A computational model of watermark algorithmic robustness capable of resisting image cropping for remote sensing images

Various watermarking algorithms have been studied to better enable the copyright protection of remote sensing images. The robustness of such algorithms against image cropping attacks has subsequently been verified mainly by various experiments. However, to date, the experimental results are subject to the differences in experimental factors and computational resource costs. Hence, the study presented in this paper proposes a robustness computation model of watermarking remote sensing images in terms of the image cropping attack. The robustness computation model consists of three parts: analysis principles, an evaluation index, and a computation method. The robustness analysis principles are provided based on the salient features of watermarking remote sensing images and attacking properties. A probability-based evaluation index is then defined to more comprehensively measure the robustness of different algorithms. The computation method developed in this study is based on permutations and the inclusion-exclusion principle to theoretically calculate robustness. The experiments conducted to verify the effectiveness of the computation model, revealed true closeness between both the calculated and experimental results. Finally, the relationships between the robustness and the different parameters used in the watermarking algorithms are investigated by using the proposed computation model.