Visual cryptography scheme (VCS) is a secure method that encrypts a secret image by breaking it into shadow images. Due to the nature of encryption there are two types of VCS: one is the deterministic VCS (DVCS), and the other is the probabilistic VCS (PVCS). For the DVCS, we use m (known as the pixel expansion) subpixels to represent a secret pixel. The PVCS uses only one subpixel to represent a secret pixel, while the quality of reconstructed image is degraded. It is evident that one can combine both VCSs simultaneously over shadow images to develop their specialities: the DVCS retains the resolution and the PVCS considerably reduces the shadow size. This article has two main contributions: (1) the authors prove that this two-in-one VCS still satisfies the contrast and security conditions of VCS; (2) the authors show how to arrange subpixels with two different pixel expansions to retain the visual quality of reconstructed image.
Ching-Nung Yang, An-Guo Peng, Tse-Shih Chen, "Secret Image Sharing: DPVCS A Two-in-One Combination of (D)eterministic and (P)robabilistic (V)isual (C)ryptography (S)chemes" in Journal of Imaging Science and Technology, 2008, pp 60508-1 - 60508-12, https://doi.org/10.2352/J.ImagingSci.Technol.(2008)52:6(060508)