For effective watermarking, the majority of watermarking schemes have been developed to meet two basic requirements: robustness and transparency, which conflict with each other from a signal processing perspective. In this paper, we propose an image-adaptive watermarking algorithm for digital images, based on the warped discrete cosine transform (WDCT) and visual models. The WDCT has been developed in the context of image compression, however, the WDCT is utilized for an image-adaptive digital watermarking scheme to enhance transparency and robustness, while preserving the visual quality of the images. Also the visual models are adapted to determine image dependent upper bounds on an embedded watermark. Through intensive computer simulations, it is shown that the proposed scheme yields more effective and better performance, both in terms of transparency and robustness, than the conventional algorithms.