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.     

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     

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.     

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.     

Least-squares model-based halftoning

A least-squares model-based (LSMB) approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an optimal halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. It has been shown that the one-dimensional (1-D) least-squares problem, in which each row or column of the image is halftoned independently, can be implemented using the Viterbi algorithm to obtain the globally optimal solution. Unfortunately, the Viterbi algorithm cannot be used in two dimensions. In this paper, the two-dimensional (2-D) least-squares solution is obtained by iterative techniques, which are only guaranteed to produce a total optimum. Experiments show that LSMB halftoning produces better textures and higher spatial and gray-scale resolution than conventional techniques. We also show that the least-squares approach eliminates most of the problems associated with error diffusion. We investigate the performance of the LSMB algorithms over a range of viewing distances, or equivalently, printer resolutions. We also show that the LSMB approach gives us precise control of image sharpness.     

A fast, high-quality inverse halftoning algorithm for errordiffused halftones

Halftones and other binary images are difficult to process with causing several degradation. Degradation is greatly reduced if the halftone is inverse halftoned (converted to grayscale) before scaling, sharpening, rotating, or other processing. For error diffused halftones, we present (1) a fast inverse halftoning algorithm and (2) a new multiscale gradient estimator. The inverse halftoning algorithm is based on anisotropic diffusion. It uses the new multiscale gradient estimator to vary the tradeoff between spatial resolution and grayscale resolution at each pixel to obtain a sharp image with a low perceived noise level. Because the algorithm requires fewer than 300 arithmetic operations per pixel and processes 7x7 neighborhoods of halftone pixels, it is well suited for implementation in VLSI and embedded software. We compare the implementation cost, peak signal to noise ratio, and visual quality with other inverse halftoning algorithms.     

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.     

Look-up table (LUT) method for inverse halftoning

In this paper we propose look-up table (LUT) based methods 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. The method is extremely fast (no filtering is required) and the PSNR and visual image quality achieved is comparable to the best methods known for inverse halftoning. The LUT inverse halftoning method does not depend on the specific properties of the halftoning method, and can be applied to any halftoning method. Then, an algorithm for template selection for LUT inverse halftoning is introduced. We demonstrate the performance of the LUT inverse halftoning algorithm on error diffused images and ordered dithered images. We also extend LUT inverse halftoning to color halftones.     

Inverse halftoning using wavelets

This work introduces a new approach to inverse halftoning using nonorthogonal wavelets. The distinct features of this wavelet-based approach are: (1) edge information in the highpass wavelet images of a halftone image is extracted and used to assist inverse halftoning, (2) cross-scale correlations in the multiscale wavelet decomposition are used for removing background halftoning noise while preserving important edges in the wavelet lowpass image, and (3) experiments show that our simple wavelet-based approach outperforms the best results obtained from inverse halftoning methods published in the literature, which are iterative in nature.     

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.     

Halftone image classification using LMS algorithm and naive Bayes

Former research on inverse halftoning most focus on developing a general-purpose method for all types of halftone patterns, such as error diffusion, ordered dithering, etc., while fail to consider the natural discrepancies among various halftoning methods. To achieve optimal image quality for each halftoning method, the classification of halftone images is highly demanded. This study employed the least mean-square filter for improving the robustness of the extracted features, and employed the naive Bayes classifier to verify all the extracted features for classification. Nine of the most well-known halftoning methods were involved for testing. The experimental results demonstrated that the classification performance can achieve a 100% accuracy rate, and the number of distinguishable halftoning methods is more than that of a former method established by Chang and Yu.     

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.     

Training-based descreening.

Conventional halftoning methods employed in electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material, such as books and magazines. We present a novel approach for descreening color scanned documents aimed at providing an efficient solution to the Moiré problem in practical imaging devices, including copiers and multifunction printers. The algorithm works by combining two nonlinear image-processing techniques, resolution synthesis-based denoising (RSD), and modified smallest univalue segment assimilating nucleus (SUSAN) filtering. The RSD predictor is based on a stochastic image model whose parameters are optimized beforehand in a separate training procedure. Using the optimized parameters, RSD classifies the local window around the current pixel in the scanned image and applies filters optimized for the selected classes. The output of the RSD predictor is treated as a first-order estimate to the descreened image. The modified SUSAN filter uses the output of RSD for performing an edge-preserving smoothing on the raw scanned data and produces the final output of the descreening algorithm. Our method does not require any knowledge of the screening method, such as the screen frequency or dither matrix coefficients, that produced the printed original. The proposed scheme not only suppresses the Moiré artifacts, but, in addition, can be trained with intrinsic sharpening for deblurring scanned documents. Finally, once optimized for a periodic clustered-dot halftoning method, the same algorithm can be used to inverse halftone scanned images containing stochastic error diffusion halftone noise.     

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.     

Enhancing inverse halftoning via coupled dictionary training

Inverse halftoning is a challenging problem in image processing. Traditionally, this operation is known to introduce visible distortions into reconstructed images. This paper presents a learning-based method that performs a quality enhancement procedure on images reconstructed using inverse halftoning algorithms. The proposed method is implemented using a coupled dictionary learning algorithm, which is based on a patchwise sparse representation. Specifically, the training is performed using image pairs composed by images restored using an inverse halftoning algorithm and their corresponding originals. The learning model, which is based on a sparse representation of these images, is used to construct two dictionaries. One of these dictionaries represents the original images and the other dictionary represents the distorted images. Using these dictionaries, the method generates images with a smaller number of distortions than what is produced by regular inverse halftone algorithms. Experimental results show that images generated by the proposed method have a high quality, with less chromatic aberrations, blur, and white noise distortions.     

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.     

基于JPEG格式的激光图像扫描技术研究

提出了基于JPEG格式的激光图像扫描技术，利用JPEG图像格式的高压缩比以及通用性等特点，克服了以往激光图像扫描中采用BMP图像格式所存在的耗费大量存储空间的缺点，同时扩展了激光图像扫描的应用范围。通过对JPEG的解码，将JPEG文件格式转化为顺序存储像素信息的临时文件作为待输出的图像数据。在数据输出前，还需要对图像数据进行数字半色调处理，采用多级误差扩散算法可以使输出的图像数据保留更多的原始图像信息，使输出图像更加逼真。提出了在DSP系统下采用这种基于JPEG的激光图像扫描技术，可以更加快捷地实现解码和半色调处理，减少了成本，增加了实用性。     

On the phase response of the error diffusion filter for imagehalftoning

Conventional error diffusion halftoning uses a causal error filter. We propose the iterative error diffusion algorithm by extending the error diffusion to accommodate noncausal error filters. We realize the importance of the phase response of the error filter in the error diffusion halftoning method, and demonstrate it using examples. Iterative error diffusion is able to realize a zero phase error filter. We also trace a drawback of error diffusion to the shape of the error filter, and provide a remedy. The results obtained using a zero phase error filter in the iterative error diffusion algorithm are, in our opinion, superior to the error diffusion halftones.     

Wavelet-based inverse halftoning for error diffused halftones

This paper describes a technique for inverse halftoning based on the wavelet domain deconvolution that comprises Fourier-domain followed by wavelet-domain noise suppression, in order to benefit from the advantages of each of them. The proposed algorithm can be formulated as a linear deconvolution problem. In fact, we model such a gray-scale image to be the result of a convolution of the original image with a point spread function (PSF) and a colored noise. Our method performs inverse halftoning by first inverting the model specified convolution operator and then attenuating the residual noise using scalar wavelet-domain shrinkage. Using simulations, we verify that the proposed method is competitive with state-of-the-art inverse halftoning techniques in the mean-square-sense and that has also good visual performance. We illustrate the results with simulations on some examples.