Optimal Contrast Grayscale Visual Cryptography Schemes With Reversing

The visual cryptography scheme (VCS) is an encryption technique that utilizes the human visual system in recovering a secret image and it does not require any complex calculation. However, the contrast of the reconstructed image could be quite low. A number of reversing-based VCSs (or VCSs with reversing) (RVCS) have been proposed for binary secret images, allowing participants to perform a reversing operation on shares (or shadows). This reversing operation can be easily implemented by current copy machines. Some existing traditional VCS schemes without reversing (nRVCS) can be extended to RVCS with the same pixel expansion for binary image, and the RVCS can achieve ideal contrast, significantly higher than that of the corresponding nRVCS. In the application of grayscale VCS, the contrast is much lower than that of the binary cases. Therefore, it is more desirable to improve the contrast in the grayscale image reconstruction. However, when grayscale images are involved, one cannot take advantage of this reversing operation so easily. Many existing grayscale nRVCS cannot be directly extended to RVCS. In this paper, we first give a new grayscale nRVCS with minimum pixel expansion and propose an optimal-contrast grayscale RVCS (GRVCS) by using basis matrices of perfect black nRVCS. Also, we propose an optimal GRVCS even though the basis matrices are not perfectly black. Finally, we design an optimal-contrast GRVCS with a minimum number of shares held by each participant. The proposed schemes can satisfy different user requirements; previous RVCSs for binary images can be viewed as special cases in the schemes proposed here.