Digital image watermarking has become a popular technique for authentication and copyright protection. For verifying the security and robustness of watermarking algorithms, specific attacks have to be applied to test the proposed algorithms. In contrast to the known Stirmark attack, which degrades the quality of the image while destroying the watermark, this paper presents a new approach which is based on the estimation of a watermark and the exploitation of the properties of Human Visual System (HVS). The new attack satisfies two important requirements. First, image quality after the attack as perceived by the HVS is not worse than the quality of the stego image. Secondly, the attack uses all available prior information about the watermark and cover image statistics to perform the best watermark removal or damage. The proposed attack is based on a stochastic formulation of the watermark removal problem considering the embedded watermark as additive noise with some probability distribution. The attack scheme consists of two main stages: watermark estimation based a Maximum a Posteriori (MAP) approach and watermark alteration through addition of the noise to the filtered image taking into account the statistics of the embedded watermark and exploiting HVS characteristics. Experiments on a number of real world and computer generated images show the high efficiency of the proposed attack against several known academic and commercial methods: the watermark is completely destroyed in all tested images without altering the image quality. The approach can be used against watermark embedding schemes that operate either in coordinate domain, or transform domains like Fourier, DCT or wavelet.