A dual interpretation for direct binary search and its implications for tone reproduction and texture quality

A Machine Learning Approach to Design of Aperiodic, Clustered-Dot Halftone Screens via Direct Binary Search

Aperiodic, clustered-dot, halftone patterns have recently become popular for commercial printing of continuous-tone images with laser, electrophotographic presses, because of their inherent stability and resistance to moiré artifacts. Halftone screens designed using the multistage, multipass, clustered direct binary search (MS-MP-CLU-DBS) algorithm can yield halftone patterns with very high visual quality. But the characteristics of these halftone patterns depend on three input parameters for which there are no known formulas to choose their values to yield halftone patterns of a certain quality level and scale. Using machine learning methods, two predictors are developed that take as input these three parameters. One predicts the quality level of the halftone pattern. The other one predicts the scale of the halftone pattern. To provide ground truth information for training these predictors, human subjects viewed a large number of halftone patches generated from MS-MP-CLU-DBS-designed screens and assigned each patch to one of four quality levels. For each patch, the location of the peak in the radially averaged power spectrum (RAPS) is calculated as a measure of the scale or effective line frequency of the pattern. Experimental results demonstrate the accuracy of the two predictors and the effectiveness of screen design procedures based on these predictors to generate both monochrome and color high quality halftone images.

Structure-Aware Halftoning Using the Iterative Method Controlling the Dot Placement

Abstract Many image reproduction devices, such as printers, are limited to only a few numbers of printing inks. Halftoning, which is the process to convert a continuous-tone image into a binary one, is, therefore, an essential part of printing. An iterative halftoning method, called Iterative Halftoning Method Controlling the Dot Placement (IMCDP), which has already been studied by research scholars, generally results in halftones of good quality. In this paper, we propose a structure-based alternative to this algorithm that improves the halftone image quality in terms of sharpness, structural similarity, and tone preservation. By employing appropriate symmetrical and non-symmetrical Gaussian filters inside the proposed halftoning method, it is possible to adaptively change the degree of sharpening in different parts of the continuous-tone image. This is done by identifying a dominant line in the neighborhood of each pixel in the original image, utilizing the Hough Transform, and aligning the dots along the dominant line. The objective and subjective quality assessments verify that the proposed structure-based method not only results in sharper halftones, giving more three-dimensional impression, but also improves the structural similarity and tone preservation. The adaptive nature of the proposed halftoning method makes it an appropriate algorithm to be further developed to a 3D halftoning method, which could be adapted to different parts of a 3D object by exploiting both the structure of the images being mapped and the 3D geometrical structure of the underlying printed surface.

Theoretical Bounds of Direct Binary Search Halftoning

Direct binary search (DBS) produces the images of the best quality among half-toning algorithms. The reason is that it minimizes the total squared perceived error instead of using heuristic approaches. The search for the optimal solution involves two operations: (1) toggle and (2) swap. Both operations try to find the binary states for each pixel to minimize the total squared perceived error. This error energy minimization leads to a conjecture that the absolute value of the filtered error after DBS converges is bounded by half of the peak value of the autocorrelation filter. However, a proof of the bound's existence has not yet been found. In this paper, we present a proof that shows the bound existed as conjectured under the condition that at least one swap occurs after toggle converges. The theoretical analysis also indicates that a swap with a pixel further away from the center of the autocorrelation filter results in a tighter bound. Therefore, we propose a new DBS algorithm which considers toggle and swap separately, and the swap operations are considered in the order from the edge to the center of the filter. Experimental results show that the new algorithm is more efficient than the previous algorithm and can produce half-toned images of the same quality as the previous algorithm.

Progressive halftone watermarking using multilayer table lookup strategy

In this paper, a halftoning-based multilayer watermarking of low computational complexity is proposed. An additional data-hiding technique is also employed to embed multiple watermarks into the watermark to be embedded to improve the security and embedding capacity. At the encoder, the efficient direct binary search method is employed to generate 256 reference tables to ensure the output is in halftone format. Subsequently, watermarks are embedded by a set of optimized compressed tables with various textural angles for table lookup. At the decoder, the least mean square metric is considered to increase the differences among those generated phenotypes of the embedding angles and reduce the required number of dimensions for each angle. Finally, the naïve Bayes classifier is employed to collect the possibilities of multilayer information for classifying the associated angles to extract the embedded watermarks. These decoded watermarks can be further overlapped for retrieving the additional hidden-layer watermarks. Experimental results show that the proposed method requires only 8.4 ms for embedding a watermark into an image of size 512×512 , under the 32-bit Windows 7 platform running on 4GB RAM, Intel core i7 Sandy Bridge with 4GB RAM and IDE Visual Studio 2010. Finally, only 2 MB is required to store the proposed compressed reference table.

Local learned dictionaries optimized to edge orientation for inverse halftoning

A method is proposed for fully restoring local image structures of an unknown continuous-tone patch from an input halftoned patch with homogenously distributed dot patterns, based on a locally learned dictionary pair via feature clustering. First, many training sets consisting of paired halftone and continuous-tone patches are collected, and then histogram-of- oriented-gradient (HOG) feature vectors that describe the edge orientations are calculated from every continuous-tone patch, to group the training sets. Next, a dictionary learning algorithm is separately conducted on the categorized training sets, to obtain the halftone and continuous-tone dictionary pairs, optimized to edge-oriented patch representation. Finally, an adaptively smoothing filter is applied to the input halftone patch, to predict the HOG feature vector of an unknown continuous-tone patch, and to select one of the previously learned dictionary pairs, based on the Euclidean distance between the HOG mean feature vectors of the grouped training sets and the predicted HOG vector. In addition to using the local dictionary pairs, a patch fusion technique is used to reduce some artifacts, such as color noise and overemphasized edges on smooth regions. Experimental results show that the use of the paired dictionary selected by the local edge orientation and patch fusion technique not only reduced the artifacts in smooth regions, but also provided well expressed fine details and outlines, especially in the areas of textures, lines, and regular patterns.

Improved block truncation coding using optimized dot diffusion

Block truncation coding (BTC) has been considered a highly efficient compression technique for decades. However, its inherent artifacts, blocking effect and false contour, caused by low bit rate configuration are the key problems. To deal with these, an improved BTC, namely dot-diffused BTC (DDBTC), is proposed in this paper. Moreover, this method can provide excellent processing efficiency by exploiting the nature parallelism advantage of the dot diffusion, and excellent image quality can also be offered through co-optimizing the class matrix and diffused matrix of the dot diffusion. According to the experimental results, the proposed DDBTC is superior to the former error-diffused BTC in terms of various objective image quality assessment methods as well as processing efficiency. In addition, the DDBTC also shows a significant image quality improvement comparing with that of the former ordered-dither BTC.

Efficient halftoning based on multiple look-up tables

Look-up table (LUT) halftoning is an efficient way to construct halftone images and approximately simulate the dot distribution of the learned halftone image set. In this paper, a general mechanism named multiple look-up table (MLUT) halftoning is proposed to generate the halftones of direct binary search (DBS), whereas the high efficient characteristic of the LUT is still preserved. In the MLUT, the standard deviation is adopted as an important feature to classify various tables. In addition, the proposed quick standard deviation evaluation is employed to yield an extremely low computational complexity in calculating the standard deviation. In the parameter optimization, the autocorrelation is adopted because it can fully characterize the periodicity of dot distribution. Experimental results demonstrate that the dot distribution generated by the proposed method approximates to that of the DBS, which enables the proposed scheme as a very competitive candidate in the copying and printing industry.

Clustered-dot halftoning with direct binary search

In this paper, we present a new algorithm for aperiodic clustered-dot halftoning based on direct binary search (DBS). The DBS optimization framework has been modified for designing clustered-dot texture, by using filters with different sizes in the initialization and update steps of the algorithm. Following an intuitive explanation of how the clustered-dot texture results from this modified framework, we derive a closed-form cost metric which, when minimized, equivalently generates stochastic clustered-dot texture. An analysis of the cost metric and its influence on the texture quality is presented, which is followed by a modification to the cost metric to reduce computational cost and to make it more suitable for screen design.

Oriented modulation for watermarking in direct binary search halftone images

In this paper, a halftoning-based watermarking method is presented. This method enables high pixel-depth watermark embedding, while maintaining high image quality. This technique is capable of embedding watermarks with pixel depths up to 3 bits without causing prominent degradation to the image quality. To achieve high image quality, the parallel oriented high-efficient direct binary search (DBS) halftoning is selected to be integrated with the proposed orientation modulation (OM) method. The OM method utilizes different halftone texture orientations to carry different watermark data. In the decoder, the least-mean-square-trained filters are applied for feature extraction from watermarked images in the frequency domain, and the naïve Bayes classifier is used to analyze the extracted features and ultimately to decode the watermark data. Experimental results show that the DBS-based OM encoding method maintains a high degree of image quality and realizes the processing efficiency and robustness to be adapted in printing applications.

Alleviating dirty-window effect in medium frame-rate binary video halftones

A video display device having a lower number of bits per pixel than that required by the video to be displayed quantizes the video prior to its display. Halftoning can perform this quantization while attempting to reduce the visibility of certain quantization artifacts. Quantization artifacts are, nevertheless, not eliminated. A temporal artifact known as dirty-window effect (DWE) can be commonly observed in medium frame-rate binary video halftones. In this paper, we propose video halftone enhancement algorithms to reduce DWE. We assess the performance of the proposed algorithms by presenting objective measures for DWE in the original and the improved halftone videos. The expected contributions of this paper include three medium frame-rate binary video halftone enhancement algorithms that do the following: 1) reduce DWE under a spatial quality constraint; 2) reduce DWE under a spatial quality constraint with reduced complexity; and 3) reduce DWE under spatial and temporal quality constraints.

Hierarchical colorant-based direct binary search halftoning

Colorant-based direct binary search (CB-DBS) halftoning proposed in provides an image quality benchmark for dispersed-dot halftoning algorithms. The objective of this paper is to further push the image quality limit. An algorithm called hierarchical colorant-based direct binary search (HCB-DBS) is developed in this paper. By appropriately integrating yellow colorant into dot-overlapping and dot-positioning controls, it is demonstrated that HCB-DBS can achieve better halftone texture of both individual and joint dot-color planes, without compromising the dot distribution of more visible halftone of cyan and magenta colorants. The input color specification is first converted from colorant space to dot-color space with minimum brightness variation principle for full dot-overlapping control. The dot-colors are then split into groups based upon dot visibility. Hierarchical monochrome DBS halftoning is applied to make dot-positioning decision for each group, constrained on the already generated halftone of the groups with higher priority. And dot-coloring is decided recursively with joint monochrome DBS halftoning constrained on the related total dot distribution. Experiments show HCB-DBS improves halftone texture for both individual and joint dot-color planes. And it reduces the halftone graininess and free of color mottle artifacts, comparing to CB-DBS.

The hybrid screen--improving the breed

The hybrid screen is a halftoning method that generates stochastic dispersed dot textures in highlights and periodic clustered dot textures in midtones. Each tone level is sequentially designed from highlight to midtone by applying an iterative halftoning algorithm such as direct binary search (DBS). By allowing random seeding followed by swap-only DBS in a predefined core region within each microcell, each level can be designed while satisfying the stacking constraint and guaranteeing a smooth transition between levels. This paper describes a complete design process for the hybrid screen, introduces a number of enhancements to the original hybrid screen, and evaluates their impact on print quality. These enhancements include a multilevel screen design based on either extending a bilevel screen or directly generating a multilevel screen on a high resolution grid, and extending the hybrid screen design procedure to color by jointly optimizing the color screens using color DBS. For the multilevel screen, we show that the best choice for the core size critically depends on the bit depth and screen frequency. For the color hybrid screen, we demonstrate a significant improvement in the highlights over halftones generated by independently designed screens.

Generating stochastic dispersed and periodic clustered textures using a composite hybrid screen

In electrophotographic printing, a periodic clustered-dot halftone pattern is preferred for a smooth and stable result. In addition, the screen frequency should be high enough to minimize the visibility of the halftone textures and to ensure good detail rendition. However, at these frequencies, the halftone cell may contain too few pixels to provide a sufficient number of distinct gray levels. This will result in contouring and posterization. The traditional solution is to grow the clusters asynchronously within a repeating block of clusters known as a supercell. The growth of each individual cluster is governed by a microscreen. The order in which the clusters grow within the supercell is determined by a macroscreen. Typically, the macroscreen is a recursive pattern due to Bayer. In highlights and shadows, this ordering results in visible artifacts. Replacing the Bayer screen by a stochastic macroscreen eliminates these artifacts, but results in new artifacts. In this paper, we propose a new composite screen architecture that employs multiple microscreens and multiple macroscreens in the highlights and shadows. These screens are jointly designed by using the direct binary search (DBS) algorithm.

Quantization of accumulated diffused errors in error diffusion

Due to its high image quality and moderate computational complexity, error diffusion is a popular halftoning algorithm for use with inkjet printers. However, error diffusion is an inherently serial algorithm that requires buffering a full row of accumulated diffused error (ADE) samples. For the best performance when the algorithm is implemented in hardware, the ADE data should be stored on the chip on which the error diffusion algorithm is implemented. However, this may result in an unacceptable hardware cost. In this paper, we examine the use of quantization of the ADE to reduce the amount of data that must be stored. We consider both uniform and nonuniform quantizers. For the nonuniform quantizers, we build on the concept of tone-dependency in error diffusion, by proposing several novel feature-dependent quantizers that yield improved image quality at a given bit rate, compared to memoryless quantizers. The optimal design of these quantizers is coupled with the design of the tone-dependent parameters associated with error diffusion. This is done via a combination of the classical Lloyd-Max algorithm and the training framework for tone-dependent error diffusion. Our results show that 4-bit uniform quantization of the ADE yields the same halftone quality as error diffusion without quantization of the ADE. At rates that vary from 2 to 3 bits per pixel, depending on the selectivity of the feature on which the quantizer depends, the feature-dependent quantizers achieve essentially the same quality as 4-bit uniform quantization.

Model-based color halftoning using direct binary search

In this paper, we develop a model-based color halftoning method using the direct binary search (DBS) algorithm. Our method strives to minimize the perceived error between the continuous tone original color image and the color halftone image. We exploit the differences in how the human viewers respond to luminance and chrominance information and use the total squared error in a luminance/chrominance based space as our metric. Starting with an initial halftone, we minimize this error metric using the DBS algorithm. Our method also incorporates a measurement based color printer dot interaction model to prevent the artifacts due to dot overlap and to improve color texture quality. We calibrate our halftoning algorithm to ensure accurate colorant distributions in resulting halftones. We present the color halftones which demonstrate the efficacy of our method.

Inkjet printer model-based halftoning

The quality of halftone prints produced by inkjet (IJ) printers can be limited by random dot-placement errors. While a large literature addresses model-based halftoning for electrophotographic printers, little work has been done on model-based halftoning for IJ printers. In this paper, we propose model-based approaches to both iterative least-squares halftoning and tone-dependent error diffusion (TDED). The particular approach to iterative least-squares halftoning that we use is direct binary search (DBS). For DBS, we use a stochastic model for the equivalent gray-scale image, based on measured dot statistics of printed IJ halftone patterns. For TDED, we train the tone-dependent weights and thresholds to mimic the spectrum of halftone textures generated by model-based DBS. We do this under a metric that enforces both the correct radially averaged spectral profile and angular symmetry at each radial frequency. Experimental results generated with simulated printers and a real printer show that both IJ model-based DBS and IJ model-based TDED very effectively suppress IJ printer-induced artifacts.

Clustered-minority-pixel error diffusion

We present a clustered-minority-pixel error-diffusion halftoning algorithm for which the quantizer threshold is modified on the basis of the past output and a dot activation map. Dot area, dot shape, and dot distribution are more controllable than with other clustered-dot halftone algorithms such as Levien's algorithm. This method also effectively reduces structured mazelike artifacts in midtones that occur in Levien's algorithm. The dot distribution is further improved by using different error-diffusion weights for different input gray levels.

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.

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.

Halftoning via direct binary search using analytical and stochastic printer models

We incorporate models for printer dot interactions within the iterative direct binary search (DBS) halftoning algorithm. Monochrome electro-photographic printers are considered. Both analytical and stochastic models are studied. In the analytical model it is assumed that the printer can generate a circular spot with constant absorptance at each printer addressable location, whereas the stochastic model is based on microscopic absorptance and variance measurements. We also present an efficient strategy for evaluating the change in computational cost as the search progresses. With our scheme, updating the change in error only involves a few fetches from two look-up-tables and some scalar multiplications and additions. Experimental results are provided that show that DBS with an appropriate model for printer dot interactions yields enhanced detail rendition, and improved tonal gradation in shadow areas.

Multilevel screen design using direct binary search

Screening is an efficient halftoning algorithm that is easy to implement. With multilevel devices, there is a potential to improve the overall image quality by using multilevel screening, which allows us to choose among multiple native tones at each addressable pixel. We propose a methodology for multilevel screen design using direct binary search (DBS). We refer to one period of the screen as a multitone cell. We define a multitone schedule, which for each absorptance level specifies the fraction of each native tone used in the multitone cell. Traditional multitoning uses only one native tone in smooth areas corresponding to absorptance values near the native tones, an approach that introduces contouring artifacts. To reduce contouring, we employ schedules that use more than one native tone at each absorptance level. On the basis of the multitone schedule, multitone patterns are designed level by level by adding native tones under the stacking constraint. At each level the spatial arrangement of the native tones is determined by a modified DBS search. We explore several different multitone schedules that illustrate the image-quality trade-offs in multitone screen design.

Impact of HVS models on model-based halftoning

A model for the human visual system (HVS) is an important component of many halftoning algorithms. Using the iterative direct binary search (DBS) algorithm, we compare the halftone texture quality provided by four different HVS models that have been reported in the literature. Choosing one HVS model as the best for DBS, we then develop an approximation to that model which significantly improves computational performance while minimally increasing the complexity of the code. By varying the parameters of this model, we find that it is possible to tune it to the gray level being rendered, and to thus yield superior halftone quality across the tone scale. We then develop a dual-metric DBS algorithm that effectively provides a tone-dependent HVS model without a large increase in computational complexity.

Electrophotographic process embedded in direct binary search

A novel halftoning approach that has embedded in it a model for the electrophotographic process is presented. Models for the laser beam, exposure of the organic photoconductor, and the resulting absorptance on the paper are embedded into the direct binary search (DBS) halftoning algorithm. The algorithm is applicable to any arbitrary pixel modulation scheme and is also highly portable between different electrophotographic print engines. Computational issues are addressed to make the approach viable. Results show good exploitation of pixel modulation and improvement over DBS with no printer model throughout most of the tone scale.