<title>Error diffusion with delayed decision</title>

A dot-to-dot error diffusion algorithm is presented that combines traditional halftoning (clustered-dot ordered dithering) and error diffusion. Error diffusion can create a large number of nonprintable individualpixels. Therefore, it is not suitable forhard-copy printing. On the other hand, traditional halftoning has only limited output gray levels. With the algorithm we proposed, we try to avoid the problems of both techniques, yet retain their merits. In our algorithm, the error diffusion is performed on halftone dots instead of pixels, and the error diffusion is performed only on full dots. To accommodate the dot-to-dot error propagation, a modified but equivalent version of error diffusion is introduced. The success of the algorithm is demonstrated by the experimental results.

Color halftoning is a method for representing continuous tone color images with limited colors. To implement halftone, error diffusion is one of the most popular algorithms due to its highperformance results. In the conventional error diffusion, the fixed thresholds and filter weights are used. In the process, many artifacts are introduced in the halftone images as side effects. With the color aspect, each of the three color planes is independently calculated during the process of traditional error diffusion. However, the pattern of dots formed independently by combining the dots of each of color planes is often not visually pleasing because no effort is made to insure that the dots of each of the different color planes are ideally distributed relative to the dots of the other color planes. In this paper, we present an integrated error diffusion algorithm in which variable filter weights, threshold matrix, serpentine scan path and multi-color halftoning are used to reduce the noises generated during the halftone process. Our experimental results showed that worm-like artifacts, structural artifacts and start-up artifacts are successfully decreased and the color halftoned images are more comfortable to the human visual system.

A halftone watermarking method of high quality, robustness, and capacity flexibility is presented in this paper. An objective halftone image quality evaluation method based on the human visual system obtained by least-mean-square is also introduced. In the encoder, the kernels-alternated error diffusion (KAEDF) is applied. This is able to maintain the computational complexity at the same level as ordinary error diffusion. Compared with Hel-Or (2001) using ordered dithering, the proposed KAEDF yields a better image quality through using error diffusion. We also propose a weighted lookup table (WLUT) in the decoder instead of LUT, as proposed by Pei and Guo (2003), so as to achieve a higher decoded rate. As the experimental results demonstrated, this technique is able to guard against degradation due to tampering, cropping, rotation, as well as print-and-scan processes in error-diffused halftone images.

We have previously developed a two-dimensional monochromatic halftoning with error diffusion neural networks (EDNs). We showed that EDNs find local minima of frequency-weighted error between a binary halftone output and corresponding smoothly varying input, an ideal framework for solving halftone problems. The advantage of the neural algorithm is that all pixel quantization decisions are computed in parallel and therefore the error diffusion process becomes un-directional and symmetric. Thus eliminates the artifacts caused by the traditional error diffusion method. This paper casts color halftoning as four related sub-problems: the first three are to compute good binary halftones for each primary color and the fourth is to simultaneously minimize frequency-weighted error in the luminosity of the composite result. We show that an EDN with a three-dimensional interconnect scheme can solve all four problems in parallel with user-adjustable emphasis on the relative importance of weighted error in luminosity. Our results show that the three-dimensional EDN matrix not only shapes the error to frequencies that human visual system (HVS) is least sensitive but also shapes the error in colors to which the HVS is least sensitive - namely it satisfies the minimum brightness variation criterion.

Dot diffusion is an efficient approach which utilizes concepts of block-wise and parallel-oriented processing to generate halftones. However, the block-wise nature of processing reduces image quality much more significantly as compared to error diffusion. In this work, four types of filters with various sizes are employed in co-optimization procedures with class matrices of size 8 n 8 and 16 x 16 to improve the image quality. The optimal diffused weighting and area are determined through simulations. Many well-known halftoning methods, some of which includes direct binary search (DBS), error diffusion, ordered dithering, and prior dot diffusion methods, are also included for comparisons. Experimental results show that the proposed dot diffusion achieved quality close to some forms of error diffusion, and additionally, superior to the well-known Jarvis and Stucki error diffusion and Mese's dot diffusion. Moreover, the inherent parallel processing advantage of dot diffusion is preserved, allowing us to reap higher executing efficiency than both DBS and error diffusion.

In this paper, a low computational complexity method is proposed to embed a multi-tone visual pattern using the concept of secret sharing. One halftone image is obtained using regular error diffusion, and the other image is obtained using the proposed Generalized Noise-Balanced Error Diffusion (GNBEDF) in considering the properties of the watermark and the first halftone image in the same time. With the proposed method, the bi-level watermark embedding becomes a special case to this technology. The bi-level watermark decoding can be simply achieved via printing the two halftone images onto two transparencies and then superimposing them together to reveal the watermark pattern. However, as the multi-tone watermark is involved, the proposed Gaussian Difference (GD) approach is needed to perform the decoding to produce a decoded multi-tone watermark. Throughout this work, a lowpass filter obtained by Least-Mean-Square is employed to assess the image quality.

Halftoning is a crucial part of image reproduction in print. For large format prints, especially at higher resolutions, it is important to have very fast and computationally feasible halftoning methods of good quality. The authors have already introduced an approach to obtain image-independent threshold matrices generating both first- and second-order frequency modulated (FM) halftones with different clustered dot sizes. Predetermined and image-independent threshold matrices make the proposed halftoning method a point-by-point process and thereby very fast. In this article, they report a comprehensive quality evaluation of first-and second-order FM halftones generated by this technique and compare them with each other, employing several quality metrics. These generated halftones are also compared with error diffusion (ED) halftones employing two different error filters. The results indicate that the second-order FM halftoning with small clustered dot size performs best in almost all studied quality aspects than the first-and second-order FM halftoning with larger clustered dot size. It is also shown that the first- and second-order FM halftones with small clustered dot sizes are of almost the same quality as ED halftones using Floyd–Steinberg error filter and of higher quality than halftones generated by ED employing Jarvis, Judice, and Ninke error filter.

Reproduction couleur par trames irrégulières et semi-régulières

The performance of Fourier transform optical processors, e.g. optical correlators, beam steering systems, associative memories, etc., depends intimately both on the physical characteristics of the particular spatial light modulator (SLM) and on the particular algorithms that map the signal into the available modulation range of the device. For the most general Fourier systems the information/signal is complex-valued. This is an essential requirement for multi- spot beam steering systems and composite pattern recognition filters. Since practical and/or affordable SLM's only represent a limited range of values in the complex plane (e.g. phase-only or quantized phase), numerous approaches have been proposed and demonstrated for representing, approximating, encoding or mapping complex values to the available SLM states. The best approach depends on the space bandwidth product of the signal, the number of SLM pixels, the computation time of the encoding algorithm, the time available for the application, and the quality of the optical processor, as measured by an application-specific performance metric. Based on the low pixel count and the high cost per pixel of most current SLM's we argue for encoding algorithms that map one signal value to one pixel value, as opposed to group-oriented encoding. This maximized the usable area of the frequency plane. We also recommend algorithms that maximize the fidelity over the entire frequency range as opposed to maximum diffraction efficiency/minimum mean squared error design. These ideas are illustrated with several simulated and experimental results for pseudorandom, minimum Euclidean distance, error diffusion and hybrid/blended encoding algorithms.

To solve error propagation and exorbitant computational complexity of signal detection in wireless multiple-input multiple-output-orthogonal frequency division multiplexing (MIMO-OFDM) systems, a low-complex and efficient signal detection with iterative feedback is proposed via a constellation point feedback optimization of minimum mean square error-ordered successive interference cancellation (MMSE-OSIC) to approach the optimal detection. The candidate vectors are formed by selecting the candidate constellation points. Additionally, the vector most approaching received signals is chosen by the maximum likelihood (ML) criterion in formed candidate vectors to reduce the error propagation by previous erroneous decision, thus improving the detection performance. Under a large number of matrix inversion operations in the above iterative MMSE process, effective and fast signal detection is hard to be achieved. Then, a symmetric successive relaxation iterative algorithm is proposed to avoid the complex matrix inversion calculation process. The relaxation factor and initial iteration value are reasonably configured with low computational complexity to achieve good detection close to that of the MMSE with fewer iterations. Simultaneously, the error diffusion and complexity accumulation caused by the successive detection of the subsequent OSIC scheme are also improved. In addition, a method via a parallel coarse and fine detection deals with several layers to both reduce iterations and improve performance. Therefore, the proposed scheme significantly promotes the MIMO-OFDM performance and thus plays an irreplaceable role in the future sixth generation (6G) mobile communications and wireless sensor networks, and so on.

Gamma correction is an indispensable process due to the nonlinear I/O characteristics of modern display devices such as CRT and LCD. However, coarse and imprecise gamma correction degrades the image quality significantly by causing false contours in the low luminance regions. This paper proposes a new gamma correction method with error diffusion. This method employs a relatively small LUT, while providing an efficient and precise way for indexing the gamma corrected values. Moreover, we adopt a revised piecewise gamma correction curve to enhance the contrast of the dark area and make error diffusion in an edge directed strategy. Experiment results indicate this method gives good performances in gamma correction, especially for the dark area of images.

In order to be able to print an image on a binary output device, the image has to be rendered as a sequence of on/off (black/white) states. The image quality of the printed binary image strongly depends on the actual distribution of the black/white pixels. In order to increase the fidelity of the reproduction it is desirable that a feedback algorithm in the form of error diffusion be used. This type of algorithm, however, produces patterns that are not reproducible by standard xerographic printers, where a clustering of pixels into dots is required. This talk demonstrates a method to combine error diffusion with standard halftoning by first using a pixel based error correction followed by a halftone cell based error correction. This combination allows the generation of printable patterns that incorporate characteristics of feedback algorithms.

Currently, many low-cost computers can only simultaneously display a palette of 256 colors. However, this palette is usually selectable from a very large gamut of available colors. For many applications, this limited palette size imposes a significant constraint on the achievable image quality. We propose a method for designing an optimized universal color palette for use with halftoning methods such as error diffusion. The advantage of a universal color palette is that it is fixed and therefore allows multiple images to be displayed simultaneously. To design the palette, we employ a new vector quantization method known as sequential scalar quantization (SSQ) to allocate the colors in a visually uniform color space. The SSQ method achieves near-optimal allocation, but may be efficiently implemented using a series of lookup tables. When used with error diffusion, SSQ adds little computational overhead and may be used to minimize the visual error in an opponent color coordinate system. We compare the performance of the optimized algorithm to standard error diffusion by evaluating a visually weighted mean-squared-error measure. Our metric is based on the color difference in CIE L *a *b , but also accounts for the lowpass characteristic of human contrast sensitivity.

Inverse color to black-and-white halftone conversion via dictionary learning and color mapping

As vector error filters are capable of passing errors generated in one color component to other color components, it provides more flexibility in shaping the halftone texture. As a result, it may potentially produce halftones with better image quality. In this paper, we analyze color error diffusion with vector error filters. In particular, we will discuss its halftone spectrum features and its stability conditions with respect to the filter coefficients. For spectrum analysis, we will derive the high-pass and average color preservation conditions, which ensure decent image quality. Since error diffusion is a feedback system, the vector error filters may cause instability, if it is not properly designed. This may potentially generate ever-increasing quantization error that masks the input and produces unacceptable output images. The stability conditions we will discuss provide guidelines for designing stable systems.