$k$ Out of $n$ Region-Based Progressive Visual Cryptography

Recently, multiple (k, n) region-incrementing VCSs (RIVCSs) have been proposed that can gradually reconstruct secrets in a single image. In (k, n)-RIVCS, the secret image is subdivided into multiple regions in such a way that any t shadow images, where k ≤ t ≤ n, can be used to reveal the secret in the (t - k + 1)th region. This region-incrementing property provides progressive decoding. However, the regions in previous RIVCSs are disjointed: no two regions have overlapping areas. In this paper, we discuss a (k, n) region-in-region progressive VCS (RPVCS). Our (k, n)-RPVCS has (n - k + 1) secrecy-level regions, and each region can be located within any previous region. This new type of region allocation not only provides more areas in which to hide the secret compared with the non-overlapping regions in RIVCS but also provides different presentation methods in progressive decoding.