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Quantization-based watermarking techniques are sensitive to valumetric scaling, a wide class of distortions applied to images and videos, such as contrast change or gamma correction. Several methods have been proposed to counteract valumetric attacks, but the common approach to the problem is to take only the linear ones into account. This paper presents an extension to the rational dither modulation (RDM) data-hiding scheme which provides robustness against nonlinear distortions modelled by a power-law attack. The algorithm makes use of proper mapping of the pixel values from the Cartesian to hyperbolic coordinates. This mapping is able to render the problem similar to the classical RDM scheme, since fixed multiplicative scaling is cancelled out while the exponentiation of a nonlinear distortion is transformed into a gain scaling. The validity of the approach has been confirmed by applying the watermarking scheme to Gaussian host and real images; experimental results confirm its intrinsic invariance against the power-law attack. Finally, it will be shown that under the white Gaussian noise addition, the proposed scheme achieves a good bit-error rate (BER). The measured BER is affected by the properties of the embedding domain, as supported by the theoretical analysis given in this paper.