Droste [CRYPTO’96] proposed a construction of threshold visual cryptography scheme (TVCS) under the visual cryptography model of Naor and Shamir, i.e. the visual cryptography model with the underlying operation OR. In this article, we give three extensions of TVCS. First, we prove that the TVCS proposed by Droste which was based on the OR operation is still a valid TVCS under the XOR operation, and then we propose a method to further reduce its pixel expansion. We then propose an interesting construction of TVCS with all shares being concolorous. Finally, we give a construction of threshold extended visual cryptography scheme (TEVCS) with the underlying operation OR or XOR. All of our schemes can be applied to the visual cryptography model introduced by Tuyls et al. (First Int. Conf. Security in Pervasive Computing 2004, International Patent with Application No.: PCT/IB2003/000261).