1.2 Design of Periodic, Clustered-Dot Screens

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

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

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

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

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

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.

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.

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.

Rendering of Detail - Partial Dotting

Partial Dotting - Example

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

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

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.

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

Start With a Lattice Continuous Parameter Halftone Cell (CPHC)

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

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

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

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

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

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

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

Parameter Specifications Orthogonal Screen Nonorthogonal Screen

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

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

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 2 + 1

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

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

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

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

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

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