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.     

Restoration of error-diffused images using projection onto convexsets

A novel inverse halftoning method is proposed to restore a continuous tone image from a given half-tone image. A set theoretic formulation is used where three sets are defined using the prior information about the problem. A new space-domain projection is introduced assuming the halftoning is performed using error diffusion, and the error diffusion filter kernel is known. The space-domain, frequency-domain, and space-scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution.     

JPEG-compliant perceptual coding for a grayscale image printingpipeline

We describe a procedure by which Joint Photographic Experts Group (JPEG) compression may be customized for gray-scale images that are to be compressed before they are scaled, halftoned, and printed. Our technique maintains 100% compatibility with the JPEG standard, and is applicable with all scaling and halftoning methods. The JPEG quantization table is designed using frequency-domain characteristics of the scaling and halftoning operations, as well as the frequency sensitivity of the human visual system. In addition, the Huffman tables are optimized for low-rate coding. Compression artifacts are significantly reduced because they are masked by the halftoning patterns, and pushed into frequency bands where the eye is less sensitive. We describe how the frequency-domain effects of scaling and halftoning may be measured, and how to account for those effects in an iterative design procedure for the JPEG quantization table. We also present experimental results suggesting that the customized JPEG encoder typically maintains "near visually lossless" image quality at rates below 0.5 b/pixel (with reference to the number of pixels in the original image) when it is used with bilinear interpolation and either error diffusion or ordered dithering. Based on these results, we believe that in terms of the achieved bit rate, the performance of our encoder is typically at least 20% better than that of a JPEG encoder using the suggested baseline tables.     

Color error-diffusion halftoning

Grayscale halftoning converts a continuous-tone image (e.g., 8 bits per pixel) to a lower resolution (e.g., 1 bit per pixel) for printing or display. Grayscale halftoning by error diffusion uses feedback to shape the quantization noise into high frequencies where the human visual system (HVS) is least sensitive. In color halftoning, the application of grayscale error-diffusion methods to the individual colorant planes fails to exploit the HVS response to color noise. Ideally the quantization error must be diffused to frequencies and colors, to which the HVS is least sensitive. Further it is desirable for the color quantization to take place in a perceptual space so that the colorant vector selected as the output color is perceptually closest to the color vector being quantized. This article discusses the design principles of color error diffusion that differentiate it from grayscale error diffusion, focusing on color error diffusion halftoning systems using the red, green, and blue (RGB) space for convenience.     

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.     

Hardcopy image barcodes via block-error diffusion.

Error diffusion halftoning is a popular method of producing frequency modulated (FM) halftones for printing and display. FM halftoning fixes the dot size (e.g., to one pixel in conventional error diffusion) and varies the dot frequency according to the intensity of the original grayscale image. We generalize error diffusion to produce FM halftones with user-controlled dot size and shape by using block quantization and block filtering. As a key application, we show how block-error diffusion may be applied to embed information in hardcopy using dot shape modulation. We enable the encoding and subsequent decoding of information embedded in the hardcopy version of continuous-tone base images. The encoding-decoding process is modeled by robust data transmission through a noisy print-scan channel that is explicitly modeled. We refer to the encoded printed version as an image barcode due to its high information capacity that differentiates it from common hardcopy watermarks. The encoding/halftoning strategy is based on a modified version of block-error diffusion. Encoder stability, image quality versus information capacity tradeoffs, and decoding issues with and without explicit knowledge of the base image are discussed.     

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.     

基于多级误差扩散的多灰度图像激光雕刻算法研究

多灰度图像的激光雕刻算法是研究如何通过激光雕刻来逼真再现具有连续色调的灰度图像。作者构造了“多级误差扩散”的算法,利用图像四叉树来表示输入灰度图像与输出图像之间的区别,并在全图的范围内按照“最大亮度”规则选择误差扩散的像素,这样有效的消除了模式噪声、边界效应与黑洞效应,使利用激光雕刻出的图像很好的再现了原始图像,具有良好的视觉效果。     

Halftone to continuous-tone conversion of error-diffusion codedimages

Considers the problem of reconstructing a continuous-tone (contone) image from its halftoned version, where the halftoning process is done by error diffusion. The authors present an iterative nonlinear decoding algorithm for halftone-to-contone conversion and show simulation results that compare the performance of the algorithm to that of conventional linear low-pass filtering. They find that the new technique results in subjectively superior reconstruction. As there is a natural relationship between error diffusion and SigmaDelta modulation, the reconstruction algorithm can also be applied to the decoding problem for SigmaDelta modulators.     

基于双向反馈的自适应误差扩散半色调算法

误差扩散算法是图像进行半色调处理的主要方法,广泛地应用于各种二值图像处理设备.针对传统误差扩散中的"龟纹"和"伪轮廓"现象,在基于双向反馈误差扩散算法的基础上,提出一种双向反馈自适应误差扩散半色调算法,它不仅在误差扩散后的高频和低频成分中加入了中间频带,使图像更趋于均匀和柔和,并且通过自适应的方法,随图像特性动态修改误差扩散滤波器系数,最大程度地克服由于固定系数扩散所产生的方向性纹理缺陷,使处理后的二值图像更加充分地表现原图像信息.采用激光雕刻设备证明了该算法的有效性.     

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 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.     

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.     

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.     

A POCS-based restoration algorithm for restoring halftoned color-quantized images.

This paper studies the restoration of images which are color-quantized with error diffusion. Though there are many reported algorithms proposed for restoring noisy blurred color images and inverse halftoning, restoration of color-quantized images is rarely addressed in the literature especially when the images are color-quantized with halftoning. Direct application of existing restoration techniques are generally inadequate to deal with this problem. In this paper, a restoration algorithm based on projection onto convex sets is proposed. This algorithm makes use of the available color palette and the mechanism of a halftoning process to derive useful a priori information for restoration. Simulation results showed that it could improve the quality of a halftoned color-quantized image remarkably in terms of both SNR and CIELAB color difference metric.     

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.     

Optimized quadtree for Karhunen-Loeve transform in multispectralimage coding

A new multispectral image compression technique based on the Karhunen-Loeve transform (KLT) and the discrete cosine transform (DCT) is proposed. The quadtree for determining the transform block size and the quantizer for encoding the transform coefficients are jointly optimized in a rate-distortion sense. The problem is solved by a Lagrange multiplier approach. After a quadtree is determined by this approach, a one-dimensional (1-D) KLT is applied to the spectral axis for each block before the DCT is applied on the spatial domain. The eigenvectors of the autocovariance matrix, the quantization scale, and the quantized transform coefficients for each block are the output of the encoder. The overhead information required in this scheme is the bits for the quadtree, KLT, and quantizer representation.     

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     

Efficient quadtree coding of images and video

The quadtree data structure is commonly used in image coding to decompose an image into separate spatial regions to adaptively identify the type of quantizer used in various regions of an image. The authors describe the theory needed to construct quadtree data structures that optimally allocate rate, given a set of quantizers. A Lagrange multiplier method finds these optimal rate allocations with no monotonicity restrictions. They use the theory to derive a new quadtree construction method that uses a stepwise search to find the overall optimal quadtree structure. The search can be driven with either actual measured quantizer performance or ensemble average predicted performance. They apply this theory to the design of a motion compensated interframe video coding system using a quadtree with vector quantization.