Ink Drop Displacement Model-Based Direct Binary Search

A novel statistical ink drop displacement (IDD) printer model for the direct binary search (DBS) halftoning algorithm is proposed. It is intended primarily for pagewide inkjet printers that exhibit dot displacement errors. The tabular approach in the literature predicts the gray value of a printed pixel based on the halftone pattern in some neighborhood of that pixel. However, memory retrieval time and the complexity of memory requirements hamper its feasibility in printers that have a very large number of nozzles and produce ink drops that affect a large neighborhood. To avoid this problem, our IDD model embodies dot displacements by moving each perceived ink drop in the image from its nominal location to its actual location, rather than manipulating the average gray values. This enables DBS to directly compute the appearance of the final printout without retrieving values from a table. In so doing, the memory issue is eliminated and the computation efficiency is enhanced. The deterministic cost function of DBS is replaced by the expectation over the ensemble of the displacements for the proposed model such that the statistical behavior of the ink drops is accounted for. Experimental results show significant improvement in the quality of the printed image over the original DBS. Besides, the image quality obtained by the proposed approach appears to be slightly better than that obtained by the tabular approach.

The Cell Tracking Challenge: 10 years of objective benchmarking

The Cell Tracking Challenge is an ongoing benchmarking initiative that has become a reference in cell segmentation and tracking algorithm development. Here, we present a significant number of improvements introduced in the challenge since our 2017 report. These include the creation of a new segmentation-only benchmark, the enrichment of the dataset repository with new datasets that increase its diversity and complexity, and the creation of a silver standard reference corpus based on the most competitive results, which will be of particular interest for data-hungry deep learning-based strategies. Furthermore, we present the up-to-date cell segmentation and tracking leaderboards, an in-depth analysis of the relationship between the performance of the state-of-the-art methods and the properties of the datasets and annotations, and two novel, insightful studies about the generalizability and the reusability of top-performing methods. These studies provide critical practical conclusions for both developers and users of traditional and machine learning-based cell segmentation and tracking algorithms.

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.

Steady-State and Transient Performance of Ion-Sensitive Electrodes Suitable for Wearable and Implantable Electro-chemical Sensing

Traditional Potentiometric Ion-selective Electrodes (ISE) are widely used in industrial and clinical settings. The simplicity and small footprint of ISE have encouraged their recent adoption as wearable/implantable sensors for personalized healthcare and precision agriculture, creating a new set of unique challenges absent in traditional ISE. In this paper, we develop a fundamental physics-based model to describe both steady-state and transient responses of ISE relevant for wearable/implantable sensors. The model is encapsulated in a generalized Nernst formula that explicitly accounts for the analyte density, time-dynamics of signal transduction, ion-selective membrane thickness, and other sensor parameters. The formula is validated numerically by self-consistent modeling of multispecies ion-transport and experimentally by interpreting the time dynamics and thickness dependence of thin-film solid-contact and graphene-based ISE sensors for measuring soil nitrate concentration. These fundamental results will support the accelerated development of ISE for wearable/implantable applications.

Ionic Strength Influences on Biofunctional Au-Decorated Microparticles for Enhanced Performance in Multiplexed Colorimetric Sensors

The rising development of biosensors offers a great potential for health, food, and environmental monitoring. However, in many colorimetric platforms, there is a performance limitation stemming from the tendency of traditional Au nanoparticles toward nonspecific aggregation in response to changing ionic strength (salt concentration). This work puts forward a new type of colorimetric aptamer-functionalized labeling of microparticles, which allows to leverage an increase in ionic strength as a positive driver of enhanced detection performance of analytical targets. The resulting device is a cost-effective, instrument-free, portable, and reliable aptasensor that serves as basis for the fabrication of universal paper-based colorimetric platforms with the capability of multiplex, multireplicates and provides quantitative colorimetric detection. A controlled fabrication process was demonstrated by keeping 90% of the signal obtained from the as-fabricated devices (n = 40) within ± 1 standard deviation (SD) (relative SD = 5.69%) and following a mesokurtic normal-like distribution (p = 0.385). We propose for the first time a salt-induced aggregation mechanism for highly stable multilayered label particles (ssDNA-PEI-Au-PS) as the basis of the detection scheme. The use of DNA aptamers as capture biomolecules and PEI as an encapsulating agent allows for a sensitive and highly specific colorimetric response. As a proof of concept, multiplexed detection of mercury (Hg²⁺) and arsenic (As³⁺) was demonstrated. In addition, we introduced a robust image analysis algorithm for testing zone segmentation and color signal quantification that allowed for analytical detection, reaching a limit of detection of 1 ppm for both targeted analytes, with enough evidence (p > 0.05) to prove the high specificity of the fabricated device versus a pool of possible interferent ions.

New Design for Compact Color Screen Sets for High-End Digital Color Press

Digital halftoning is an essential part of the process for printing color, continuous-tone content. Traditionally, the highest quality has been achieved with analog, offset lithographic presses, using color screen sets that yield periodic, clustereddot halftone patterns. Increasingly, these systems are being supplanted by digital presses that are based on either electrophotographic or inkjet marking processes. Due to the inherent instability of the electrophotographic marking process, periodic, clustered-dot halftone patterns are also widely used with such presses. However, digital presses have much lower resolution than their analog counterparts. Simply mimicking the traditional screen designs used with commercial, offset presses will result in halftone patterns that are more susceptible to moire due to the interaction between the periodic patterns used to render the different color channels. This causes instability in the printed colors. The moire can be reduced by increasing the frequency of the halftone patterns. But this may make the print appear grainier than its analog counterpart. In this paper, we introduce a principled design procedure that allows one to design color screen sets that generate periodic, clustered-dot halftone patterns that improve color stability without increasing graininess. We present experimental results to support the benefits of our new color screen set design framework.

Inkjet Printed Nanopatterned Aptamer-Based Sensors for Improved Optical Detection of Foodborne Pathogens

The increasing incidence of infectious outbreaks from contaminated food and water supply continues imposing a global burden for food safety, creating a market demand for on-site, disposable, easy-to-use, and cost-efficient devices. Despite of the rapid growth of biosensors field and the generation of breakthrough technologies, more than 80% of the platforms developed at lab-scale never will get to meet the market. This work aims to provide a cost-efficient, reliable, and repeatable approach for the detection of foodborne pathogens in real samples. For the first time an optimized inkjet printing platform is proposed taking advantage of a carefully controlled nanopatterning of novel carboxyl-functionalized aptameric ink on a nitrocellulose substrate for the highly efficient detection of E. coli O157:H7 (25 colony forming units (CFU) mL^-1 in pure culture and 233 CFU mL^-1 in ground beef) demonstrating the ability to control the variation within ±1 SD for at least 75% of the data collected even at very low concentrations. From the best of the knowledge this work reports the lowest limit of detection of the state of the art for paper-based optical detection of E. coli O157:H7, with enough evidence (p > 0.05) to prove its high specificity at genus, species, strain, and serotype level.

Three-dimensional range geometry compression via phase encoding

One of the state-of-the-art methods for three-dimensional (3D) range geometry compression is to encode 3D data within a regular 24-bit 2D color image. However, most existing methods use all three color channels to solely encode 3D data, leaving no room to store other information (e.g., texture) within the same image. This paper presents a novel method which utilizes geometric constraints, inherent to the structured light 3D scanning device, to reduce the amount of data that need be stored within the output image. The proposed method thus only requires two color channels to represent 3D data, leaving one channel free to store additional information (such as a texture image). Experimental results verify the overall robustness of the proposed method. For example, a compression ratio of 3038:1 can be achieved, versus the STL format, with a root-mean-square error of 0.47% if the output image is compressed with JPEG 80%.

The Lattice-Based Screen Set: A Square N -Color All-Orders Moiré-Free Screen Set

Periodic clustered-dot screens are widely used for electrophotographic printers due to their print stability. However, moiré is a ubiquitous problem that arises in color printing due to the beating together of the clustered-dot, periodic halftone patterns that are used to represent different colorants. The traditional solution in the graphic arts and printing industry is to rotate identical square screens to angles that are maximally separated from each other. However, the effectiveness of this approach is limited when printing with more than four colorants, i.e., N -color printing, where N > 4 . Moreover, accurately achieving the angles that have maximum angular separation requires a very high-resolution plate writer, as is used in commercial offset printing. Commercially available high-end digital printers cannot achieve this resolution. In this paper, we propose a systematic way to design color screen sets for periodic, clustered-dot screens that offer more explicit control of the moiré properties of the resulting screens when used in color printing. We develop a principled approach for the moiré-free screen design that is called lattice-based screen design. The basic concept behind our approach is the creation of the screen set on a 2D lattice in the frequency domain, and then picking each fundamental frequency vector of the individual colorant planes in the created spectral lattice according to the desired properties. The lattice-based screen design offers more flexibility in designing N -color screen sets with different halftone geometries, and all of them are guaranteed to be all-orders moiré-free. We demonstrate the efficacy of our proposed method by introducing several new screen designs, and a comparison with published screen designs.

Halftone Blending Between Smooth and Detail Screens to Improve Print Quality With Electrophotographic Printers

In this paper, we consider a dual-mode process for the electrophotographic laser printer--a low-frequency halftoning for smooth regions and a high-frequency halftoning for detail regions. These regions are described by an object map that is extracted from the page description language version of the document. This manner of switching screens depending on the local content provides a stable halftone without artifacts in smooth areas and preserves the detail rendering in detail or texture areas. However, when switching between halftones with two different frequencies, jaggies may occur along the boundaries between areas halftoned with low- and high-frequency screens. To reduce the jaggies, our screens obey a harmonic relationship. In addition, we implement a blending process based on a transition region. We propose a nonlinear blending process in which at each pixel, we choose the maximum of the two weighted halftones, where the weights vary according to the position in the transition region. Moreover, we describe an online tone-mapping for the boundary blending process, based on an offline calibration procedure that effectively assures the desired tone values within the transition region.

Fast space-varying convolution using matrix source coding with applications to camera stray light reduction

Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

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.

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.

Adaptive bilateral filter for sharpness enhancement and noise removal

In this paper, we present the adaptive bilateral filter (ABF) for sharpness enhancement and noise removal. The ABF sharpens an image by increasing the slope of the edges without producing overshoot or undershoot. It is an approach to sharpness enhancement that is fundamentally different from the unsharp mask (USM). This new approach to slope restoration also differs significantly from previous slope restoration algorithms in that the ABF does not involve detection of edges or their orientation, or extraction of edge profiles. In the ABF, the edge slope is enhanced by transforming the histogram via a range filter with adaptive offset and width. The ABF is able to smooth the noise, while enhancing edges and textures in the image. The parameters of the ABF are optimized with a training procedure. ABF restored images are significantly sharper than those restored by the bilateral filter. Compared with an USM based sharpening method-the optimal unsharp mask (OUM), ABF restored edges are as sharp as those rendered by the OUM, but without the halo artifacts that appear in the OUM restored image. In terms of noise removal, ABF also outperforms the bilateral filter and the OUM. We demonstrate that ABF works well for both natural images and text images.

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.

A subspace matching color filter design methodology for a multispectral imaging system

In this paper, we present a methodology to design filters for an imaging system to improve the accuracy of the spectral measurements for families of reflective surfaces. We derive the necessary and sufficient conditions that the sensor space of the system must obey in order to measure the spectral reflectance of the surfaces accurately. Through simulations, we show how these conditions can be applied to design filters using a set of sample spectral data acquired from extracted teeth. For this set of data, we also compare our results to those of Wolski's method, a conventional filter design method which produces filters that recover tristimulus values of surfaces accurately under several illuminants. We show that our method produces filters that capture the spectral reflectance better given the same number of measurements. The errors in predicting the color of the sample data are much lower under every test illuminant when the filters designed with our method are used.

A new framework for characterization of halftone textures

Characterization of halftone texture is important for quantitative assessment of halftone quality. In this paper, we develop a new framework based on directional local sequency analysis and a filter bank structure. We decompose a halftone image into subband images, from which we can easily reconstruct the original halftone. Based on these subband images, we define the directional sequency spectrum which is analogous to the two-dimensional Fourier spectrum, and formulate several texture measures. Two test image sets are used to justify these measures.

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.

Look-up-table based halftoning algorithm

Screening is a low complexity halftoning algorithm that has been widely used in many applications. However, screen design requires that the stacking property be obeyed. This constraint limits the texture quality at each gray level. We present a look-up-table based halftoning algorithm for which the stacking constraint is not necessarily satisfied; but the binary patterns for individual levels are still correlated. The binary patterns are designed level by level using the direct binary search method. The algorithm improves halftone image quality compared with screening.

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

The direct binary search (DBS) algorithm employs a search heuristic to minimize the mean-squared perceptually filtered error between the halftone and continuous-tone original images. Based on an efficient method for evaluating the effect on the mean squared error of trial changes to the halftone image, we show that DBS also minimizes in a pointwise sense the absolute error under the same visual model, but at twice the viewing distance associated with the mean-squared error metric. This dual interpretation sheds light on the convergence properties of the algorithm, and clearly explains the tone bias that has long been observed with halftoning algorithms of this type. It also demonstrates how tone bias and texture quality are linked via the scale parameter, the product of printer resolution and viewing distance. Finally, we show how the tone bias can be eliminated by tone-correcting the continuous-tone image prior to halftoning it.

Sequential linear interpolation of multidimensional functions

We introduce a new approach that we call sequential linear interpolation (SLI) for approximating multidimensional nonlinear functions. The SLI is a partially separable grid structure that allows us to allocate more grid points to the regions where the function to be interpolated is more nonlinear. This approach reduces the mean squared error (MSE) between the original and approximated function while retaining much of the computational advantage of the conventional uniform grid interpolation. To obtain the optimal grid point placement for the SLI structure, we appeal to an asymptotic analysis similar to the asymptotic vector quantization (VQ) theory. In the asymptotic analysis, we assume that the number of interpolation grid points is large and the function to be interpolated is smooth. Closed form expressions for the MSE of the interpolation are obtained from the asymptotic analysis. These expressions are used to guide us in designing the optimal SLI structure. For cases where the assumptions underlying the asymptotic theory are not satisfied, we develop a postprocessing technique to improve the MSE performance of the SLI structure. The SLI technique is applied to the problem of color printer characterization where a highly nonlinear multidimensional function must be efficiently approximated. Our experimental results show that the appropriately designed SLI structure can greatly improve the MSE performance over the conventional uniform grid.

Optimization of sensor response functions for colorimetry of reflective and emissive objects

This paper describes the design of color filters for a surface color measurement device. The function of the device is to return the XYZ tristimulus vector characterizing the color of the surface. The device is designed to measure emissive as well as reflective surfaces. It uses an internal set of LEDs to illuminate reflective surfaces while characterizing their color under assumed standard illuminants. In the design of the filters, we formulate a nonlinear optimization problem with the goal of minimizing error in the uniform color space CIE L*a*b*. Our optimization criteria employs a technique to retain a linear structure while approximating the true L*a*b* error. In addition, our solution is regularized to account for system noise, filter roughness, and filter implementation errors. Experimental results indicate average and worst-case device accuracy of 0.27 L*a*b* DeltaE units and 1.56 L*a*b* DeltaE units for a "system tolerance" of 0.0005.

Sequential scalar quantization of vectors: an analysis

Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.

Motion estimation based on time-sequentially sampled imagery

Determining the parameters of motion within a time-varying scene is an important problem in such fields as computer vision, motion compensated video coding, and tracking. Most motion estimation algorithms operate on image data that has been sampled in both space and time. However, very little work has been done to investigate the impact of the underlying sampling strategy on the motion estimation problem. The authors investigate motion estimation with time-sequentially sampled image data. They consider both centroid-displacement-based and Fourier-based approaches to motion estimation with this type of data. For comparision, they also examine the performance of these estimators with conventional, frame-instantaneously sampled data. The motion estimators are developed and evaluated in the context of the tracking problem. In particular, they present extensive numerical results showing the performance of the motion estimators in a simulated tracking environment within which the assumptions underlying the development of the estimators are violated. These results suggest empirical rules for choosing parameter values for the estimators.

Multiple scattering by a planar array of parallel dielectric cylinders

The solution of the multiple-scattering problem for N parallel dielectric cylinders is considered for plane-wave illumination perpendicular to the cylinder axes. We describe a nonlinear programming approach to solve the multiple-scattering matrix for an arbitrary planar array of N parallel dielectric cylinders. To our knowledge, no calculations have been made previously for multiple scattering by more than two parallel dielectric cylinders. Numerical results for four abutting cylinders with end-on illumination demonstrate damping of internal resonance features similar to previously published results for two cylinders. Furthermore, we present numerical examples of scattering from eight unequally spaced, parallel dielectric cylinders with broadside illumination. Because of coupling between the cylinders, the incident energy is spread evenly between the intensity peaks behind the array of cylinders.

Synthesis of diffractive optical bar codes

A new type of diffractive optical bar code (DOBC) is proposed. Rather than scanning directly, the DOBC is coherently illuminated, and the first diffraction order is sensed. The spacing between the bars is chosen so that the thresholded diffraction pattern yields a specified binary code. Two approaches are investigated for synthesis of the DOBC: phase shaping and a gradient-based, nonlinear, constrained optimization technique. The two design methods are compared based on numerical results, and the validity of the overall design approach is verified by optically sensing the diffraction patterns for a number of fabricated DOBC's.

Synthesis of digital holograms by direct binary search

A new approach to the design of computer-generated holograms makes optimal use of the available device resolution. An iterative search algorithm minimizes an error criterion by directly manipulating the binary hologram and observing the effect on the desired reconstruction. Several measures of error and efficiency useful in assessing the optimality of digital holograms are defined. Methods for designing digital holograms that are based on projections and error diffusion are presented as established techniques for comparison to direct binary search.

Optical median filtering using threshold decomposition

A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magnetooptic spatial light modulator as the input device and a computergenerated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images.

Representation-related errors in binary digital holograms: a unified analysis

Images reconstructed from binary digital holograms are degraded by errors due to the binary representation of the complex-valued object spectrum and by errors due to computational and plotter limitations. In this paper, representation-related errors are analyzed in terms of false images that appear in the desired reconstruction order and in adjacent diffraction orders. It is shown that the false images are strongly dependent on the manner in which the object spectrum is sampled and on the mapping from spectral sample to binary transmittance. Three categories of digital holograms are distinguished: those that sample the object spectrum at the center of each hologram cell; those that sample at the center of each aperture; and those that sample at each resolvable spot. In going from the first to the third category, the reconstruction is successively less degraded by false images. For the third category, there are no false images in the desired reconstruction order and only one false image in each adjacent order. The two methods in this category differ only in the suppression of these false images.

Binary display of images when spot size exceeds step size

Many binary digital devices for display or printing of images are capable of placing spots of size S at an array of addressable points spaced R apart where S < R. A new representation is described for display or printing of continuous-tone images with such devices for which S/R < 2. The presentation takes into account spot overlap to assure correct tone reproduction, minimize pattern visibility, and maximize detail rendition. The algorithm is a modification of ordered dither that utilizes in one direction the subspot size addressibility of the device to increase the number of available levels of tone per unit area and enhance the good visual properties of the dither matrix. While not implementable by thresholding, the algorithm may be implemented by a nearly point-to-point spatially periodic mapping from continuous-tone image-to-device input. Fourier analysis provides a theoretical basis for the representation. Experimental work is presented that confirms the results of the analysis.

Computer-aided design of dither signals for binary display of images

The quality of binary images displayed using ordered dither is strongly dependent on the spatial arrangement of the thresholds in the dither signal. In the frequency domain, this dependence may be viewed as a consequence of aliasing. A computer-aided approach to the design of dither signals that uses a pairwise exchange algorithm to minimize a measure of susceptibility to aliasing is described. The susceptibility measure may be chosen to take into account many factors that affect perceived image quality. Experimental results are presented that illustrate the potential of the method.

Aliasing error in digital holography

The use of the discrete Fourier transform in digital holography introduces aliasing error in the reconstructed image. Spectrum shaping to reduce dynamic range may also result in a serious increase in aliasing error. The effect of aliasing in digital holography is analyzed. It is proposed that the bandwidth be constrained when shaping the image spectrum. Experimental results show the approach to be quite effective.

Minimax spectrum shaping with a bandwidth constraint

A new approach to spectrum shaping, in which the maximum of the spectrum is minimized subject to a constraint on the bandwidth, is considered. The results can be applied to a variety of methods of digital holography. A lower bound for the maximum and a figure of merit are obtained. Practical methods for minimax shaping of the spectrum are described and compared via computer simulations. The results of these simulations indicate that the lower bound is relatively tight, and the figure of merit is a good one.