Simple formulation of structural similarity for halftoning and its application to Visual secret sharing

The secret sharing (SS) scheme is a cryptosystem which encrypts a secret into multiple pieces, called shares, so that only qualified combination of shares can be employed to recover the secret. The visual secret sharing (VSS) scheme is an example of SS schemes whose decryption can be performed by a human without any numerical computations. This paper is an attempt to modify the structural similarity (SSIM) index so that the modified one can measure both the structural and tonal similarities simultaneously and then to employ the modified index to give an optimization-based halftoning suitable for the encryption of VSS schemes.