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Visual secret sharing (VSS) is a way to protect a secret image among a group of participants by using the notions of perfect ciphers and secret sharing. However, each share generated by conventional VSS is m times as big as the original secret image, where m is called pixel expansion. Random grid (RG) is an alternative approach to implement VSS without pixel expansion. However, reported RG-based VSS methods are threshold schemes. In this study, RG-based VSS for general access structures is presented. Secret image is encoded into n RGs while qualified sets can recover the secret visually and forbidden sets cannot. The proposed scheme is a generalisation of the threshold methods, where those reported RG-based schemes can be considered as the special cases of the proposed scheme. Experimental results are provided, demonstrating the effectiveness and advantages of the proposed scheme.