Human visual system (HVS) modeling has become a
critical component in the design of digital halftoning algorithms.
Methods that exploit the characteristics of the HVS include the direct
binary search (DBS) and optimized tone-dependent halftoning approaches.
The spatial sensitivity of the HVS is low-pass in nature,
reflecting the physiological characteristics of the eye. Several HVS
models have been proposed in the literature, among them, the
broadly used Näsänen’s exponential model, which was later shown
to be constrained in shape. Richer models are needed to attain
better halftone attributes and to control the appearance of undesired
patterns. As an alternative, models based on the mixture of bivariate
Gaussian density functions have been proposed. The mathematical
characteristics of the HVS model thus play a key role in the synthesis
of model-based halftoning. In this work, alpha stable functions,
an elegant class of functions richer than mixed Gaussians, are exploited
to design HVS models to be used in two different contexts:
monochrome halftoning over rectangular and hexagonal sampling
grids. In the two scenarios, alpha stable models prove to be more
efficient than Gaussian mixtures, as they use less parameters to
characterize the tails and bandwidth of the model. It is shown that a
decrease in the model’s bandwidth leads to homogeneous halftone
patterns, and conversely, models with heavier tails yield smoother
textures. These characteristics, added to their simplicity, make alpha
stable models a powerful tool for HVS characterization.
Human visual system (HVS) modeling has become a critical component in the design of digital halftoning algorithms. Methods that exploit the characteristics of the HVS include the direct binary search (DBS) and optimized tone-dependent halftoning approaches. The spatial sensitivity of the HVS is lowpass in nature, reflecting the physiological characteristics of the eye. Several HVS models have been proposed in the literature, among them, the broadly used Nasanen's exponential model. As shown experimentally by Kim and Allebach,1 Nasanen's model is constrained in shape and richer models are needed in order to attain better halftone attributes and to
control the appearance of undesired patterns. As an alternative, they proposed a class of HVS models based on mixtures of bivariate Gaussian density functions. The mathematical characteristics of the HVS model thus play a key role in the synthesis of model-based halftoning. In this work, alpha stable functions, an elegant class of
models richer than mixed Gaussians, are exploited. These are more efficient than Gaussian mixtures as they use less parameters to characterize the tails and bandwidth of the model. It is shown that a decrease in the model's bandwidth leads to homogeneous halftone patterns and conversely, models with heavier tails yield smoother
textures. These characteristics, added to their simplicity, make alpha stable models a powerful tool for HVS characterization.
Halftoning approaches to image rendering on binary devices have traditionally relied on rectangular grids for dot placement. This practice has been followed mainly due to restrictions on printer hardware technology. However, recent advances on printing devices coupled with the availability of efficient interpolation and resampling algorithms are making the implementation of halftone prints over alternate dot placement tessellations feasible. This is of particular interest since blue noise dithering principles indicate that the visual artifacts at several tone densities, which appear in rectangular-grid halftones, can be overcome through the use of hexagonal tessellations. While the spectral analysis of blue noise dithering provides the desired spectral characteristics one must attain, it does not provide the dithering structures needed to achieve these. In this paper, these optimal dithering mechanisms are developed through modifications of the Direct Binary Search (DBS) algorithm extensively used for rectangular grids. Special attention is given to the effects of the new geometry on the Human Visual System
(HVS) models and on the efficient implementation of the hexagonal-grid DBS. This algorithm provides the best possible output at the expense of high computational complexity, and while the DBS algorithm is not practical in most applications, it provides a performance benchmark for other more practical algorithms. Finally, a tone-dependent, hexagonal-grid, error-diffusion algorithm is developed, where the DBS algorithm is used to optimize the underlying filter weights. The characteristics of the HVS are thus implicitly used in the optimization. Extensive simulations show that hexagonal grids do indeed reduce disturbing artifacts, providing smoother halftone textures over the entire gray-scale region. Results also show that tone-dependent error-diffusion can provide comparable results to that of the DBS algorithms but at a significantly lower computational complexity.
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