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.     

Embedded multilevel error diffusion

We present an algorithm for image browsing systems that embeds the output of binary Floyd-Steinberg (1975) error diffusion, or a low bit-depth gray-scale or color error diffused image into higher bit-depth gray-scale or color error diffused images. The benefits of this algorithm are that a low bit-depth halftoned image can be directly obtained from a higher bit-depth halftone for printing or progressive transmission simply by masking one or more bits off of the higher bit-depth image. The embedding can be done in any bits of the output, although the most significant or the least significant bits are most convenient. Due to constraints on the palette introduced by embedding, the image quality for the higher bit-depth halftone may be reduced. To preserve the image quality, we present algorithms for color palette organization, or binary index assignment, to be used as a preprocessing step to the embedding algorithm.     

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.     

Threshold modulation and stability in error diffusion

Many modifications to error diffusion have been proposed to improve the algorithm and to extend its application to print media and to color. In this article, we describe some of the lessons that have been learned in two areas of error-diffusion research: threshold modulation and error stability. Both of these areas are important in understanding how to improve and extend the algorithm. Many suggested modifications have been made over the years to eliminate these unwanted textures. One method to improve the algorithm involves different ways of calculating and distributing the errors. Some of the modified algorithms have even proposed amplifying or suppressing the errors. Strange effects can occur, however, when the errors are amplified or if negative components are introduced. The stability analysis presented in this article will illustrate these instabilities and explain their relationship to changes in the error distribution.     

Fault and error models for VLSI

This paper describes a variety of fault and error models which are used as the basis for designing fault-tolerant Very Large Scale Integrated (VLSI) systems. The fault models describe physical defects and failures and the input patterns which will expose them, and are suitable for testing, while error models describe the effects on the functional outputs of defects and are useful for on-line error detection. The models are described at various levels of abstraction. The differences between fault and error models for identical functional modules are also illustrated.     

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.     

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.     

Adaptive error diffusion method for image quantisation

An adaptive error diffusion method for image quantisation is presented. The error filter coefficients are adapted using a generalised two-dimensional LMS algorithm and the quantisation scale is calculated on the basis of the image histogram. The developed method provides a minimum reconstruction error, a decrease in false contours in the homogeneous areas and precise reproduction of the edges in the output image.<>     

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.     

Row-oriented multiscale error diffusion technique for digitalhalftoning

A digital halftoning method is proposed to diffuse error with a more symmetric error distribution by making use of the concept of multiscale error diffusion. The method can improve the diffusion performance by effectively reducing directional hysteresis. The diffusion is row-oriented rather than frame-oriented and hence can reduce the latency and computational effort as compared with conventional multiscale error diffusion schemes. This makes it possible for real-time applications     

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     

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.     

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.     

GVF-based anisotropic diffusion models.

In this paper, the gradient vector flow fields are introduced in image restoration. Within the context of flow fields, the shock filter, mean curvature flow, and Perona-Malik equation are reformulated. Many advantages over the original models can be obtained; these include numerical stability, large capture range, and high-order derivative estimation. In addition, a fairing process is introduced in the anisotropic diffusion, which contains a fourth-order derivative and is reformulated as the intrinsic Laplacian of curvature under the level set framework. By applying this fairing process, the shape boundaries will become more apparent. In order to overcome numerical errors, the intrinsic Laplacian of curvature is computed from the gradient vector flow fields instead of the observed images.     

A multiscale error diffusion technique for digital multitoning

Multitoning is the representation of digital pictures using a given set of available color intensities, which are also known as tones or quantization levels. It can be viewed as the generalization of halftoning, where only two such quantization levels are available. Its main application is for printing and, similar to halftoning, can be applied to both colored and grayscale images. In this paper, we present a method to produce multitones based on the multiscale error diffusion technique. Key characteristics of this technique are: 1) the use of an image quadtree; 2) the quantization order of the pixels being determined through "maximum intensity guidance" on the image quadtree; and 3) noncausal error diffusion. Special care has been given to the problem of banding, which is one of the inherent limitations in error diffusion when applied to multitoning. Banding is evident in areas of the image with values close to one of the available quantization levels; our approach is to apply a preprocessing step to alleviate part of the problem. Our results are evaluated both in terms of visual appearance and using a set of standard metrics, with the latter demonstrating the blue-noise characteristics and very low anisotropy of the proposed method.     

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.     

基于奇偶校验的块误差分散半调水印算法

提出了一种顽健的半调水印算法。算法通过比较像素块的均值和一个图像自相关阈值的大小确定像素块的奇偶性,利用噪声平衡块误差分散方法调整像素块的奇偶性实现水印嵌入。通过像素块的奇偶性和投票策略来实现水印的盲提取。实验结果表明,与同类算法相比,提出算法能够获得较高且灵活的水印率,并能从被攻击的嵌水印图像直接提取水印,无需将其先转化成半调图,同时能够很好地抵抗各种常见攻击以及不同型号设备的打印—扫描攻击。     

Watermarking in halftone images with parity-matched error diffusion

In this paper, a halftone watermarking technique of high watermark rate, robustness, and watermark-rate flexibility is presented. This technique, namely the parity-matched error diffusion (PMEDF) method, is capable of achieving an embedded watermark rate as high as 6.25-25% with good image quality and without the need for the original image as the reference for the decoding. The proposed PMEDF method employs the high efficient parity-matching strategy to spread a watermark bit to each pixel of a block of the host image. Thus, the majority voting mechanism can be applied for decoding to achieve an advantage of high robustness. As documented in the experimental results, this technique is capable of guarding against degradation, due to cropping, tampering, as well as print-and-scan process in error-diffused halftone images.     

Improved block truncation coding using modified error diffusion

Block truncation coding (BTC) is an efficient compression technique, offering good image quality. Nonetheless, the blocking effect inherent in BTC causes severe perceptual artefact when compression ratio is increased. Conversely, error diffusion (EDF) enjoys the benefit of diffusing the quantised error into neighbouring pixels. Consequently, the average tones in any local areas of the error-diffused image are preserved unchanged. Presented is a hybrid approach which combines the proposed modified EDF with BTC. As documented in experimental results, image quality is much better than BTC, and the complexity is even lower than traditional BTC.