1. 1.2 Design of Periodic, Clustered-Dot Screens

2. Synopsis Screening architecture Screen taxonomy Screen descriptors
Analysis of tone and detail
Periodic, clustered-dot screens (hybrid screen)

3. Screening is a Thresholding Process
Simple point-to-point transformation of each pixel in the continuous-tone image to a binary value.
Process requires no memory or neighborhood information.
Threshold

4. 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.
Continuous-tone original image
Result of applying a fixed threshold at midtone

5. Basic Structure of Screening Algorithm
The threshold matrix is periodically tiled over the entire continuous-tone image.

6. 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 pixel-to-pixel comparision with thresholds in a matrix.
The following are equivalent terms for the threshold matrix:
screen
dither matrix
mask

7. 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.

8. 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 one-to-one relationship between the dot profile and the screen.

9. 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.

10. Rendering of Detail - Partial Dotting

11. Partial Dotting - Example

12. Spatial Arrangement of Thresholds
For clustered dot textures, thresholds that are close in value are located close together in the threshold matrix

13. Spatial Arrangement of Thresholds (cont.)
For dispersed dot textures, thresholds that are close in value are located far apart in the threshold matrix.

14. 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.

15. Clustered-Dot Screen
Gray levels are realized by changing the clustered-dot 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
Clustered-dot screen
Dispersed-dot screen

16. Start With a Lattice
Continuous Parameter Halftone Cell (CPHC)

17. Finding Discrete Parameter Halftone Cell (DPHC)
Compute number of pixels in unit cell = |det(N)|
Assign pixels to unit cell in order of decreasing area of overlap with CPHC
Skip over pixels that are congruent to a pixel that has already been assigned to DPHC
DPHC
Area

18. Threshold Assignment by Growing Dots and Holes Simultaneously
Abs. = 0.74
Abs. = 0.26
Abs. = 0.53

19. Simple Clustered-Dot Screen
a=127/255
a=16/255
a=0
Continuous-tone input
Contouring
Halftone using simple clustered-dot screen

20. 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
with macrocell growing sequence 2 1 3
microcell 1 1 4 2 6 2 2 8 10
14.93° 1 1 3 7 1 5
15.9° 2 2 11 9
Creating more accurately angled screen
Increasing the gray levels

21. Limitation on Supercell
Periodic dot withdrawal pattern
Abrupt
texture change
- Bayer structure
Clustered-dot microcell with Bayer macrocell growing sequence
Stochastic dot withdrawal pattern
Homogeneous
dot distribution
Maze-like artifact
Clustered-dot microscreen with stochastic-dispersed macrocell growing sequence

22. The Hybrid Screen Smooth transition
The hybrid screen is a screening algorithm which generates stochastic dispersed-dot textures in highlights and shadows, and periodic clustered-dot textures in midtones.
Dispersed-dot
Clustered-dot
Periodic
recursive ordering pattern
regularly nucleated clusters
Stochastic
blue noise
green noise
Smooth transition

23. The Hybrid Screen (cont.)
Two major idea for the hybrid screen: supercell + core
To remove the maze-like 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 blue-noise-like texture
No noticeable
dot withdrawal pattern
Blue-noise-like
texture
The hybrid screen – clustered-dot microcell with 2x2 core
with DBS macrocell growing sequence

24. Parameter Specifications
Orthogonal Screen
Nonorthogonal Screen

25. Microcell Design Microcell Design Procedure
Continuous Parameter Halftone Cell
Line Quantization
Copy Boundaries
Number of pixels in the microcell: Nmicro = |det N| = 17

26. Supercell Design
Basic screen block (BSB): Smallest rectangle tiled in vertical and horizontal directions
Core size and shape: 4-pixel core when f ~ 140 to 190 lpi
Microcell growing sequence 11 5 8 6 16 15 2 4 3 9 14 10 7 17 13 12 1 15 14 4 5 9 17 16 10 2 12 7 1 6 13 11 3 8
Cyan
Magenta

27. Hybrid Screen Generation
Determining the macrocell growing sequence dmacro[m,n]
Use the first dot-on sequence from FM seeding
The index matrix for midtone: use composite screen index for supercell approach
Index matrix generation
with macrocell growing sequence 2 1 3
microcell 1 4 2 6
Screen generation 2 8 10 3 7 1 5
Halftoning operation 11 9
e.g. 9 = 4 X

28. Multilevel Hybrid Screen Design
Two approaches for creating multilevel hybrid screens
Tile vectors are all integer-valued  screen design by bilevel screen extension
Tile vector contains non-integer value that corresponds to high resolution grid  multilevel hybrid screen design using high resolution grid
Construct bilevel hybrid screen
Extension to multilevel screen
1. Multilevel hybrid screen by bilevel hybrid screen extension
2. Multilevel hybrid screen design using high resolution grid

29. Multilevel Hybrid Screen Design by Bilevel Hybrid Screen Extension
Screen design by bilevel screen extension: tile vectors must be all integer-valued 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 p4 p6 p9

30. Relation between bit depth and core size - 1 bpp
Periodic texture
Noticeable dot withdrawal pattern
Supercell with Bayer macroscreen
Hybrid screen with 1x1 core
Blue-noise-like texture
Dot withdrawal pattern removed
Hybrid screen with 2x2 core

31. 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

32. 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

33. 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
Bit depth become higher
The screen frequency become higher