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.     

Impact of HVS models on model-based halftoning

A model for the human visual system (HVS) is an important component of many halftoning algorithms. Using the iterative direct binary search (DBS) algorithm, we compare the halftone texture quality provided by four different HVS models that have been reported in the literature. Choosing one HVS model as the best for DBS, we then develop an approximation to that model which significantly improves computational performance while minimally increasing the complexity of the code. By varying the parameters of this model, we find that it is possible to tune it to the gray level being rendered, and to thus yield superior halftone quality across the tone scale. We then develop a dual-metric DBS algorithm that effectively provides a tone-dependent HVS model without a large increase in computational complexity.     

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.     

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.     

Quantization of accumulated diffused errors in error diffusion.

Due to its high image quality and moderate computational complexity, error diffusion is a popular halftoning algorithm for use with inkjet printers. However, error diffusion is an inherently serial algorithm that requires buffering a full row of accumulated diffused error (ADE) samples. For the best performance when the algorithm is implemented in hardware, the ADE data should be stored on the chip on which the error diffusion algorithm is implemented. However, this may result in an unacceptable hardware cost. In this paper, we examine the use of quantization of the ADE to reduce the amount of data that must be stored. We consider both uniform and nonuniform quantizers. For the nonuniform quantizers, we build on the concept of tone-dependency in error diffusion, by proposing several novel feature-dependent quantizers that yield improved image quality at a given bit rate, compared to memoryless quantizers. The optimal design of these quantizers is coupled with the design of the tone-dependent parameters associated with error diffusion. This is done via a combination of the classical Lloyd-Max algorithm and the training framework for tone-dependent error diffusion. Our results show that 4-bit uniform quantization of the ADE yields the same halftone quality as error diffusion without quantization of the ADE. At rates that vary from 2 to 3 bits per pixel, depending on the selectivity of the feature on which the quantizer depends, the feature-dependent quantizers achieve essentially the same quality as 4-bit uniform quantization.     

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.     

Digital color halftoning with generalized error diffusion andmultichannel green-noise masks

In this paper, we introduce two novel techniques for digital color halftoning with green-noise-stochastic dither patterns generated by homogeneously distributing minority pixel clusters. The first technique employs error diffusion with output-dependent feedback where, unlike monochrome image halftoning, an interference term is added such that the overlapping of pixels of different colors can be regulated for increased color control. The second technique uses a green-noise mask, a dither array designed to create green-noise halftone patterns, which has been constructed to also regulate the overlapping of different colored pixels. As is the case with monochrome image halftoning, both techniques are tunable, allowing for large clusters in printers with high dot-gain characteristics, and small clusters in printers with low dot-gain characteristics.     

Tree-structured method for LUT inverse halftoning and for imagehalftoning

The authors previously proposed a look up table (LUT) based method 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. Many of the entries in the LUT are unused because the corresponding binary patterns hardly occur in commonly encountered halftones. These are called nonexistent patterns. In this paper, we propose a tree structure which will reduce the storage requirements of an LUT by avoiding nonexistent patterns. We demonstrate the performance on error diffused images and ordered dither images. Then, we introduce LUT based halftoning and tree-structured LUT (TLUT) halftoning. Even though the TLUT method is more complex than LUT halftoning, it produces better halftones and requires much less storage than LUT halftoning. We demonstrate how the error diffusion characteristics can be achieved with this method. Afterwards, our algorithm is trained on halftones obtained by direct binary search (DBS). The complexity of TLUT halftoning is higher than the error diffusion algorithm but much lower than the DBS algorithm. Also, the halftone quality of TLUT halftoning increases if the size of the TLUT gets bigger. Thus, the halftone image quality between error diffusion and DBS will be achieved depending on the size of the tree-structure in the TLUT algorithm     

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.     

Printer models and error diffusion

A new model-based approach to digital halftoning is proposed. It is intended primarily for laser printers, which generate "distortions" such as "dot overlap". Conventional methods, such as clustered-dot ordered dither, resist distortions at the expense of spatial and gray-scale resolution. The proposed approach relies on printer models that predict distortions, and rather than merely resisting them, it exploits them to increase, rather than decrease, both spatial and gray-scale resolution. We propose a general framework for printer models and find a specific model for laser printers. As an example of model-based halftoning, we propose a modification of error diffusion, which is often considered the best halftoning method for CRT displays with no significant distortions. The new version exploits the printer model to extend the benefits of error diffusion to printers. Experiments show that it provides high-quality reproductions with reasonable complexity. The proposed modified error diffusion technique is compared with Stucki's (1981) MECCA, which is a similar but not widely known technique that accounts for dot overlap. Model-based halftoning can be especially useful in transmission of high-quality documents using high-fidelity gray-scale image encoders.     

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.     

The Hybrid Screen—Improving the Breed

The hybrid screen is a halftoning method that generates stochastic dispersed dot textures in highlights and periodic clustered dot textures in midtones. Each tone level is sequentially designed from highlight to midtone by applying an iterative halftoning algorithm such as direct binary search (DBS). By allowing random seeding followed by swap-only DBS in a predefined core region within each microcell, each level can be designed while satisfying the stacking constraint and guaranteeing a smooth transition between levels. This paper describes a complete design process for the hybrid screen, introduces a number of enhancements to the original hybrid screen, and evaluates their impact on print quality. These enhancements include a multilevel screen design based on either extending a bilevel screen or directly generating a multilevel screen on a high resolution grid, and extending the hybrid screen design procedure to color by jointly optimizing the color screens using color DBS. For the multilevel screen, we show that the best choice for the core size critically depends on the bit depth and screen frequency. For the color hybrid screen, we demonstrate a significant improvement in the highlights over halftones generated by independently designed screens.      

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.     

Halftoning via direct binary search using analytical and stochastic printer models

We incorporate models for printer dot interactions within the iterative direct binary search (DBS) halftoning algorithm. Monochrome electro-photographic printers are considered. Both analytical and stochastic models are studied. In the analytical model it is assumed that the printer can generate a circular spot with constant absorptance at each printer addressable location, whereas the stochastic model is based on microscopic absorptance and variance measurements. We also present an efficient strategy for evaluating the change in computational cost as the search progresses. With our scheme, updating the change in error only involves a few fetches from two look-up-tables and some scalar multiplications and additions. Experimental results are provided that show that DBS with an appropriate model for printer dot interactions yields enhanced detail rendition, and improved tonal gradation in shadow areas.     

Least-squares model-based halftoning

A least-squares model-based (LSMB) approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an optimal halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. It has been shown that the one-dimensional (1-D) least-squares problem, in which each row or column of the image is halftoned independently, can be implemented using the Viterbi algorithm to obtain the globally optimal solution. Unfortunately, the Viterbi algorithm cannot be used in two dimensions. In this paper, the two-dimensional (2-D) least-squares solution is obtained by iterative techniques, which are only guaranteed to produce a total optimum. Experiments show that LSMB halftoning produces better textures and higher spatial and gray-scale resolution than conventional techniques. We also show that the least-squares approach eliminates most of the problems associated with error diffusion. We investigate the performance of the LSMB algorithms over a range of viewing distances, or equivalently, printer resolutions. We also show that the LSMB approach gives us precise control of image sharpness.     

Binary grayscale halftone pattern generation using binary artificial bee colony (bABC)

In grayscale context, digital halftoning can be considered as binary pattern generation task where 0- and 1-valued pixels represent black and white, respectively. This paper presents application of artificial bee colony (ABC) in its modified binary form called binary ABC (bABC) toward generation of optimized binary halftone patterns. The human visual system incorporated cost function formulation addresses the tonal and structural parity between the original and halftone images along with pleasant halftone appearance. A pattern look-up table (p-LUT) approach is investigated including edge enhancement in halftone images. The results are presented pictorially and evaluated objectively. Comparison between the presented method and established halftoning techniques is also drawn to judge the potential of the presented bABC generated p-LUT approach. The pictorial presentations as well as objective evaluation show that the presented method may be potentially useful in the field of digital halftoning.     

Inverse halftoning using wavelets

This work introduces a new approach to inverse halftoning using nonorthogonal wavelets. The distinct features of this wavelet-based approach are: (1) edge information in the highpass wavelet images of a halftone image is extracted and used to assist inverse halftoning, (2) cross-scale correlations in the multiscale wavelet decomposition are used for removing background halftoning noise while preserving important edges in the wavelet lowpass image, and (3) experiments show that our simple wavelet-based approach outperforms the best results obtained from inverse halftoning methods published in the literature, which are iterative in nature.     

Training-based descreening.

Conventional halftoning methods employed in electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material, such as books and magazines. We present a novel approach for descreening color scanned documents aimed at providing an efficient solution to the Moiré problem in practical imaging devices, including copiers and multifunction printers. The algorithm works by combining two nonlinear image-processing techniques, resolution synthesis-based denoising (RSD), and modified smallest univalue segment assimilating nucleus (SUSAN) filtering. The RSD predictor is based on a stochastic image model whose parameters are optimized beforehand in a separate training procedure. Using the optimized parameters, RSD classifies the local window around the current pixel in the scanned image and applies filters optimized for the selected classes. The output of the RSD predictor is treated as a first-order estimate to the descreened image. The modified SUSAN filter uses the output of RSD for performing an edge-preserving smoothing on the raw scanned data and produces the final output of the descreening algorithm. Our method does not require any knowledge of the screening method, such as the screen frequency or dither matrix coefficients, that produced the printed original. The proposed scheme not only suppresses the Moiré artifacts, but, in addition, can be trained with intrinsic sharpening for deblurring scanned documents. Finally, once optimized for a periodic clustered-dot halftoning method, the same algorithm can be used to inverse halftone scanned images containing stochastic error diffusion halftone noise.     

Data hiding watermarking for halftone images

In many printer and publishing applications, it is desirable to embed data in halftone images. We proposed some novel data hiding methods for halftone images. For the situation in which only the halftone image is available, we propose data hiding smart pair toggling (DHSPT) to hide data by forced complementary toggling at pseudo-random locations within a halftone image. The complementary pixels are chosen to minimize the chance of forming visually undesirable clusters. Our experimental results suggest that DHSPT can hide a large amount of hidden data while maintaining good visual quality. For the situation in which the original multitone image is available and the halftoning method is error diffusion, we propose the modified data hiding error diffusion (MDHED) that integrates the data hiding operation into the error diffusion process. In MDHED, the error due to the data hiding is diffused effectively to both past and future pixels. Our experimental results suggest that MDHED can give better visual quality than DHSPT. Both DHSPT and MDHED are computationally inexpensive.     

A fast, high-quality inverse halftoning algorithm for errordiffused halftones

Halftones and other binary images are difficult to process with causing several degradation. Degradation is greatly reduced if the halftone is inverse halftoned (converted to grayscale) before scaling, sharpening, rotating, or other processing. For error diffused halftones, we present (1) a fast inverse halftoning algorithm and (2) a new multiscale gradient estimator. The inverse halftoning algorithm is based on anisotropic diffusion. It uses the new multiscale gradient estimator to vary the tradeoff between spatial resolution and grayscale resolution at each pixel to obtain a sharp image with a low perceived noise level. Because the algorithm requires fewer than 300 arithmetic operations per pixel and processes 7x7 neighborhoods of halftone pixels, it is well suited for implementation in VLSI and embedded software. We compare the implementation cost, peak signal to noise ratio, and visual quality with other inverse halftoning algorithms.