Robust Watermarking with Kernels-Alternated Error Diffusion and Weighted Lookup Table in Halftone Images

A halftone watermarking method of high quality, robustness, and capacity flexibility is presented in this paper. An objective halftone image quality evaluation method based on the human visual system obtained by a least-mean-square algorithm is also introduced. In the encoder, the kernels-alternated error diffusion （KAEDF） is applied. It is able to maintain the computational complexity at the same level as ordinary error diffusion. Compared with Hel-Or using ordered dithering, the proposed KAEDF yields a better image quality through using error diffusion. We also propose a weighted lookup table （WLUT） in the decoder instead of lookup table （LUT）, as proposed by Pei and Guo, so as to achieve a higher decoded rate. As the experimental results demonstrate, this technique is able to guard against degradation due to tampering, cropping, rotation, and print-and-scan processes in error-diffused halftone images.

Optimization of a Segmented Filter with a New Error Diffusion Approach

The segmented filters, based on spectral cutting, proved their efficiency for the multi-correlation. In this article we propose an optimisation of this cutting according to a new error diffusion method.

Gas diffusion in a cylindrical coal sample – A general solution,approximation and error analyses

The analytical mathematical solutions of gas concentration and fractional gas loss for the diffusion of gas in a cylindrical coal sample were given with detailed mathematical derivations by assuming that the diffusion of gas through the coal matrix is concentration gradient-driven and obeys the Fick’s Second Law of Diffusion.The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken.The results indicate that the square root relationship of gas release in the early stage of desorption,which is widely used to provide a simple and fast estimation of the lost gas,is the first term of the approximation,and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a cylindrical coal sample.

A POSTERIORI ENERGY-NORM ERROR ESTIMATES FOR ADVECTION-DIFFUSION EQUATIONS APPROXIMATED BY WEIGHTED INTERIOR PENALTY METHODS

We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion. The weights, which play a key role in the analysis, depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method. The error upper bounds, in which all the constants are specified, consist of three terms： a residual estimator which depends only on the elementwise fluctuation of the discrete solution residual, a diffusive flux estimator where the weights used in the method enter explicitly, and a non-conforming estimator which is nonzero because of the use of discontinuous finite element spaces. The three estimators can be bounded locally by the approximation error. A particular attention is given to the dependency on problem parameters of the constants in the local lower error bounds. For moderate advection, it is shown that full robustness with respect to diffusion heterogeneities is achieved owing to the specific design of the weights in the discontinuous Galerkin method, while diffusion anisotropies remain purely local and impact the constants through the square root of the condition number of the diffusion tensor. For dominant advection, it is shown, in the spirit of previous work by Verfiirth on continuous finite elements, that the local lower error bounds can be written with constants involving a cut-off for the ratio of local mesh size to the reciprocal of the square root of the lowest local eignevalue of the diffusion tensor.

An improved parallel contrast-aware halftoning

Digital image halftoning is a widely used technique. However, achieving high fidelity tone reproduction and structural preservation with low computational time cost remains a challenging problem. This paper presents a highly parallel algorithm to boost real-time application of serial structure-preserving error diffusion. The contrast-aware halftoning approach is one such technique with superior structure preservation, but it offers only a limited opportunity for graphics processing unit(GPU) acceleration. Our method integrates contrast-aware halftoning into a new parallelizable error-diffusion halftoning framework. To eliminate visually disturbing artifacts resulting from parallelization, we propose a novel multiple quantization model and space-filling curve to maintain tone consistency, blue-noise property, and structure consistency. Our GPU implementation on a commodity personal computer achieves a real-time performance for a moderately sized image. We demonstrate the high quality and performance of the proposed approach with a variety of examples, and provide comparisons with state-of-the-art methods.