dots sufficiently small.
 Ex. Flexography.

5.2%
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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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Hybrid halftoning
Example 2
AM
Hybrid
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Hybrid Halftoning
Example 2
AM
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Hybrid
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Hybrid Halftoning
AM
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Hybrid
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Hybrid Halftoning
Hybrid, The FM method is Error diffusion
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Hybrid, The FM method is ...
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Color Mixing (Additive)
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Color Mixing (Subtractive)
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Color Mixing
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Three primary
colors
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CYAN (C)
MAGENTA (M)
YELLOW (Y)
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Color Mixing
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Three secondary
colors
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RED (R, MY)
GREEN (G, CY)
BLUE (B, CM)
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Color Mixing
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And Black
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BLACK (K, CMY)
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3-Color Print
Original
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AM Halftone
Konventionellt raster
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FM Halftone
FM- raster
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AM Halftone, same angle
for C, M, Y & K
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AM Halftone, same angle for C & M
Miss-registration
Correct registration
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Position error
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AM Halftone, same angle for C & M
Miss-registration
Correct registration
Angle error
Moiré pattern
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AM Halftone, different angles for C, M,Y & K
15, 75, 0 and 45 degrees
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Rosette Pattern
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Rosette Pattern
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FM (Stochastic) Halftone, 4-color print
“Moiré pattern” and “Rosette pattern” disappear
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NUEGEBAUER’S
Equations
X 
X
Y    a  Y
 

 Z 
 Z
i
i
i
i
i




a 1
i
i
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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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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