Digital Halftoning Algorithms Research Articles

Alpha stable modeling of human visual systems for digital halftoning in rectangular and hexagonal grids

Human visual system (HVS) modeling has become a critical component in the design of digital halftoning algorithms. Methods that exploit the characteristics of the HVS include the direct binary search (DBS) and optimized tone-dependent halftoning approaches. The spatial sensitivity of the HVS is low-pass in nature, reflecting the physiological characteristics of the eye. Several HVS models have been proposed in the literature, among them, the broadly used Näsänen’s exponential model, which was later shown to be constrained in shape. Richer models are needed to attain better halftone attributes and to control the appearance of undesired patterns. As an alternative, models based on the mixture of bivariate Gaussian density functions have been proposed. The mathematical characteristics of the HVS model thus play a key role in the synthesis of model-based halftoning. In this work, alpha stable functions, an elegant class of functions richer than mixed Gaussians, are exploited to design HVS models to be used in two different contexts: monochrome halftoning over rectangular and hexagonal sampling grids. In the two scenarios, alpha stable models prove to be more efficient than Gaussian mixtures, as they use less parameters to characterize the tails and bandwidth of the model. It is shown that a decrease in the model’s bandwidth leads to homogeneous halftone patterns, and conversely, models with heavier tails yield smoother textures. These characteristics, added to their simplicity, make alpha stable models a powerful tool for HVS characterization.

Digital color halftoning

Digital color halftoning is the process of transforming continuous-tone color images into images with a limited number of colors. The importance of this process arises from the fact that many color imaging systems use output devices such as color printers and low-bit depth displays that are bilevel or multilevel with a few levels. The goal is to create the perception of a continuous-tone color image using the limited spatiochromatic discrimination capability of the human visual system. In decreasing order of how locally algorithms transform a given image into a halftone and, therefore, in increasing order of computational complexity and halftone quality, monochrome digital halftoning algorithms can be placed in one of three categories: 1) point processes (screening or dithering), 2) neighborhood algorithms (error diffusion), and 3) iterative methods. All three of these algorithm classes can be generalized to digital color halftoning with some modifications. For an in-depth discussion of monochrome halftoning algorithms, the reader is directed to the July 2003 issue of IEEE Signal Processing Magazine. In the remainder of this article, we only address those aspects of halftoning that specifically have to do with color. For a good overview of digital color halftoning, the reader is directed to Haines et al. (2003). In addition, Agar et al. (2003) contains a more in-depth treatment of some of the material found in this work.

A Unified Framework for Digital Halftoning and Dither Mask Construction: Variations on a Theme and Implementation Issues

We present a unified algorithmic framework for some classes of digital halftoning algorithms including Direct Binary Search (DBS) and dither mask generation algorithms such as Void and Cluster, BIPPSMA, and clustered dot with blue noise interpolation. Although these algorithms are different and used in different ways, e.g. Direct Binary Search is a global halftoning process, whereas dither masks are used in point halftoning processes, we show that they are all variations of a core algorithm. This makes it easier to compare the performance of these algorithms. Furthermore, by viewing these algorithms in the same framework, algorithmic extensions and implementation tricks and techniques among these algorithms can be more easily shared and their benefits exploited.The core algorithm is essentially an optimization algorithm using pixel swapping where the cost function describes the perceptual difference between the halftone image and the color image when viewed at a distance. We compare various algorithms in the literature as they are cast in this framework. In particular, this framework allows us to derive a more efficient implementation of DBS.

A dithering algorithm for local composition control with three-dimensional printing

A dithering algorithm is presented for application to local composition control (LCC) with three-dimensional printing (3D printing) to convert continuous-tone representation of objects with LCC into discrete (pointwise) version of machine instructions. The algorithm presented effectively reduces undesirable low frequency textures of composition for individual 3D layers and also for 3D volumes. Peculiarities of the 3D printing machine, including anisotropic geometry of its picture elements (PELs) and uncertainties in droplet placement, are addressed by adapting a standard digital halftoning algorithm. Without loss of generality, our algorithm also accounts for technical limitations in the printing device, only generating lattices that can be represented within the finite memory limits of the hardware.

Objective quality measures for halftoned images

Digital halftoning algorithms can produce results of very different quality and characteristics. To evaluate and improve the algorithms, it is important to have robust image quality measures. We propose a method to evaluate objectively the quality of halftoned images. The method is capable of evaluating any kind of monochrome original and is not limited by the choice of halftoning method. To perform the evaluation with respect to the perception of printed halftones, we use models for dot gain in prints and the human visual system. The main contribution and novelty of the method is an adaptive filter used to separate the halftone characteristics from the information about the original in the halftoned image. This approach facilitates the evaluation of the halftoned image’s resemblance to the original as well as of the characteristics of the halftoning method.

Estimating from outputs of oversampled delta-sigma modulation

Oversampling a delta-sigma-modulated sequence, one can compute unbiased sample estimates of averages of consecutive input elements for a wide variety of inputs. We prove that these estimates are most efficient in their class (that is, variances of sample means are minimum in the class of random binary sequences g n n = 1,…, N, such that the expected values of g n are equal to the values of the corresponding inputs of delta-sigma modulation) and consistent. Delta-sigma modulation may also be described as one-dimensional error diffusion (a technique for digital halftoning). However, delta-sigma modulation is not a practical digital halftoning algorithm, because human vision averages small luminance deviations in two dimensions. We pose an open problem that invites the reader to extend our approach to the two-dimensional case for the purpose of development of a practical digital halftoning algorithm.

A dither pattern ensemble method for digital halftoning

The ordered dither digital halftoning algorithm is generalized to a dither pattern ensemble (DPE) method. The DPE method allows ensembles which contain patterns optimized, for instance, to have smooth frequency behavior to be used to form the binary image representation. Different ensembles are studied by comparing the composite Fourier spectra of the result patterns. Examples of rendered images illustrate the efficacy of the approach.

Digital Halftoning of Images

Most printers and some display devices are bilevel (black or white) and therefore not capable of reproducing continuous tone pictures. Digital halftoning algorithms transform digital gray scale images into bilevel ones which give the appearance of containing various shades of gray. A halftoning algorithm is presented in which novel concepts are combined resulting in an output image in which moire patterns are suppressed and, at the same time, the edges are enhanced. Various other artifacts associated with the halftoning process, such as contouring due to coarse quantization or to textural changes, are also absent from the output images in the proposed scheme. The algorithm separates the image into many small clusters which are processed independently and, therefore, it is capable of parallel implementation.