Model-based digital halftoning

Digital halftoning is the process of generating a pattern of pixels with a limited number of colors that, when seen by the human eye, is perceived as a continuous-tone image. Digital halftoning is used to display continuous-tone images in media in which the direct rendition of the tones is impossible. The most common example of such media is ink or toner on paper, and the most common rendering devices for such media are, of course, printers. Halftoning works because the eye acts as a spatial low-pass filter that blurs the rendered pixel pattern, so that it is perceived as a continuous-tone image. Although all halftoning methods rely at least implicitly, on some understanding of the properties of human vision and the display device, the goal of model-based halftoning techniques is to exploit explicit models of the display device and the human visual system (HVS) to maximize the quality of the displayed images. Based on the type of computation involved, halftoning algorithms can be broadly classified into three categories: point algorithms (screening or dithering), neighborhood algorithms (error diffusion), and iterative algorithms [least squares and direct binary search (DBS)]. All of these algorithms can incorporate HVS and printer models. The best halftone reproductions, however, are obtained by iterative techniques that minimize the (squared) error between the output of the cascade of the printer and visual models in response to the halftone image and the output of the visual model in response to the original continuous-tone image.     

Inverse halftoning via MAP estimation

There has been a tremendous amount of research in the area of image halftoning, where the goal has been to find the most visually accurate representation given a limited palette of gray levels (often just two, black and white). This paper focuses on the inverse problem, that of finding efficient techniques for reconstructing high-quality continuous-tone images from their halftoned versions. The proposed algorithms are based on a maximum a posteriori (MAP) estimation criteria using a Markov random field (MRF) model for the prior image distribution. Image estimates obtained with the proposed model accurately reconstruct both the smooth regions of the image and the discontinuities along image edges. Algorithms are developed and example gray-level reconstructions are presented generated from both dithered and error-diffused halftone originals. Application of the technique to the problems of rescreening and the processing of halftone images are shown.     

Joint halftoning and watermarking

A framework to jointly halftone and watermark a grayscale images is presented. The framework needs the definition of three components: a human visual system (HVS)-based error metric between the continuous-tone image and a halftone, a watermarking scheme with a corresponding watermark detection measure, and a search strategy to traverse the space of halftones. We employ the HVS-based error metric used in the direct binary search (DBS) halftoning algorithm, and we use a block-based spread spectrum watermarking scheme and the toggle and swap search strategy of DBS. The halftone is printed on a desktop printer and scanned using a flatbed scanner. The watermark is detected from the scanned image and a number of post-processed versions of the scanned image, including one restored in Adobe PhotoShop. The results show that the watermark is extremely resilient to printing, scanning, and post-processing; for a given baseline image quality, joint optimization is better than watermarking and halftoning independently. For this particular algorithm, the original continuous-tone image is required to detect the watermark.     

A dual interpretation for direct binary search and its implicationsfor tone reproduction and texture quality

The direct binary search (DBS) algorithm employs a search heuristic to minimize the mean-squared perceptually filtered error between the halftone and continuous-tone original images. Based on an efficient method for evaluating the effect on the mean squared error of trial changes to the halftone image, we show that DBS also minimizes in a pointwise sense the absolute error under the same visual model, but at twice the viewing distance associated with the mean-squared error metric. This dual interpretation sheds light on the convergence properties of the algorithm, and clearly explains the tone bias that has long been observed with halftoning algorithms of this type. It also demonstrates how tone bias and texture quality are linked via the scale parameter, the product of printer resolution and viewing distance. Finally, we show how the tone bias can be eliminated by tone-correcting the continuous-tone image prior to halftoning it.     

连续图像数字半调处理及性能分析

本文阐述了连续图像数字半调处理的基本理论,包括有序抖动数字半调处理、误差扩散数字半调处理,并对2种处理进行了性能分析。     

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 new class of B/W halftoning algorithms

A new class of dithering algorithms for black and white (B/W) images is presented. The basic idea behind the technique is to divide the image into small blocks and minimize the distortion between the original continuous-tone image and its low-pass-filtered halftone. This corresponds to a quadratic programming problem with linear constraints, which is solved via standard optimization techniques. Examples of B/W halftone images obtained by this technique are compared to halftones obtained via existing dithering algorithms.     

Adaptive error diffusion and its application in multiresolutionrendering

Error diffusion is a procedure for generating high quality bilevel images from continuous-tone images so that both the continuous and halftone images appear similar when observed from a distance. It is well known that certain objectionable patterning artifacts can occur in error-diffused images. Here, we consider a method for adjusting the error-diffusion filter concurrently with the error-diffusion process so that an error criterion is minimized. The minimization is performed using the least mean squares (LMS) algorithm in adaptive signal processing. Using both raster and serpentine scanning, we show that such an algorithm produces better halftone image quality compared to traditional error diffusion with a fixed filter. Based on the adaptive error-diffusion algorithm, we propose a method for constructing a halftone image that can be rendered at multiple resolutions. Specifically, the method generates a halftone from a continuous tone image such that if the halftone is down-sampled, a binary image would result that is also a high quality rendition of the continuous-tone image at a reduced resolution. Such a halftone image is suitable for progressive transmission, and for cases where rendition at several resolutions is required. Cases for noninteger scaling factors are also considered.     

Permutation filter lattices: a general order-statistic filteringframework

A general nonlinear filtering framework-permutation order-statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination. Permutation filters, much like polynomial filters, are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions. At the simplest level in the filter lattice, permutation filters reduce to either a simple linear (FIR) or to an order statistic (OS) filter, but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties. In order to enhance the robustness of permutation fitters, we develop α-trimmed permutation indicators and their associated filter lattices. We conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system. This paper, thus extends the potential of order-statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems     

An adaptive inverse halftoning algorithm

A class of inverse halftoning algorithms that recovers grayscale (continuous-tone) images from halftone images is proposed. The basic structure is an optimized linear filter. Then, a properly designed adaptive postprocessor is employed to enhance the recovered image quality. Finally, a multistage space-varying algorithm is developed that uses the basic linear filter structure as before but with spatially adaptive parameters.     

A Survey of Electronic Techniques for Pictorial Image Reproduction

This paper is a tradeoff study of image processing algorithms that can be used to transform continuous tone and halftone pictorial image input into spatially encoded representations compatible with binary output processes. A large percentage of the electronic output marking processes utilize a binary mode of operation. The history and rationale for this are reviewed and thus the economic justification for the tradeoff is presented. A set of image quality and processing complexity metrics are then defined. Next, a set of algorithms including fixed and adaptive thresholding, orthographic pictorial fonts, electronic screening, ordered dither, and error diffusion are defined and evaluated relative to their ability to reproduce continuous tone input. Finally, these algorithms, along with random nucleated halftoning, the alias reducing image enhancement system (ARIES), and a new algorithm, selective halftone rescreening (SHARE), are defined and evaluated as to their ability to reproduce halftone pictorial input.     

自适应反馈视觉感知差的误差扩散半色调算法

文章基于人眼对亮度的视觉感受特性。提出了一种自适应反馈视觉感知差的误差扩散算法（PEF Error Diffusion算法）。首先提出视觉感知差的概念，然后根据原图像区域的灰度特征，自适应地计算反馈系数，将视觉感知差反馈给原连续调图像，以补偿误差扩散所引起的不同区域的灰度损失。实验结果表明，由于视觉感知差的引入及反馈系数的自适应变化。PEF Error Diffusion算法能够明显增强图像的整体对比度．减弱点增益现象的不良影响，并准确再现更多的图像细节．因而表现出比传统算法更好的主观视觉效果。     

Filters involving derivatives with application to reconstructionfrom scanned halftone images

This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters.     

Permutation weighted order statistic filter lattices

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window. Hence, PWOS filters are in essence time-varying WOS filters. By varying the amount of temporal-rank order information used in selecting the output for a given observation window size, we obtain a wide range of filters that are shown to comprise a complete lattice structure. At the simplest level in the lattice, PWOS filters reduce to the well-known WOS filter, but for higher levels in the lattice, the obtained selection filters can model complex nonlinear systems and signal distortions. It is shown that PWOS filters are realizable by a N! piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory. Simulations are included to show the advantages of PWOS filters for the processing of image and video signals.     

Data hiding in ordered dithered halftone images

In this paper, we propose a novel method called data hiding ordered dithering (DHOD) to hide a relatively large amount of invisible watermarking data in ordered dithered halftone images while retaining good visual quality. We assume that both the original image and the ordered dithering screen are available. The proposed method includes two techniques:screen modification andthreshold selection. First, one out of everyM pseudo-random locations is selected usingthreshold selection to embed one bit of hidden data. Second, at the selected locations,screen modification is applied to change the ordered dithering screen in a local neighborhood to achieve the desired data hiding while attaining good visual quality. Some custom-made quality measures are proposed to evaluate DHOD. Simulation results suggest that DHOD can hide a large amount of data while maintaining good visual quality.This work has been supported by the Research Grants Council of the Hong Kong Special Administrative Region, China.     

Permutation filters: a class of nonlinear filters based on setpermutations

Introduces and analyzes a new class of nonlinear filters that have their roots in permutation theory. The authors show that a large body of nonlinear filters proposed to date constitute a proper subset of permutation filters (𝒫 filters). In particular, rank-order filters, weighted rank-order filters, and stack filters embody limited permutation transformations of a set. Indeed, by using the full potential of a permutation group transformation, one can design very efficient estimation algorithms. Permutation groups inherently utilize both rank-order and temporal-order information; thus, the estimation of nonstationary processes in Gaussian/nonGaussian environments with frequency selection can be effectively addressed. An adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion. Simulation results are presented to illustrate the performance of permutation filters in comparison with other widely used filters     

Halftone visual cryptography.

Visual cryptography encodes a secret binary image (SI) into n shares of random binary patterns. If the shares are xeroxed onto transparencies, the secret image can be visually decoded by superimposing a qualified subset of transparencies, but no secret information can be obtained from the superposition of a forbidden subset. The binary patterns of the n shares, however, have no visual meaning and hinder the objectives of visual cryptography. Extended visual cryptography [1] was proposed recently to construct meaningful binary images as shares using hypergraph colourings, but the visual quality is poor. In this paper, a novel technique named halftone visual cryptography is proposed to achieve visual cryptography via halftoning. Based on the blue-noise dithering principles, the proposed method utilizes the void and cluster algorithm [2] to encode a secret binary image into n halftone shares (images) carrying significant visual information. The simulation shows that the visual quality of the obtained halftone shares are observably better than that attained by any available visual cryptography method known to date.     

Hybrid LMS-MMSE inverse halftoning technique

The objective of this work is to reconstruct high quality gray-level images from bilevel halftone images. We develop optimal inverse halftoning methods for several commonly used halftone techniques, which include dispersed-dot ordered dither, clustered-dot ordered dither, and error diffusion. At first, the least-mean-square (LMS) adaptive filtering algorithm is applied in the training of inverse halftone filters. The resultant optimal mask shapes are significantly different for various halftone techniques, and these mask shapes are also quite different from the square shape that was frequently used in the literature. In the next step, we further reduce the computational complexity by using lookup tables designed by the minimum mean square error (MMSE) method. The optimal masks obtained from the LMS method are used as the default filter masks. Finally, we propose the hybrid LMS-MMSE inverse halftone algorithm. It normally uses the MMSE table lookup method for its fast speed. When an empty cell is referred, the LMS method is used to reconstruct the gray-level value. Consequently, the hybrid method has the advantages of both excellent reconstructed quality and fast speed. In the experiments, the error diffusion yields the best reconstruction quality among all three halftone techniques.     

秩排序非线性滤波器的自适应优化算法

在图像处理中，秩排序非线性滤波器具有非常重要的作用。本文从加权顺序统计滤波器的自适应优化算法出发，导出了加权中值滤波器、秩选择滤波器和置换滤波器等几种重要的秩排序非线性滤波器的自适应优化设计算法，这些算法采用迭代计算实现，并可以在MAE、MSE和／Z准则下得到最优解。模拟实验表明，这些算法具有非常好的收敛效果，并可以很好地用于类似图像的非平稳信号的处理。     

Look-up table (LUT) method for inverse halftoning

In this paper we propose look-up table (LUT) based methods for inverse halftoning of images. The LUT for inverse halftoning is obtained from the histogram gathered from a few sample halftone images and corresponding original images. The method is extremely fast (no filtering is required) and the PSNR and visual image quality achieved is comparable to the best methods known for inverse halftoning. The LUT inverse halftoning method does not depend on the specific properties of the halftoning method, and can be applied to any halftoning method. Then, an algorithm for template selection for LUT inverse halftoning is introduced. We demonstrate the performance of the LUT inverse halftoning algorithm on error diffused images and ordered dithered images. We also extend LUT inverse halftoning to color halftones.