Most visual secret sharing (VSS) schemes need to encrypt a pixel of the secret image into m subpixels on the share; obviously, the shares are enlarged and so are the stacked images. A handful of studies try to solve the problem of pixel expansion, but little information is available on improving the visual effect of the stacked image. In addition, most of them do not mention how to deal with grey-level images. Since the secret is decoded by the human eye, the visual effect of the stacked image is an important issue in the study of the VSS scheme. This paper proposes two visual cryptographic methods to solve the problem of pixel expansion and to improve the visual effect of the stacked image at the same time. Unlike in previous studies, multiple pixels are simultaneously encoded each time. With the help of halftoning, the methods can be applied to encoding grey-level images. The experimental results show that these methods have a better visual effect on the stacked image compared with other researchers' methods. The methods are based on two basis matrices and hence can satisfy the security and contrast conditions required by the VSS scheme.
