In this paper, we give a brief introduction of the parallel error diffusion and classify various approaches into three classes - partitioned area, concurrent, and inter-area error diffusions. These approaches, including intra-dot diffusion, space-filling curve traversal, Fibonacci-like sequence, multi-center dot diffusion, dispersed-dot diffusion, concurrent processing, neural network, and inter-dot diffusion are discussed and examples are given. Comparisons are made with other deterministic error filters (e.g. Floyd-Steinberg, Schroeder, Stucki, and Shiau-Fan) and with the corresponding clustered-dot and dispersed-dot ordered dithers. We also provide several extensions to the existing techniques. The conditions for parallel line error diffusions of horizontal, vertical, and diagonal lines are recognized and new parallel error diffusions are developed.
Halftone screen encoding method provides a means for seamlessly tiling a digital halftone screen to cover the whole image plane. The encoding method has a major effect on the performance of the digital halftoning. Three encoding methods - Holladay algorithm, PostScript Type 10 halftone dictionary, and single-square encoding - are reviewed. We derive the relationships and develop conversion mechanisms between them. Finally, we compare these encoding methods with respect to the implementation complexity and memory cost. The advantages and disadvantages of these methods are discussed.
New implementations of error diffusion algorithms are proposed. These methods replace the complex, real time computations with a series of table lookups and a summation. They lower the computational cost and increase the processing speed. Implementation details are given in this paper. These implementations make the level-dependent error diffusion possible that an optimal error filter is used for a certain range of tone levels. Other advantages of these methods are also discussed.
Microcluster halftoning is a hybrid approach between clustered-dot and dispersed-dot ordered dithers. The concept and design principles of microcluster dots have been published elsewhere. This paper reports the frequency analyses of microcluster line screens. First, the Fourier transform for the frequency-domain analysis is briefly reviewed. Several line screens are proposed, ranging from 8 to 144 levels. At each level, three dot growth patterns of the conventional, interlace, and microcluster line screens are provided. Frequency analyses of these screens and the corresponding dispersed-dot are presented and compared. Results indicate that the line screens can be made into high frequency and high tone levels. Generally, they behave like a dispersed dot in the highlight region, a line screen in the midtone region, and an inverted dispersed dot in the shadow region.
This paper reviews the color image processing techniques used in the printing industry for the color space transformation. Generally, the techniques can be classified as the color mixing models, multiple regression, 3D lookup table (LUT) with interpolation, neural network, and fuzzy logic. The following techniques are briefly discussed. (1) Color mixing models such as the Neugebauer equations, Yule-Nielsen model, Clapper-Yule model, Beer-Bouguer law, and Kubelka-Munk theory. (2) Multiple regression. (3) 3D LUT with four geometric interpolations - trilinear, prism, pyramid, and tetrahedral. (4) Artificial neural networks of the multilayer feed-forward and cascade correlation nets. (5) Fuzzy logic. These techniques are compared, whenever possible, with respect to the accuracy, memory requirement, speed, and computational cost.
Several 3D interpolation techniques for the color space transformation are compared via software simulations. Comparisons are made among four geometric interpolations, trilinear, prism, pyramid, and tetrahedral, with respect to the look-up table (LUT) size and packing. Three different LUT sizes and two ways of packing, uniform and nonuniform, are applied to the forward and inverse transformations of the XeroxRGB and CIELAB. Each simulation is tested by a set of 3072 points that are sampled around the entire RGB color space. Results indicate: (1) Interpolation errors of various 3D geometric interpolations are about the same and the errors with respect to the true values decrease as the LUT size increases. (2) The interpolation error peaks at the center of the cell and diminishes at nodes (lattice points). (3) The highest error occurs at the darkest region. For equally spaced LUTs, the error drops quickly as the level increases. (4) Nonuniform LUTs have a much lower fundamental error peak but the errors are rippled to the higher levels; this gives a more even error distribution and a better average value. From this study, it is conceivable that the colorimetric reproduction can be achieved to a very high degree of precision. With proper packing, the 3D interpolation provides the capability to closely approximate the true values in all regions of the color space. From the considerations of the implementation cost and computation speed, the tetrahedral interpolation is particularly attractive.
The purpose of this study is to obtain some quantitative measures for the applicability of several color mixing models to a halftone printer. The printer, a Canon Color Laser Copier 500 (CLC-500), is treated as a black box and the measures are the difference between the calculated and measured spectra and ΔEab. Well-known color mixing theories of the Neugebauer equations, Yule-Nielsen model (YN), Clapper-Yule multiple internal reflections (CY), Beer-Bouguerlaw (BB), and Kubelka-Munk theories (KM) are applied to CLC-500 to see how well they can fit the experimental data. Results indicate that the spectral 8-color Neugebauer model has marginal success in fitting the experimental data and the relaxed 3-color version does not fit the data weli. Both YN and CY approaches can fit the data within printer variability. The fittings are rather poor for BB and KM. By using the halftone correction factor, good agreements are obtained for the BB and single-constant KM.
A new approach to the gray component replacement (GCR) has been developed. It employs the color mixing theory for modeling the spectral fit between the 3-color and 4-color prints. To achieve this goal, we first examine the accuracy of the models with respect to the experimental results by applying them to the prints made by a Canon Color Laser Copier-500 (CLC-500). An empirical halftone correction factor is used for improving the data fitting. Among the models tested, the halftone corrected Kubelka-Munk theory gives the closest fit, followed by the halftone corrected Beer-Bouguer law and the Yule-Neilsen approach. We then apply the halftone corrected BB law to GCR. The main feature of this GCR approach is based on the spectral measurements of the primary color step wedges and a software package implementing the color mixing model. The software determines the amount of the gray component to be removed, then adjusts each primary color until a good match of the peak wavelengths between the 3-color and 4-color spectra is obtained. Results indicate that the average (Delta) Eab between cmy and cmyk renditions of 64 color patches is 3.11 (Delta) Eab. Eighty-seven percent of the patches has (Delta) Eab less than 5 units. The advantage of this approach is its simplicity; there is no need for the black printer and under color addition. Because this approach is based on the spectral reproduction, it minimizes the metamerism.
This paper presents a methodological approach for integrating non-colorimetric scanners with CIE
standards as a means toward a device independent process. The calibration is aimed at reflected samples by
employing photographic, thermal transfer, and xerographic prints. Correlations between scanner responses to
CIE standards are established through a common test object using a two-step process of the gray balancing and
the matrix transformation.
A series of polynomials, ranging from a three-term linear combination to a twenty-term cubic equation, is
used for converting device values to a CIE color space. The ability to fit colors that are not in the training set by
a polynomial is examined. Results indicate that lower order polynomials fit colors equally well whether a color
is in the training set or not, but the accuracy of interpolation decreases as the number of terms in the
We study the generality of this calibration method with respect to input materials. The transformation is
material-dependent. Within the experimental uncertainty, however, there exists a unified transfer matrix for
photographic materials and another one for paper substrates.
Finally, we extended this method to deal with the mismatched illuminants for viewing and calibration.
An empirical white point conversion method is proposed and tested; good approximations to the measured
results are obtained when the interchange of illuminants occurs.
In the context of colorimetric matching, the intent of color scanner and printer calibrations is to characterize the devicedependent responses to the device-independent representations such as CIEXYZ or CIE 1976 L*a*b* (CIELAB). Usually, this is accomplished by a two-step process of gray balancing and a matrix transformation, using a transfer matrix obtained from multiple polynomial regression. Color calibrations, printer calibrations in particular,
are highly nonlinear. Thus, a new technique, the neural network with the Cascade Correlation learning architecture, is employed for representing the map of device values to CIE standards. Neural networks are known for their capabilities to learn highly nonlinear
relationships from presented examples. Excellent results are obtamed using this particular neural net; in most training sets, the average color differences are about one Eab. This approach is compared to the polynomial approximations ranging from a 3-term
linear fit to a 14-term cubic equation. The results from training sets indicate that the neural net outperforms the polynomial approximation. However, the comparison is not made in the same ground
and the generalizations, using the trained neural net to predict relationships it has not been trained with, are sometimes rather poor. Nevertheless, the neural network is a very promising tool for use in
color calibrations and other color technologies in general.