Fractional Krawtchouk Transform is a generalization of the Krawtchouk transforms which has two fractional orders. By adjusting these fractional orders in the weighted two dimensional Krawtchouk polynomials, local image features can be located. This paper proposes a robust image watermarking method using FrKT with firefly and cuckoo search optimization algorithms. The frequency domain image is obtained by applying FrKT for the input image blocks. The optimal fractional parameters of the transform improve the imperceptibility of the secret data in the host images. The fractional parameter selection for the image transformation is performed by Firefly optimization algorithm. Also, the optimal location in each block to hide the secret data is identified by the cuckoo search algorithm. The histogram shifting technique is used to embed the secret data in the optimal locations due to its less computational complexity. The parameters like Peak Signal to Noise Ratio, Normalized Correlation Coefficient, Structural SIMilarity index, Bit Error Rate are used for comparison of the proposed method using the optimization algorithms. The experimental results of the proposed method FrKT with combination of both Firefly and cuckoo search optimization shows better quality of the watermark, robustness and imperceptibility against various attacks. It can be concluded that the proposed FrKT + CS + FA provides an average of 0.92 for most of the attacks that prove the robustness of the proposed scheme.
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Ramasamy, R., Arumugam, V. RETRACTED ARTICLE: Robust image watermarking using fractional Krawtchouk transform with optimization. J Ambient Intell Human Comput 12, 7121–7132 (2021). https://doi.org/10.1007/s12652-020-02379-z