A digital watermarking scheme permits embedding additional information into digital contents as a watermark so that the embedded information can be detected afterward. 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 detection scheme for additive watermarks embedded in the spatial domain. The key idea of the proposed detection scheme is to use the difference between the brightness values. It is confirmed experimentally that the proposed scheme can control the FPE probability strictly.