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Screen Ruling, Print ResolutionAM, FM and Hybrid Halftoning
Sasan Gooran
Linköping University
LiU-Norrköping
DIGITAL IMAGES (pixel based)
Scanning
Photo Digital image
ppi (pixels per inch): Number of samples per inch
ppi (pixels per inch)
• ppi (scanning resolution): Number of samples per inch
• The higher ppi the better the representation of the con-tone image (Photo)
• Higher ppi requires more memory
• ppi should not be unncessarily high
• Choice of ppi????
DIGITAL HALFTONING
• Since most printers and image setters are not able to reproduce different shadows of gray the original digital image has to be transformed into an image containing white (0’s) and black (1’s)
HALFTONE CELL Pixel (/a number of pixels)
Halftone cell
The fractional area covered by the ink corresponds to the value of the pixel (or the area)
SCREEN RULING/FREQUENCY
• lpi (lines per inch): Number of halftone cells per inch
• The higher lpi the better the print (?!)
• High lpi requires more stable print press etc.
• Does a higher lpi always lead to a better print? (to be answered later)
RULE OF THUMB
lpisizeOriginalsDppi *2* ize esired
Ex. A 10 x 15 cm2 photo that is supposed to be 20 x 30 cm2
when printed at 150 lpi has to be scanned with a ppi about 2*2*150 = 600.
HALFTONE CELLMicro dot
dpi: Number of micro dots per inch
This halftone cell represents at most 82 + 1= 65 gray tones
HALFTONE CELL
Halftone cellHalftone cell Resolution: number of micro dots per inch (dpi)Resolution: number of micro dots per inch (dpi)
Micro dotMicro dot
In this case:17 gray tonesIn this case:17 gray tones
Screen ruling: number of halftone cells per inch (lpi)Screen ruling: number of halftone cells per inch (lpi)
lpi & dpi
• lpi: Number of halftone cells per inch
• A halftone cell consists of micro dots
• dpi: Number of micro dots per inch
• The ratio dpi/lpi decides the size of the halftone cell
lpi & dpi (Example)
• Assume that dpi is fixed at 600
• lpi = 150 only gives 17 gray tones
• lpi = 100 only gives 37 gray tones
• lpi = 50 gives 145 gray tones
• Does a higher lpi always lead to a better print? Not necessarily!
AM & FM HALFTONING
• AM (Amplitude Modulated)– The size of the dots is variable, their frequency
is constant
• FM (Frequency Modulated) 1st generation– The size of the dots is constant, their frequency
varies
• FM (Frequency Modulated) 2nd generation– The size of the dots and their frequency vary
THRESHOLDING
),(),( if ,0
),(),( if ,1),(
nmtnmg
nmtnmgnmb
g and b are the original and the halftoned image, respectively.
t is the threshold matrix.
THRESHOLDING
0.6
0.1
1
0.3
0.2 0
Original Image Halftoned imageThreshold matrix
This threshold matrix represents 10 gray tones
THRESHOLD MATRIXExample: Line
1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 9 10 11 12 9 10 11 12 13 14 15 1613 14 15 16
THRESHOLD MATRIXExample: Spiral
1 2 3 4 1 2 3 4 12 13 14 5 12 13 14 5 11 16 15 6 11 16 15 6 10 9 8 710 9 8 7
THRESHOLD MATRIX Clustered & Dispersed, 45 degrees
14 12 13 16 19 21 20 1714 12 13 16 19 21 20 17 5 4 3 10 28 29 30 23 5 4 3 10 28 29 30 23 6 1 2 11 27 32 31 22 6 1 2 11 27 32 31 22 9 7 8 15 24 26 25 18 9 7 8 15 24 26 25 1819 21 20 17 14 12 13 1619 21 20 17 14 12 13 1628 29 30 23 5 4 3 10 28 29 30 23 5 4 3 10 27 32 31 22 6 1 2 1127 32 31 22 6 1 2 1124 26 25 18 9 7 8 15 24 26 25 18 9 7 8 15
1 30 8 28 2 29 7 271 30 8 28 2 29 7 2717 9 24 16 18 10 23 1517 9 24 16 18 10 23 15 5 25 3 32 6 26 4 31 5 25 3 32 6 26 4 3121 13 19 11 22 14 20 1221 13 19 11 22 14 20 12 2 29 7 27 1 30 8 28 2 29 7 27 1 30 8 28 18 10 23 15 17 9 24 16 18 10 23 15 17 9 24 16 6 26 4 31 5 25 3 32 6 26 4 31 5 25 3 32 22 14 20 12 21 13 19 11 22 14 20 12 21 13 19 11
Clustered Dispersed
FM HALFTONING Error Diffusion
0.7
Threshold0.5
Original image Halftoned Image
0.3
error-Filter
7
3 5 1(*1/16)
COLOR PRINT
• Three secondary colors
• And Black
• RED (R, MY)• GREEN (G, CY)• BLUE (B, CM)
• BLACK (K, CMY)
Conventional Color Halftoning Different raster angle, 0, 15, 75 and 45 degrees
AM different anglesRosette patterns
FM