Clustered-dot-ordered Dither

Bui Hai Thanh

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

Introduction

Clustered orderedDescribed by

Screen angleScreen frequencyDot patternLevel assignment

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

Introduction

Important developmentScreen functionsThreshold arrayHolladay algorithmRational/Irrational tangent screensSupercellMulticenter dot

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

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

Screen Functions

Guide for creating threshold array

Mathematical functions are usedRound dot: s(x,y)= 1-(x2+y2)

0

1

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

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

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

Tone level

With M x N screen: MN+1 level

Tone level assignment may haveUniform (linear density function)Non-uniform (non-linear density function)

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

Holladay Algorithm

Using general parallelogram Width L Height H Shift S=L-D Area: (x+u)(y+v)-xy-uv=xv+yu

Holladay Algorithm

Halftone cell can be described by an equivalent rectangular cellWidth LHeight HShift S

Postscript Halftone

Partial Dotting

Mixture of full dots

Provide details and preserve edges

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

Rational screen

Nishikawa

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

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

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

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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