In this paper, an optimal estimation of the embedding strength for the digital image water-mark is discussed. Under the assumptions that the original image data are an i. i. d. random sequence from a Guassian distribution, it's shown that this embedding strength should be estimated by observing the averages of the watermarked image and briefly calculating between them. The approach is based on maximum-likelihood estimation of the watermark embedding strength. The experimental results show that this method is effective for watermark extraction. Moreover, according to the addition, multiplicatio...