Reducing the pixel expansion and improving the display quality of recovered images are still major issues in visual cryptography schemes (VCSs), particularly for large  k  and  n . Moreover, the development of a systematic and practical approach for threshold VCSs is a challenge. In this paper, a pixel-expansion-free threshold VCSs approach based on an optimization technique is proposed in order to encrypt binary secret images. In addition to contrast, we consider blackness as a performance metric in the evaluation of the display quality of recovered images. We first formulate the problem as a mathematical optimization model in order to maximize the contrast of recovered images that are subject to density-balance and blackness constraints. We then develop a simulated-annealing-based algorithm to solve this problem. Furthermore, we try to promote the contrast by slightly relaxing the density-balance constraint. The experimental results show that the proposed optimization-based approach significantly outperforms previous methods in terms of both the pixel expansion factor and the display quality of recovered images.
['Pei-Ling Chiu', 'Kai-Hui Lee']
A Simulated Annealing Algorithm for General Threshold Visual Cryptography Schemes