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.     

Adaptive threshold modulation for error diffusion halftoning

Grayscale digital image halftoning quantizes each pixel to one bit. In error diffusion halftoning, the quantization error at each pixel is filtered and fed back to the input in order to diffuse the quantization error among the neighboring grayscale pixels. Error diffusion introduces nonlinear distortion (directional artifacts), linear distortion (sharpening), and additive noise. Threshold modulation, which alters the quantizer input, has been previously used to reduce either directional artifacts or linear distortion. This paper presents an adaptive threshold modulation framework to improve halftone quality by optimizing error diffusion parameters in the least squares sense. The framework models the quantizer implicitly, so a wide variety of quantizers may be used. Based on the framework, we derive adaptive algorithms to optimize 1) edge enhancement halftoning and 2) green noise halftoning. In edge enhancement halftoning, we minimize linear distortion by controlling the sharpening control parameter. We may also break up directional artifacts by replacing the thresholding quantizer with a deterministic bit flipping (DBF) quantizer. For green noise halftoning, we optimize the hysteresis coefficients.     

A multiscale error diffusion technique for digital halftoning

A new digital halftoning technique based on multiscale error diffusion is examined. We use an image quadtree to represent the difference image between the input gray-level image and the output halftone image. In iterative algorithm is developed that searches the brightest region of a given image via "maximum intensity guidance" for assigning dots and diffuses the quantization error noncausally at each iteration. To measure the quality of halftone images, we adopt a new criterion based on hierarchical intensity distribution. The proposed method provides very good results both visually and in terms of the hierarchical intensity quality measure.     

Inverse halftoning and kernel estimation for error diffusion

Two different approaches in the inverse halftoning of error-diffused images are considered. The first approach uses linear filtering and statistical smoothing that reconstructs a gray-scale image from a given error-diffused image. The second approach can be viewed as a projection operation, where one assumes the error diffusion kernel is known, and finds a gray-scale image that will be halftoned into the same binary image. Two projection algorithms, viz., minimum mean square error (MMSE) projection and maximum a posteriori probability (MAP) projection, that differ on the way an inverse quantization step is performed, are developed. Among the filtering and the two projection algorithms, MAP projection provides the best performance for inverse halftoning. Using techniques from adaptive signal processing, we suggest a method for estimating the error diffusion kernel from the given halftone. This means that the projection algorithms can be applied in the inverse halftoning of any error-diffused image without requiring any a priori information on the error diffusion kernel. It is shown that the kernel estimation algorithm combined with MAP projection provide the same performance in inverse halftoning compared to the case where the error diffusion kernel is known.     

Modeling and quality assessment of halftoning by error diffusion

Digital halftoning quantizes a graylevel image to one bit per pixel. Halftoning by error diffusion reduces local quantization error by filtering the quantization error in a feedback loop. In this paper, we linearize error diffusion algorithms by modeling the quantizer as a linear gain plus additive noise. We confirm the accuracy of the linear model in three independent ways. Using the linear model, we quantify the two primary effects of error diffusion: edge sharpening and noise shaping. For each effect, we develop an objective measure of its impact on the subjective quality of the halftone. Edge sharpening is proportional to the linear gain, and we give a formula to estimate the gain from a given error filter. In quantifying the noise, we modify the input image to compensate for the sharpening distortion and apply a perceptually weighted signal-to-noise ratio to the residual of the halftone and modified input image. We compute the correlation between the residual and the original image to show when the residual can be considered signal independent. We also compute a tonality measure similar to total harmonic distortion. We use the proposed measures for edge sharpening, noise shaping, and tonality to evaluate the quality of error diffusion algorithms.     

Digital half-toning by error diffusion with perturbation

An error diffusion method is well known as one of the half-toning methods for displaying grey tone pictures on a bilevel display. However, the error diffusion method has some shortcomings, such as the appearance of correlated artefacts and directional hysteresis. To overcome these shortcomings, the author proposes a new error diffusion method with perturbation     

Model-based halftoning of color images

We present a new class of models for color printers. They form the basis for model-based techniques that exploit the characteristics of the printer and the human visual system to maximize the quality of the printed images. We present two model-based techniques, the modified error diffusion (MED) algorithm and the least-squares model-based (LSMB) algorithm. Both techniques are extensions of the gray-scale model-based techniques and produce images with high spatial resolution and visually pleasant textures. We also examine the use of printer models for designing blue-noise screens. The printer models cam account for a variety of printer characteristics. We propose a specific printer model that accounts for overlap between neighboring dots of ink and the spectral absorption properties of the inks. We show that when we assume a simple "one-minus-RGB" relationship between the red, green, and blue image specification and the corresponding cyan, magenta, and yellow inks, the algorithms are separable. Otherwise, the algorithms are not separable and the modified error diffusion may be unstable, The experimental results consider the separable algorithms that produce high-quality images for applications where the exact colorimetric reproduction of color is not necessary. They are computationally simple and robust to errors in color registration, but the colors are device dependent.     

Algorithms of halftoning color images with edge enhancement

Printers usually generate a limited number of colors and lack the ability of producing continuous-tone color images. Traditional error-diffusion algorithms are used to solve this problem. Compared with other approaches, the approaches of using error-diffusion in general can generate halftoned images of better quality. However, smeared edges and textures may occur in these halftoned images. To produce halftoned images of higher quality, these artifacts due to unstable images, dot-overlap, and error-diffusion must be eliminated or reduced. In this paper, we show that unstable images can be eliminated or reduced through using a proper color difference formula to select the reproduction colors even vector error-diffusion is performed in the RGB domain. We also present a method of using different filters to halftone different components of a color. This approach may have clearer and sharper edges for halftoned color images. Unexpected colors may be generated due to dot-overlap in the printing process. We have presented a method to eliminate this color distortion in the process of error-diffusion. Halftoning a color image by our proposed error-diffusion algorithm with edge enhancement has the following characteristics: the unstable images do not exist; the color-error caused by dot-overlap is corrected; and the smeared edges are sharpened.     

Design and analysis of vector color error diffusion halftoningsystems

Traditional error diffusion halftoning is a high quality method for producing binary images from digital grayscale images. Error diffusion shapes the quantization noise power into the high frequency regions where the human eye is the least sensitive. Error diffusion may be extended to color images by using error filters with matrix-valued coefficients to take into account the correlation among color planes. For vector color error diffusion, we propose three contributions. First, we analyze vector color error diffusion based on a new matrix gain model for the quantizer, which linearizes vector error diffusion. The model predicts the key characteristics of color error diffusion, esp. image sharpening and noise shaping. The proposed model includes linear gain models for the quantizer by Ardalan and Paulos (1987) and by Kite et al. (1997) as special cases. Second, based on our model, we optimize the noise shaping behavior of color error diffusion by designing error filters that are optimum with respect to any given linear spatially-invariant model of the human visual system. Our approach allows the error filter to have matrix-valued coefficients and diffuse quantization error across color channels in an opponent color representation. Thus, the noise is shaped into frequency regions of reduced human color sensitivity. To obtain the optimal filter, we derive a matrix version of the Yule-Walker equations which we solve by using a gradient descent algorithm. Finally, we show that the vector error filter has a parallel implementation as a polyphase filterbank.     

Model-based color halftoning using direct binary search.

In this paper, we develop a model-based color halftoning method using the direct binary search (DBS) algorithm. Our method strives to minimize the perceived error between the continuous tone original color image and the color halftone image. We exploit the differences in how the human viewers respond to luminance and chrominance information and use the total squared error in a luminance/chrominance based space as our metric. Starting with an initial halftone, we minimize this error metric using the DBS algorithm. Our method also incorporates a measurement based color printer dot interaction model to prevent the artifacts due to dot overlap and to improve color texture quality. We calibrate our halftoning algorithm to ensure accurate colorant distributions in resulting halftones. We present the color halftones which demonstrate the efficacy of our method.     

Design of tone-dependent color-error diffusion halftoning systems.

Grayscale error diffusion introduces nonlinear distortion (directional artifacts and false textures), linear distortion (sharpening), and additive noise. Tone-dependent error diffusion (TDED) reduces these artifacts by controlling the diffusion of quantization errors based on the input graylevel. We present an extension of TDED to color. In color-error diffusion, which color to render becomes a major concern in addition to finding optimal dot patterns. We propose a visually meaningful scheme to train input-level (or tone-) dependent color-error filters. Our design approach employs a Neugebauer printer model and a color human visual system model that takes into account spatial considerations in color reproduction. The resulting halftones overcome several traditional error-diffusion artifacts and achieve significantly greater accuracy in color rendition.     

Sputtered dielectric films for GaAs diffusion masks

We have explored the use of sputtered dielectrics, rather than the more conventional thermal or plasma enhanced chemical vapor deposition films, as masks for localized zinc diffusion into GaAs. The masks employed in this study were films of Si0₂, Si₃N₄, and A1₂O₃, and part of the routine characterization included measurement of the mechanical stress within the films. Zinc diffusion was carried out for 60 min at 600° C in a “leaky tube” diffusion furnace. In short, it was found that (1) the alumina films did not work as diffusion masks, (2) the build-in stress within the SiO₂ and Si₃N₄ films was dependent upon the thickness of the film (increasing with thickness for SiO₂, and diminishing with thickness for Si₃N₄), and (3) the lateral diffusion of the zinc underneath the mask increased with the stress content of the film, regardless of the mask composition.     

Fuzzy error diffusion

Quantization errors are generally hidden by performing a dithering operation on the image. A common method is to utilize error diffusion. However, this method is prone to error accumulation, resulting in color impulses and streaks. This paper presents a new approach to error diffusion dithering through a fuzzy error diffusion algorithm. In this method, the amount of error to be diffused is determined by considering the relative location of the pixel not only to the closest codebook vector, but to all other palette entries. The goal is to hide the quantization errors by error diffusion, while preventing the excess accumulation of errors. This is achieved through an attraction-repulsion schema according to a fuzzy membership function. We also explored methods to speed up the fuzzy error diffusion process through a L-filter approach by determining a fixed set of membership values. We have implemented the fuzzy error diffusion algorithm for color images and achieved drastic improvements, resulting in superior quality dithered images and significantly lower mean squared error values. A different error measure modeling the characteristic of the human visual system also indicates the superiority of our method.     

Tone-dependent error diffusion

We present an enhanced error diffusion halftoning algorithm for which the filter weights and the quantizer thresholds vary depending on input pixel value. The weights and thresholds are optimized based on a human visual system model. Based on an analysis of the edge behavior, a tone dependent threshold is designed to reduce edge effects and start-up delay. We also propose an error diffusion system with parallel scan that uses variable weight locations to reduce worms.     

Quasi-cyclic generalized ldpc codes with low error floors

In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.     

Memory efficient error diffusion

Because of its good image quality and moderate computational requirements, error diffusion has become a popular halftoning solution for desktop printers, especially inkjet printers. By making the weights and thresholds tone-dependent and using a predesigned halftone bitmap for tone-dependent threshold modulation, it is possible to achieve image quality very close to that obtained with far more computationally complex iterative methods. However, the ability to implement error diffusion in very low cost or large format products is hampered by the requirement to store the tone-dependent parameters and halftone bitmap, and also the need to store error information for an entire row of the image at any given point during the halftoning process. For the first problem, we replace the halftone bitmap by deterministic bit flipping, which has been previously applied to halftoning, and we linearly interpolate the tone-dependent weights and thresholds from a small set of knot points. We call this implementation a reduced lookup table. For the second problem, we introduce a new serial block-based approach to error diffusion. This approach depends on a novel intrablock scan path and the use of different parameter sets at different points along that path. We show that serial block-based error diffusion reduces off-chip memory access by a factor equal to the block height. With both these solutions, satisfactory image quality can only be obtained with new cost functions that we have developed for the training process. With these new cost functions and moderate block size, we can obtain image quality that is very close to that of the original tone-dependent error diffusion algorithm.     

Digital color imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented using vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided.