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Digital watermarking is an efficient and promising approach to protect intellectual property rights of digital media. Spread spectrum (SS) is one of the most widely used image watermarking schemes because of its robustness against attacks and its support for the exploitation of the properties of the human visual system (HVS). To maximize the watermark strength without introducing visual artifacts, in SS watermarking, the watermark signal is usually modulated by the just-noticeable difference (JND) of the host image. In advanced perceptual models, the JND is characterized as a nonlinear function of local image features. The optimum detection scheme for such nonlinearly embedded watermarks, however, has rarely been studied. In this paper, we address this problem and propose a novel approach that transforms the test signal to a perceptually uniform domain and then performs Bayesian hypothesis testing in that domain. Locally optimum detectors for arbitrary host signal distributions and arbitrary JND models that exploit the self-masking property of the HVS are derived in closed forms, in which the test signal is first nonlinearly preprocessed before a linear correlator is applied. The optimality of the proposed detector is justified mathematically according to the Neyman-Pearson criterion. Simulation results demonstrate the superior performances of the proposed detector over the conventional linear correlation detector.