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Quantisation index modulation (QIM) is an important class of watermarking methods, which has been widely used in blind watermarking applications. It is well known that spread transform dither modulation (STDM), as an extension of QIM, has good performance in robustness against random noise and re-quantisation. However, the quantisation step-sizes used in STDM are random numbers not taking features of the image into account. The authors present a step projection-based approach to incorporate the perceptual model with STDM framework. Four implementations of the proposed algorithm are further presented according to different modified versions of the perceptual model. Experimental results indicate that the step projection-based approach can incorporate the perceptual model with STDM framework in a better way, thereby providing a significant improvement in image fidelity. Compared with the former proposed modified schemes of STDM, the author's best performed implementation provides powerful resistance against common attacks, especially in robustness against Gauss noise, salt and pepper noise and JPEG compression.