Error diffusion algorithm using pixel and halftone based error corrections

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.

Since the early 90's and the introduction of desktop photo-imaging, error diffusion has continued to be used as the primary FM screening method for photo-inkjet printing. Modern error diffusion algorithms continue to deliver stunning photo quality but the nature of the algorithm makes it calculation intensive and inherently slow. Much work has been done over the years to try and improve the performance of error diffusion. As a result of this work and modern hardware configurations, contemporary algorithms operate at significantly increased speeds (and image rendering quality) when compared to similar developments from the late 80's and early to mid 90's. The fact is though that however many optimisations are applied to the algorithm, a simple point process system such as that employed with a threshold array will always exhibit better performance when compared with an equivalent error diffusion algorithm operating on the same image data.

A method has been developed to induce symmetric edge enhancement in error diffusion with threshold modulation. The existing threshold modulation algorithm induces edge enhancement by subtracting a term proportional to the input image from the threshold. The edge enhancement that results in asymmetric due to the asymmetric shape of the error diffusion filter. The new method induces a symmetric edge enhancement by subtracting a term from the threshold that is proportional to a filtered version of the input image. The filtering is accomplished with a recursive filter, applied during the error diffusion algorithm, which cancels out the error diffusion filter and imposes a symmetric sharpening filter. The result is a symmetric edge enhancement that is more pleasing to the eye.

Measurements of atmosphere-surface exchange are largely limited by the availability of fast-response gas analyzers; this limitation hampers our understanding of the role of terrestrial ecosystems in atmospheric chemistry and global change. Current micrometeorological methods, compatible with slow-response gas analyzers, are difficult to implement, or rely on empirical parameters that introduce large systematic errors.Here, we develop a new micrometeorological method, optimized for slow-response gas analyzers, that directly measures exchange rates of different atmospheric constituents, with minimal requirements. The new method requires only the sampling of air at a constant rate and directing it into one of two reservoirs, depending on the direction of the vertical wind velocity. An integral component of the new technique is an error diffusion algorithm that minimizes the biases in the measured fluxes and achieves direct flux estimates.We demonstrate that the new method provides an unbiased estimate of the flux, with accuracy within 0.1% of the reference eddy covariance flux, and importantly, allows for significant enhancements in the signal-to-noise ratio of measured scalars without compromising accuracy. Our new method provides a simple and reliable way to address complex environmental questions and offers a promising avenue for advancing our understanding of ecological systems and atmospheric chemistry.

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.

This paper proposes an adaptive error diffusion algorithm for text enhancement followed by an efficient text segmentation that uses the maximum gradient difference (MGD). The gradients are calculated along with scan lines, then the MGD values are filled within a local window to merge text segments. If the value is above a threshold, the pixel is considered as potential text. Isolated segments are then eliminated in a non-text region filtering process. After the text segmentation, a conventional error diffusion method is applied to the background, while edge enhancement error diffusion is used for the text. Since it is inevitable that visually objectionable artifacts are generated when using two different halftoning algorithms, gradual dilation is proposed to minimize the boundary artifacts in the segmented text blocks before halftoning. Sharpening based on the gradually dilated text region (GDTR) then prevents the printing of successive dots around the text region boundaries. The method is extended to halftone color images to sharpen the text regions. The proposed adaptive error diffusion algorithm involves color halftoning that controls the amount of edge enhancement using a general error filter. However, edge enhancement unfortunately produces color distortion, as edge enhancement and color difference are trade-offs. The multiplicative edge enhancement parameters are selected based on the amount of edge sharpening and color difference. Plus, an additional error factor is introduced to reduce the dot elimination artifact generated by the edge enhancement error diffusion. In experiments, the text of a scanned image was sharper when using the proposed algorithm than with conventional error diffusion without changing the background.

In Digital Subtraction Angiography (DSA) image registration algorithm, the precision of the control points as well as their number and the distribution in image determine the accuracy of geometric correction and registration. Control points usually adopt the grid points; however, a more effective method is to extract control points adaptively according to the image feature. In this paper, a control point’s selection algorithm of DSA images is proposed based on adaptive multi-Scale vascular enhancement, error diffusion and means shift algorithms. Experimental results show that the proposed algorithm can adaptively put the control points to blood vessels and other key image characteristics, and can optimize the number of control points according to practical needs, which will ensure the accuracy of DSA image registration.

High-speed optical reconstruction of 3D-scenes can be achieved using digital holography with binary digital micromirror devices (DMD) or a ferroelectric spatial light modulator (fSLM). There are many algorithms for binarizing digital holograms. The most common are methods based on global and local thresholding and error diffusion techniques. In addition, hologram binarization is used in optical encryption, data compression, beam shaping, 3D-displays, nanofabrication, materials characterization, etc. This paper proposes an adaptive binarization method based on a combination of local threshold processing, hologram division into blocks, and error diffusion procedure (the LDE method). The method is applied for binarization of optically recorded and computer-generated digital holograms of flat objects and three-dimensional scenes. The quality of reconstructed images was compared with different methods of error diffusion and thresholding. Image reconstruction quality was up to 22% higher by various metrics than that one for standard binarization methods. The optical hologram reconstruction using DMD confirms the results of the numerical simulations.

Digital halftoning is essential to print or display a continuous tone with binary devices. Error Diffusion (ED) has been a major stream to produce a pictorial image on inkjet prints, but is not always acceptable for commercial printing or EP printer, because it generates the dispersed dots hard to print.This paper proposes a novel method for generating ordered dither mask using “magic square”. Magic square provides spatially balanced threshold values in row, column, and diagonal directions by the rule of “even-sum”. The proposed magic square satisfies the energy minimum criterion in the local area and is expandable to a large scale for sufficient gray scales. We selected the magic square candidates with Fourier spectra concentrated in the middle spatial frequency to produce a smoothed gradation suitable for LBP or commercial printing. The paper introduces a systematic method for expanding small mask to large mask by “master-slave” algorithm. The experimental results show the improved grayscale reproduction with reduced artifacts in comparison with the conventional Bayer dither or ED.

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.

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.

An error diffusion quantization method has been used in conjunction with computer-generated holograms. It is shown that this procedure is advantageous in the production of the power spectrum interference pattern of joint transform image correlator (JTC) configurations. The suggested error diffusion JTC permits evaluation of noisy input cases, for example, when Gaussian white noise is added to the input plane. A computer simulation comparison of correlation peak quality was carried for three cases, using several performance criterions. The analyzed cases were classical continuous JTC and nonlinearly scaled binarized JTC, quantized by either error diffusion or hard clipping.

Reproduction couleur par trames irrégulières et semi-régulières

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.

Shaping complex fields with a digital micromirror device (DMD) has attracted much attention recently due to its potential application in optical communication and microscopy. In this paper, we present an optimized Lee method to achieve dynamic shaping of orbital-angular-momentum (OAM) beams using a binary DMD. An error diffusion algorithm is introduced to enhance the accuracy for binary-amplitude hologram design, making it possible to achieve high fidelity wavefront shaping while retaining a high resolution. As a proof of concept, we apply this method to create different classes of OAM beams and experimentally demonstrate the dynamic shaping of different OAM beams including pure modes and mixed modes with a switching rate of up to 17.8 kHz.