Visual cryptography schemes with perfect reconstruction of black pixels

Conventional visual cryptography (VC) suffers from a pixel-expansion problem, or an uncontrollable display quality problem for recovered images, and lacks a general approach to construct visual secret sharing schemes (VSSs) for general access structures (GASs). We propose here in a general and systematic approach to address these issues without sophisticated codebook design. The approach can be used for binary secret images in non-computer-aided decryption environments. To avoid pixel expansion, we design a set of column vectors to encrypt secret pixels rather than use the conventional VC-based approach. We begin by formulating a mathematic model for the VC construction problem to find the column vectors for the optimal VC construction, after which we develop a simulatedannealing-based algorithm to solve the problem. It indicates that the display quality of the recovered image is superior to that of previous studies.