To address the issue of information loss in recovering multiple secret images for threshold structure, this paper develops a definition of threshold multi-secret visual cryptography with perfect recovery, which can adapt to various corresponding relationship between the threshold value and the secret number. Based on the given definition, a single-threshold multi-secret visual cryptography scheme with upper and lower thresholds is constructed, and a multiple-threshold scheme is then proposed by designing the rotation rule fusion algorithm and the region merging algorithm. Furthermore, the effectiveness is proved theoretically and verified by experiments.