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A Simulated Annealing Algorithm for General Threshold Visual Cryptography Schemes

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2 Author(s)
Pei-Ling Chiu ; Dept. of Risk Manage. & Insurance, Ming Chuan Univ., Taipei, Taiwan ; Kai-Hui Lee

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.

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Information Forensics and Security, IEEE Transactions on  (Volume:6 ,  Issue: 3 )