Error Diffusion for Color Halftoning Using Three-Dimensional Neural Interconnects

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 new halftoning algorithm is proposed that incorporates the concept of delayed decision in error diffusion. This algorithm is similar to a recently proposed tree coding halftoner in that both examine at each pixel location a neighborhood of future (with respect to the scanning direction) pixels before deciding the value of the current output pixel. Because of the feedback in the error diffusion process, one can reduce the size of the 'look ahead' window compared to a typical tree-coding halftoner, resulting in a relatively low complexity. It is shown that this algorithm improves the quality of halftone images compared to those generated by traditional error diffusion.

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.

A digital micromirror device (DMD) provides 2D- and 3D-scene reconstruction by displaying diffractive and holographic optical elements. The highest frame rates (tens of thousands of Hz) can be achieved if the displayed optical elements are binarized. Except for DMD applications, hologram binarization is useful for display creation, image encryption, information compression and storage, fast 3D printing, etc. Error diffusion is one of the most qualitative implementations of hologram binarization. In this paper, three group's weighting matrices of error diffusion are analyzed: 16 standard, eight dot and six diagonal matrices. Thus, 30 error diffusion methods were used for optically recorded off-axis digital hologram binarization. The quality of the image reconstruction from the binarized holograms was compared. Direct applications of error diffusion with large weighting matrices and dot diffusion provide the highest reconstruction quality. Seven metrics were used as the error diffusion threshold. Twelve bypass directions of error diffusion were analyzed. In addition, the joint application of Otsu threshold and complex bypass directions allows us to improve the quality of hologram binarization by 15%.

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.

The error diffusion method can effectively reduce quality degradation by propagating thresholding errors to neighboring pixels in the conversion of a gray-scale hologram to a binary hologram. In previous works, the four weighting coefficients in error diffusion are mostly set as the Floyd-Steinberg coefficient, which was determined empirically and originally proposed for photograph processing. In this work, we point out that the Floyd-Steinberg coefficients can be suboptimal for hologram error diffusion binarization. Furthermore, the weighting coefficients are optimized for each different hologram adaptively. Compared with conventional coefficients, our optimized coefficients can better preserve the fidelity of a reconstructed image after a hologram is binarized.

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.

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.

The dot diffusion method for digital halftoning has the advantage of parallelism unlike the error diffusion method. The method was recently improved by optimization of the so-called class matrix so that the resulting halftones are comparable to the error diffused halftones. In this paper we will first review the dot diffusion method. Previously, 82 class matrices were used for dot diffusion method. A problem with this size of class matrix is that enhancement of images is necessary before halftoning. However, enhancement may not be desirable in some applications. In order to eliminate the enhancement step, we increase the size of the class matrix to 162 and optimize the class matrix for a set of gray levels. In the optimization, the Human Visual System is used in the cost function. The optimization is done with the pairwise exchange algorithm. Since we increase the size of the class matrix, we are compromising the parallelism, i.e., the algorithm will terminate in 162 steps rather than 8 × 8 steps. This is the price paid for avoiding the enhancement step.

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.

Multiscale error diffusion is superior to conventional error diffusion methods in digital halftoning as it can eliminate directional hysteresis completely. However, there is a bias to favor a particular type of dots in the course of the halftoning process. A new multiscale error diffusion method is proposed to improve the diffusion performance by reducing the aforementioned bias. The proposed method can eliminate the pattern noise in flat regions and the boundary effect found in some other conventional multiscale error diffusion methods. At the same time, it can preserve the local features of the input image in the output. This is critical to quality, especially when the resolution of the output is limited by the physical constraints of the display unit.

The objective of this work is to reconstruct high quality gray-level images from halftone images, or the inverse halftoning process. We develop high performance halftone reconstruction methods for several commonly used halftone techniques. For better reconstruction quality, image classification based on halftone techniques is placed before the reconstruction process so that the halftone reconstruction process can be fine tuned for each halftone technique. The classification is based on enhanced 1D correlation of halftone images and processed with a three- layer back propagation neural network. This classification method reached 100 percent accuracy with a limited set of images processed by dispersed-dot ordered dithering, clustered-dot ordered dithering, constrained average, and error diffusion methods in our experiments. For image reconstruction, we apply the least-mean-square adaptive filtering algorithm which intends to discover the optimal filter weights and the mask shapes. As a result, it yields very good reconstruction image quality. The error diffusion yields the best reconstructed quality among the halftone methods. In addition, the LMS method generates optimal image masks which are significantly different for each halftone method. These optimal masks can also be applied to more sophisticated reconstruction methods as the default filter masks.

We developed a newhalftoning method, adaptive cell, which generates unstructured dots as by error diffusion method, but the produced binary image is less granular and more stable than that of error diffusion. The basic idea is covering the input image with cells which vary in size and shape depending on the input image data. Then appropriate number of pixels at the center of each cell are set on, to preserve the local average of the input image. The characteristics of the generated binary image shows that this method is suitable for high density electro photographic binary printers.

An analysis of the error diffusion method is presented which is based on the terminology of filter theory. The calculation of diffractive elements with the error diffusion method is shown. The stagnation of the iterative Fourier transform algorithm with a bandwidth constraint is overcome by error diffusion.