clustered-dot-ordered dither bui hai thanh. introduction ordered dither fixed pattern of number...
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Clustered-dot-ordered Dither
Bui Hai Thanh
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Introduction
Ordered ditherFixed pattern of number (halftone cell)Two approaches
Dispersed: turn on the pixel individuallyClustered: group pixels to clusters
Dispersed/Clustered: Depends on devices capability of displaying dots
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Introduction
Clustered orderedDescribed by
Screen angleScreen frequencyDot patternLevel assignment
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Introduction
Screen anglePrinting industry: clockwise fr. vertical lineFourfold symmetry: 0..90O
Color case: 45O K, 75O C, 15O M, 0O Y
Screen frequency:# of halftone cell in a unit of length (e.g.: lpi)Dot pattern: fill-in order for dot growth sequence
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Introduction
Important developmentScreen functionsThreshold arrayHolladay algorithmRational/Irrational tangent screensSupercellMulticenter dot
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Threshold Array
Discrete representationDot pattern in the form of threshold values2D signalUse threshold to decide if the pixel should be turned onGoal No moiré No contour Sharp and fine details
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Threshold Array
5 118 160 58 17
48 201 232 170 99
129 211 252 242 150
89 191 221 181 68
38 78 140 108 27
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Screen Functions
Guide for creating threshold array
Mathematical functions are usedRound dot: s(x,y)= 1-(x2+y2)
0
1
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Screen Functions
Within each ring, pixels have to be in sequence Counter clockwise spiral
Classical spiral
4 5 6 1
12 13 14 7
11 16 15 8
3 10 9 24 8 10 1
11 13 14 5
7 16 15 9
3 12 6 2
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Clustered Dot Design
Minimize edge/area ratio
Minimize dot center migration
Dot join strategy Boom dot Kiss dot
Cell boundary: squared vs. round
Dot growth: make the dot asymmetric
Dot gain
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Some special requirements
Smooth transition: The white area on black when coverage
>50% should be the negative image of black area on white
s(x,y)=cxcos(2vxx)+ cycos(2vyy)
s(x,y)=0.5[1+sin(vxx)sin(vyy)] vx,vy : are the scaling factors for screen size
cx, cy : aspect ratio without affecting screen frequency
The negative image has a shift from positive
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Tone level
With M x N screen: MN+1 level
Tone level assignment may haveUniform (linear density function)Non-uniform (non-linear density function)
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Threshold operation
The darkest element growths to the percentage of average intensity
Threshold by comparing with average value. Turn on pixel with threshold level > pixel value
Direct comparison
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Holladay Algorithm
Using general parallelogram Width L Height H Shift S=L-D Area: (x+u)(y+v)-xy-uv=xv+yu
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Holladay Algorithm
Halftone cell can be described by an equivalent rectangular cellWidth LHeight HShift S
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Postscript Halftone
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Partial Dotting
Mixture of full dots
Provide details and preserve edges
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Rational/Irrational Tangent Screens
Screen is rational if tangent angle is a ratio of integersHave exactly the same size and shapeLimited # of angle/frequency combinations
Irrational tangent screenSize and shape may varyCan have more combinations
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Rational screen
Nishikawa
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Irrational screen
Can have non integer ratiosSo can have any angle/frequencyOne or more corners are not located on junctions of grid.Cost: Different in size and shape Dot pattern and # tone level vary from cell to cell Select screen with frequency, rotate on the fly If pixel in digital grid falls between points of the
threshold array, interpolation is required
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Irrational
Rotation formulax’=x cos - y sin y’=y cos + x sin
General expressionx’=(x-x0) cos - (y-y0) sin +x0
y’=(x-x0) sin + (y-y0) cos +y0
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Supercell
Integer tangent has limited number
Small cell provides less choice of angle
Large cell causes the low frequency
Divide large cell into small subcells give more choices of screen angle, with increased frequency and reduce tone level
Supercell is rational cell consist of subcells, which can be varied in size/shape
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Multicenter Dot
Similar to supercellCell is divided into equal partsEach partial dot has nucleus growing also with clustered approach within larger dotIncrease frequencyDrawback: slight texture contouring, and tone jump in hightlight
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