Abstract
A typical watermarking scheme consists of an embedding scheme and a detection scheme. In detecting a watermark, there are two kinds of detection errors, a false positive error (FPE) and a false negative error (FNE). A detection scheme is said to be optimum if the FNE probability is minimized for a given FPE probability. In this paper, we present an optimum watermark detection scheme for an additive embedding scheme with a spatial domain. The key idea of the proposed scheme is to use the differences between two brightnesses for detecting a watermark. We prove that under the same FPE probability the FNE probability of the proposed optimum detection scheme is no more than that of the previous optimum detection scheme for the additive embedding scheme with the spatial domain. Then, it is confirmed that for an actual image, the FNE probability of the proposed optimum detection scheme is much lower than that of the previous optimum detection scheme. Moreover, it is confirmed experimentally that the proposed optimum detection scheme can control the FPE probability strictly so that the FPE probability is close to a given probability.
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