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Unformatted text preview: 4. Screening Advanced Digital Halftoning – 2 October 2011 4.1 Synopsis
•
•
•
•
•
•
• Screening architecture
Screen taxonomy
Screen descriptors
Analysis of tone and detail
Stochastic screens
Periodic, clustereddot screens (hybrid screen)
Moirefree conditions for screen design Advanced Digital Halftoning – 2 October 2011 4.2 Screening is a Thresholding Process • Simple pointtopoint transformation of each pixel in the
continuoustone image to a binary value.
• Process requires no memory or neighborhood information.
1
1
1
1 111
331
331
11 Compare 1 ContinuousTone Image Halftone Image Threshold
0.5 3.5
2.5 1.5 Threshold
Matrix
Advanced Digital Halftoning – 2 October 2011 4.3 Why Not Use a Single Threshold?
• A single threshold yields only a silhouette representation of
the image.
• No gray levels intermediate to white or black are rendered.
• To generate additional gray levels, the threshold must be
dithered, i.e. perturbed about the constant value. Continuoustone
original image
Advanced Digital Halftoning – 2 October 2011 Result of applying a fixed
threshold at midtone
4.4 Basic Structure of Screening Algorithm 1
1
1
1 111
331
331
11 Compare 1 Halftone Image ContinuousTone Image
0.5 3.5
2.5 1.5 Threshold
Matrix The threshold matrix is periodically tiled over
the entire continuoustone image. Advanced Digital Halftoning – 2 October 2011 4.5 Terminology
• The screening process is also called dithering.
• However, the term dithering is sometimes applied to any
digital halftoning process, not just that consisting of a pixeltopixel comparision with thresholds in a matrix.
• The following are equivalent terms for the threshold matrix:
– screen
– dither matrix
– mask Advanced Digital Halftoning – 2 October 2011 4.6 How Tone is Rendered
• If we threshold the screen against a constant gray value,
we obtain the binary texture used to represent that constant
level of absorptance. Advanced Digital Halftoning – 2 October 2011 4.7 Dot Profile Function
• The family of binary textures used to render each level of
constant tone is called the dot profile function.
• There is a onetoone relationship between the dot profile
and the screen. Advanced Digital Halftoning – 2 October 2011 4.8 Selection of Threshold Values
• For an MxN halftone cell,can print 0, 1, 2, …, MN dots,
yielding average absorptances 0, 1/MN, 2/MN, …, 1,
respectively.
• As the input gray level increases, each time a threshold is
exceeded, we add a new dot, thereby increasing the
rendered absorptance by 1/MN.
• It follows that the threshold levels should be uniformly
spaced over the range of gray values of the input image. Advanced Digital Halftoning – 2 October 2011 4.9 Rendering of Detail  Partial Dotting Advanced Digital Halftoning – 2 October 2011 4.10 Partial Dotting  Example Advanced Digital Halftoning – 2 October 2011 4.11 Spatial Arrangement of Thresholds
• For clustered dot textures, thresholds that are close in
value are located close together in the threshold matrix Advanced Digital Halftoning – 2 October 2011 4.12 Spatial Arrangement of Thresholds (cont.)
• For dispersed dot textures, thresholds that are close in
value are located far apart in the threshold matrix. Advanced Digital Halftoning – 2 October 2011 4.13 Detail Rendition with Dispersed Dot Screens
• Since the thresholds in any local neighborhood tend to be
uniformly spread over the full range of gray levels, the gray
level in that local neighborhood is rendered more
accurately. Advanced Digital Halftoning – 2 October 2011 4.14 Clustered vs. Dispersed Dots
Attribute
Texture Visibility
Detail Rendering
Stability Clustered Dot
High
Fair
High Dispersed Dot
Low
Good
Low • Note that these assessments are relative.
• For example, at sufficiently high resolution, clustered dot
textures will also have low visibility and good detail
rendition. Advanced Digital Halftoning – 2 October 2011 4.15 Macroscreen Design
• For a 128x128 screen, each threshold value between 0 and
255 occurs approximately 64 times in the matrix.
• Macroscreens are designed using searchbased
optimization strategies.
• The screen design is computationally intensive; but once
the screen is obtained, images are still halftoned with one
comparison/pixel.
• Macroscreens can be designed to have blue noise or green
noise characteristics.
• These terms refer to the characteristics of the halftone
textures generated by these screens, not the screens
themselves. Advanced Digital Halftoning – 2 October 2011 4.16 Spectral Properties of Blue Noise Mask Highlight Texture Halftone texture Advanced Digital Halftoning – 2 October 2011 Fourier spectrum 4.17 Spectral Properties of Blue Noise Masks Midtone Texture Halftone texture Advanced Digital Halftoning – 2 October 2011 Fourier spectrum 4.18 Spectral Properties of Green Noise Masks Highlight Texture Halftone texture Advanced Digital Halftoning – 2 October 2011 Fourier spectrum 4.19 Spectral Properties of Green Noise Masks Midtone Texture Halftone texture Advanced Digital Halftoning – 2 October 2011 Fourier spectrum 4.20 Synopsis
•
•
•
•
•
•
• Screening architecture
Screen taxonomy
Screen descriptors
Analysis of tone and detail
Stochastic screens
Periodic, clustereddot screens (hybrid screen)
Moirefree conditions for screen design Advanced Digital Halftoning – 2 October 2011 4.21 Iterative/SearchBased Methods for Screen Design
• Iterative/searchbased methods for screen design may be categorized
according to the domain and objective of the search:
– search domain
» dither(threshold) matrix
» dot profile function
– search objective
» minimize a cost function
» satisfy constraints
• The screen design methods that we will describe may be divided into four
groups according to these descriptors.
• The intent of all these methods is to either directly or indirectly push the
energy in the spectra of the binary textures away from the origin in the
frequency domain, thus yielding a blue noiselike characteristic.
• [Spaulding, Miller, and Schildkraut, 1997] contains a good overview of some,
but not all, of the screen designs discussed here. Advanced Digital Halftoning – 2 October 2011 4.22 Categorization of Methods for Screen Design Cost Function Constraints Search Objective Search Domain
Dither Matrix
Dot Profile
Rolleston &
Cohen, 1992 Mitsa & Parker,
1992 Dalton, 1989
Sullivan &
Allebach &
Ray, 1991
Stradling, 1979 Ulichney, 1993
Allebach & Lin,
1996 Advanced Digital Halftoning – 2 October 2011 4.23 Search Domains
• Dither matrix – we directly look for the best spatial arrangement of
the thresholds.
– In this way, we simultaneously optimize the entire dot profile
function. This suggests a greater liklihood of finding a global
optimum.
– In practice, however, these algorithms do not perform as well
as those based on levelbylevel design of the dot profile
function.
• Dot profile function – We design the levels in the dot profile
function one at a time.
– Each new level must satisfy the stacking constraint with
respect to the patterns that already have been designed.
– The design is greedy, since each successive level is more
highly constrained.
– Several different sequences of levels have been tried. Advanced Digital Halftoning – 2 October 2011 4.24 Increasing absorptance Stacking Constraint Upper constraint level
Level to be designed
Lower constraint level
Unconstrained pixels Advanced Digital Halftoning – 2 October 2011 4.25 Impact of order in which levels are designed
for dot profilebased methods
0 255
128
64
32 192
96 160 224 When any given level is to be designed, the next lower and
next higher levels that have already been designed serve
as constraint levels for application of the stacking
constraint. Advanced Digital Halftoning – 2 October 2011 4.26 Mitsa and Parker Screen
• [Mitsa and Parker, 1992] • This algorithm employs a levelbylevel iteration similar to
that of Rolleston and Cohen algorithm to design a mask
that satisfies constraints.
• The spatial domain constraint is that the texture at each
level must be binary. The frequency domain constraint is
that the radially averaged power spectrum have the
prescribed blue noise shape as postulated by Ulichney,
including the correct principal frequency.
• They determined empirically that scaling the principal
frequency from that specified by Ulichney for a rectangular
dot arrangement by a factor of K = 1 / 2 yielded improved
textures. Advanced Digital Halftoning – 2 October 2011 4.27 Void and Cluster Screen
• [Ulichney, 1993] • The algorithm employs a levelbylevel search to minimize
a cost function.
• It is based entirely in the spatial domain.
• Cost function is approximately C = max h[ m, n ] ∗ ∗ p( m, n; b ) − b
m, n circ – The filter h[m,n] can be interpreted as the point spread
function of the human visual system; Ulichney used a
Gaussian filter with s = 1.5 pixels.
– Convolution is circular to account for the periodicity of
the dither matrix Advanced Digital Halftoning – 2 October 2011 4.28 Swapping pixels
Location of
tightest cluster Location of
largest void c. swap hole closest to center of largest void with dot
closest to center of tightest cluster. Before Move
Advanced Digital Halftoning – 2 October 2011 After Move
4.29 Green Noise Screen Design
Using spatial statistics (Lau et al.) Iterative manipulation of the halftone to attain desired paircorrelation statistics Modeled as Typical Pair Correlation curve
for green noise halftones
• If we construct a halftone with
these characteristics, it will be
green noise
• For the purpose of
implementation, the pair
correlation curve is modeled as a
shaping function Advanced Digital Halftoning – 2 October 2011 Shaping function:
Standard form K(r)
• Independent of λg
• λg ~ input parameter that
controls coarseness of clusters
• During the design of halftone
for any level, K(r) is scaled by λg
to obtain the specific pair
correlation that we want to attain 4.30 Impact of Dispersed Macroscreen Size
• As size of screen increases, visibility of fundamental period
diminishes.
• Generally, a size between 128x128 and 256x256 is adequate. 16x16 pattern repeated 16x16 times
Advanced Digital Halftoning – 2 October 2011 32x32 pattern repeated 8x8 times
4.31 Impact of Dispersed Macroscreen Size (cont.) 64x64 pattern repeated 4x4 times 128x128 pattern repeated 2x2 times Advanced Digital Halftoning – 2 October 2011 4.32 Importance of incorporating wraparound in screen design
Level: 15/255 No
wraparound
DBS Level: 90/255 Advanced Digital Halftoning – 2 October 2011 Level: 15/255 Level: 90/255 Wraparound
DBS 4.33 Synopsis
•
•
•
•
•
•
• Screening architecture
Screen taxonomy
Screen descriptors
Analysis of tone and detail
Stochastic screens
Periodic, clustereddot screens (hybrid screen)
Moirefree conditions for screen design Advanced Digital Halftoning – 2 October 2011 4.34 Hybrid Screen Topics
[Lee and Allebach, 2007]
• Introduction To Hybrid Screen
• Bilevel Hybrid Screen Design
• Multilevel Hybrid Screen Design
• Experimental Results
• Color Hybrid Screen Design Advanced Digital Halftoning – 2 October 2011 4.35 ClusteredDot Screen
• Gray levels are realized by changing the clustereddot size (AM
halftoning) • Advantage
– Cluster is stable, robust to dot gain widely used for
electrophotographic (EP) process • Disadvantage
– Poor rendering details
– Limited gray levels contouring artifact Clustereddot screen Disperseddot screen Advanced Digital Halftoning – 2 October 2011 4.36 Simple ClusteredDot Screen
a=127/255
a=16/255
a=0
Continuoustone input Contouring Halftone using simple clustereddot screen
Advanced Digital Halftoning – 2 October 2011 4.37 Supercell Approach
•
• Supercell is a set of microcells together as a single screen
Supercell is used
To increase the number of gray levels
To create more accurately angled screen microcell 02
with macrocell
growing sequence 3 1 01
2 01
2 04
8 26 01
2 01
2 37 15
9 11 10 Increasing the gray levels Advanced Digital Halftoning – 2 October 2011 15.9° 14.93° Creating more accurately
angled screen 4.38 Limitation on Supercell
Periodic dot
withdrawal pattern Abrupt
texture change
 Bayer structure Clustereddot microcell with Bayer macrocell growing sequence Stochastic dot
withdrawal pattern
Homogeneous
dot distribution Mazelike artifact
Clustereddot microscreen with stochasticdispersed macrocell growing sequence
Advanced Digital Halftoning – 2 October 2011 4.39 The Hybrid Screen
• The hybrid screen is a screening algorithm which generates stochastic
disperseddot textures in highlights and shadows, and periodic clustereddot textures in midtones. Disperseddot Clustereddot recursive ordering pattern regularly nucleated clusters blue noise green noise Periodic Stochastic Advanced Digital Halftoning – 2 October 2011 4.40 The Hybrid Screen (cont.)
• Two major idea for the hybrid screen: supercell + core
• To remove the mazelike artifact, a small region is defined as a
“core” in each microcell.
• Inside the core, the original microcell growing sequence is ignored
and the sequence can be randomized the first dot can move
around within the core creates bluenoiselike texture No noticeable
dot withdrawal
pattern Bluenoiselike
texture The hybrid screen – clustereddot microcell with 2x2 core
with DBS macrocell growing sequence
Advanced Digital Halftoning – 2 October 2011 4.41 Parameter Specifications
w w _ j _1
j _2 z z i i Orthogonal Screen Advanced Digital Halftoning – 2 October 2011 Nonorthogonal Screen 4.42 Microcell Design
• • Microcell Design Procedure
Continuous Parameter Halftone Cell
Line Quantization
Copy Boundaries
Number of pixels in the microcell: Nmicro = det N = 17 w C C O C O O z
B
A B
A (a) Advanced Digital Halftoning – 2 October 2011 B
A (b) (c) 4.43 Supercell Design
Basic screen block (BSB): Smallest rectangle tiled in vertical
and horizontal directions
Core size and shape: 4pixel core when f ~ 140 to 190 lpi
Microcell growing sequence
17
14
12 10
13 7 9
4 5 15
2 8 16
16
3 11
Cyan 15
5
94
17 14 Advanced Digital Halftoning – 2 October 2011 6 11
12
7
13 Magenta Highlight core pixels
Midtone pixels
Shadow core pixels ( a) 16
8
3
10
12 ( b) 4.44 Highlight and Shadow Design
• • Highlight generation
– FM seeding: place one dot per core
– AM growing: grow each seed dot in the core
Designing a level of the dot profile function • Random toggle ( ~ Nmacro/Lmacro dots)
Constrained DBS swap
Index matrix for highlight • Index matrix for shadows when the core shape is
the same Advanced Digital Halftoning – 2 October 2011 After
random
toggle After swap
(1 iteration) Final
(5 iterations) 4.45 Hybrid Screen Generation
• Determining the macrocell growing sequence dmacro[m,n]
– Use the first doton sequence from FM seeding
• The index matrix for midtone: use composite screen index for
supercell approach • Index matrix generation 02
with macrocell
growing sequence 3 1 microcell • Screen generation 01
2 01
2 04
8 26 • Halftoning operation 01
2 01
2 37 15
9 11 e.g. 9 = 4 X 2 + 1 Advanced Digital Halftoning – 2 October 2011 4.46 10 Multilevel Hybrid Screen Design
• Two approaches for creating multilevel hybrid screens
Tile vectors are all integervalued screen design by bilevel
screen extension
Tile vector contains noninteger value that corresponds to high
resolution grid multilevel hybrid screen design using high
resolution grid
w Construct bilevel hybrid
screen j
z Extension to multilevel
screen
i 1. Multilevel hybrid screen by bilevel
hybrid screen extension Advanced Digital Halftoning – 2 October 2011 2. Multilevel hybrid screen design
using high resolution grid 4.47 Multilevel Hybrid Screen Design by Bilevel Hybrid
Screen Extension
• Screen design by bilevel screen extension: tile vectors must be all
integervalued so that bilevel hybrid screen can be built
Extension is done using the concept of anchor levels
– Anchor levels: Selected halftone patterns chosen from among the
dot profile function of the bilevel hybrid screen
Select 5 anchor levels: {pa0, pa1, pa2, pa3, pa4} = {p0, p1, p4, p6, p9} • • p0 p1 p2 p3 p4 p5 p6 p7 p8 p9 p0 p1 p4 p6 p9 • Partial dot growing sequence p0 p1 Advanced Digital Halftoning – 2 October 2011 p4 p6 p9 4.48 Relation between bit depth and core size  1 bpp
Periodic
texture Noticeable dot
withdrawal pattern Supercell with Bayer macroscreen Hybrid screen with 1x1 core Bluenoiselike
texture Dot withdrawal
pattern removed Hybrid screen with 2x2 core
Advanced Digital Halftoning – 2 October 2011 4.49 Relation between bit depth and core size  2 bpp
Texture is reduced, but still visible Comparable, but 2x2 is a little bit noisier than others Supercell with Bayer macroscreen Supercell with Bayer macroscreen Hybrid screen with 1x1 core Hybrid screen with 1x1 core Hybrid screen with 2x2 core Hybrid screen with 2x2 core 3 Levels 4 Levels Advanced Digital Halftoning – 2 October 2011 4.50 Relation between bit depth and core size  4 bpp Supercell with Bayer macroscreen Clean texture No visible patterns Hybrid screen with 1x1 core Noisy texture Hybrid screen with 2x2 core
Advanced Digital Halftoning – 2 October 2011 4.51 Rules of Thumb •
•
•
• In bilevel hybrid screen, the hybrid screen with 2x2 core shows
the best results in both smooth and detail mode.
In multilevel hybrid screen, the extreme highlight pattern is
greatly improved in Bayer and 1x1 core hybrid screen.
On the other hand, the hybrid screen with 2x2 core appears
noisier while growing from highlight to midtone due to stochastic
texture
As a conclusion, the core size should be decreased (stochastic
pattern must be restricted) when
1. Bit depth become higher
2. The screen frequency become higher Advanced Digital Halftoning – 2 October 2011 4.52 Color Hybrid Screen Design
• To further improve the color texture, we jointly optimize
color screens which has been separately designed.
• For the hybrid screen design, we can improve the highlight
parts by developing the error metric for joint screens.
• Among four primary colorants (C, M, Y, K), we focus on two
major colorants, C and M, because
– The joint optimization of these two colorants give as
good a result as a design based on the joint
optimization of CMY screens
– This two colorants are critical for skin tone Advanced Digital Halftoning – 2 October 2011 4.53 Color Hybrid Screen Framework
C f [m , n ] Ra ndom
T oggl e C
l −1 p [m , n ]
f
M M [m , n ] Ra ndom
T oggl e pl −1 [m , n ] e C MY [ m, n ]
C _
p lM [m , n ]
= g M [m , n ] p [m , n ]
= g C [ m, n ] T
T eMy [ m, n ]
Y
e [m , n ] D BS
Sw a p T L um i na nc e Fi l t e r
L um i na nc e Fi l t e r
L um i na nc e Fi l t e r
Chrom i na nc e Fi l t e r CM eC z [ m, n ] Chrom i na nc e Fi l t e r Advanced Digital Halftoning – 2 October 2011 1 Cha nne l 3 Cha nne l s
Col or e rror
i m a ge
c re a t i on + CM eC x [m , n ] M e [m , n ] C eYy [m , n ] CM
Yy e C MY [ m, n ]
CM +
_ C
l M e C MY [ m, n ] D BS
Sw a p e C [ m, n] C e Yy [m , n ]
M e Yy [m , n ]
CM
Yy [ m, n ]
e
C
M [m , n ]
e Cx
CM
Yy [ m, n ]
e  . 
 . 
 .  2 EC 2 E 2 E YC M
y 2 EC x 2 CM
EC z + CM  . 
 .  + M ∑ E= + α iE i i= C , , M
MC +
E CM = ∑ CM CM αj Ej j =Yy , x , z
CC 4.54 Joint Screen Design Results Ramp halftoned with separately designed cyan screen Ramp halftoned with jointly designed cyan screen
Advanced Digital Halftoning – 2 October 2011 4.55 Joint Screen Design Results Ramp halftoned with separately designed magenta screen Ramp halftoned with jointly designed magenta screen
Advanced Digital Halftoning – 2 October 2011 4.56 Joint Screen Design Results CM ramp halftoned with separately designed screens CM ramp halftoned with jointly designed screens
†Colors are modified to make cyan dots visible on the projector Advanced Digital Halftoning – 2 October 2011 4.57 Synopsis
•
•
•
•
•
•
• Screening architecture
Screen taxonomy
Screen descriptors
Analysis of tone and detail
Stochastic screens
Periodic, clustereddot screens (hybrid screen)
Moirefree conditions for screen design Advanced Digital Halftoning – 2 October 2011 4.58 Most Common 4Color CMYK Halftoning
Separately halftone each color with a different screen matrix Overall Procedure:
C Continuoustone
image
M Continuoustone
image
RGB Continuoustone
image Halftoning Halftoning ⊕ Y Continuoustone
image Halftoning K Continuoustone
image CMYK Halftone Halftoning superposed Example:
http://en.wikipedia.org/wiki/Halftone separate halftones
superposed color halftone
Advanced Digital Halftoning – 2 October 2011 4.59 Halftone Representations in Spatial/Frequency Domains
Using Periodic ClusteredDot Screens
Continuous Space Fourier Transform (CSFT): the spectral representation of periodic clustereddot is “halftone spectral lattice” in the frequency
domain. (as shown in the lower right figure) ~ tile vectors
~ periodicity matrix Periodic ClusteredDot ~ fundamental frequencies
~ frequency matrix
screen angle
~ intrascreen angle
dotperinch, dpi
Halftone spectral lattice
Advanced Digital Halftoning – 2 October 2011 4.60 What is the Moiré Formation? Amidror, 1994:
• (It is clear to describe moiré in the frequency domain) if the new frequency
component that arrives from the superposition of two colorant planes locates in
lowfrequency region, there will be moiré. spatial
domain +
(d) frequency
domain (c) (b) (a) =
(e) + (f) = (unit: cycles/inch) : new frequency component Advanced Digital Halftoning – 2 October 2011
Isaac Amidror , Roger D. Hersch , Victor Ostromoukhov ,” Spectral analysis and minimization of
moiré patterns in color separation ,” JEI, 1994. 4.61 When We Superpose Two Colorant Planes • Moiré: the new lowfrequency component that arrives from superposition One example of possible firstorder moiré Advanced Digital Halftoning – 2 October 2011 4.62 How About HighOrder Moiré in 2Color Case? • Moiré: the new lowfrequency component that arrives from superposition One example of possible highorder moiré Advanced Digital Halftoning – 2 October 2011 4.63 FirstOrder MoiréFree Conditions in 2Color Case (check
8 new frequency components)
Moiré comes from lowfrequency components.
Firstorder moiréfree condition in 2color case: Firstorder moiréfree condition: 1 We need to check 8 composite
frequencies. (blue arrows) 3 8 Periodic ClusteredDot 2 5 4 7
6
: Fundamental frequencies Frequency Components : Sums and differences of
fundamental frequencies Advanced Digital Halftoning – 2 October 2011 firstorder case 4.64 Possible HighOrder Moiré in 2Color Case
Firstorder moiréfree condition checks:
(Check 8 composite frequencies, shown as red lines) Possible highorder moiré :
(More than 8 composite frequencies) (Firstorder moiré: Frequency
domain: ( an example of highorder moiré)
Possible firstorder moiré
Possible highorder moiré
: Highorder frequency components
: Fundamental frequencies
: Sums and differences of
fundamental frequencies
: Linear combination of highorder
fundamental frequencies Advanced Digital Halftoning – 2 October 2011 4.65 FirstOrder MoiréFree Condition in 3Color Case
In the 3color case, we need to check:
(moiré comes from superimposing 2 color separations) (a) Firstorder 2color moiréfree condition: (any 2 different colors) (moiré comes from superimposing 3 color separations) (b) Firstorder 3color moiréfree condition: (all 3 colors) Advanced Digital Halftoning – 2 October 2011 Example of 3color case
(shown in frequency domain) 4.66 Previous Approaches to Minimizing Visible Moiré in Color
Printing
Traditional graphic arts industry (screen set of rotating identical, square screens):
Use set of 75°, 15°, 0°, and 45° for C,M,Y, and K Amidror, 1994
Analyze moiré formation in the frequency domain
Propose idea of “firstorder moiré” Consider
firstorder
moiré Baqai and Allebach, 2002 (3color screen set)
Provide a framework to search for nonorthogonal moiréfree screens
Apply HVS to account for human viewer Search for
nonorthogonal
screens ShenGe Wang, 2003 (3color screen set)
Derive conventional 3color moiréfree conditions
Propose a 3color moiréfree screen set Firstorder
moiréfree
condition Akira Ishii, 2003 (4color screen set)
Propose idea of “sharing screen frequency”
4color screen set which prevents moiré “sufficiently” (under 200 lpi) ShenGe Wang, 2007 (3color screen set)
Propose uniform hexagon moiréfree 3color printing
Address highorder moiréfree case as “uniform hexagon” Sharing
screen
frequency ShenGe Wang and Robert Loce, 2008 (Ncolor screen set)
Propose uniform hexagon moiréfree Ncolor printing
Advanced Digital Halftoning – 2 October 2011 Highorder
moiréfree
condition 4.67 Idea of Frequency LatticeBased Screen [4]
We can solve Ncolor highorder moiré problems by using “frequency basis spectral
lattice”: each time we select two lattice points (gray points) as one pair of fundamental
frequency vectors of a colorant plane. Repeat this procedure until Ncolorant (N pairs). One example of “frequency basis spectral lattice” (hexagonal frequency lattice): Frequency basis spectral
lattice (frequency domain) : Minimum frequency distance between any 2 lattice points: (predefined minimum permissible moiré frequency λ)
Advanced Digital Halftoning – 2 October 2011
ShenGe Wang and R. P. Loce, “Uniformrosette color halftoning for Ncolor moiréfree printing,” JEI, Apr. 2008. 4.68 Uniform Rosette Configuration C,M,K Screens Frequency Representation Moiréfree condition
Uniform rosette configuration
Advanced Digital Halftoning – 2 October 2011 4.69 Uniform Rosette Configuration – Digital Halftone CK CMK CM MK
Advanced Digital Halftoning – 2 October 2011 4.70 70 ...
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This note was uploaded on 02/19/2012 for the course ECE 638 taught by Professor Staff during the Fall '08 term at Purdue University.
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