Image Watermarking in Frequency Domain using Hu's Invariant Moments and Firefly Algorithm

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Sachin Sharma 1,* Shikha Choudhary 2 Vijay Kumar Sharma 3 Ankur Goyal 4 Meena Malik Balihar 5

1. Department of Computer Science and Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, AP, India

2. Department of Computer Engineering, Rajasthan College of Engineering for Women, Jaipur, Rajasthan, India

3. School of Computing and Information Technology, Manipal University Jaipur, Rajasthan, India

4. Department of Computer Engineering, AIT, Chandigarh University, Mohali, Punjab, India

5. Department of Computer Engineering, Sagar Institute of Science and Technology, Bhopal, Madhya Pradesh, India

* Corresponding author.


Received: 13 Dec. 2021 / Revised: 16 Jan. 2022 / Accepted: 6 Feb. 2022 / Published: 8 Apr. 2022

Index Terms

Discrete Wavelet Transform, Singular Value Decomposition, Heisenberg Decomposition, Firefly Algorithm, Hu’s Invariant Moments


Preventing the digital content from being copied, manipulated and illegal ownership claims is one of the biggest challenges that appeared with the widespread usage of computing facilities. Watermarking is one way to tag a digital document with a watermark, perceptible or imperceptible, so as to later prove the ownership or authenticity of the document, in case the need arises. Robust and Fragile watermarking is used in case of proving ownership and authenticity, respectively. This paper proposes a watermarking approach based on Discrete Wavelet Transform (DWT), Hessenberg Decomposition (HD) and Singular Value Decomposition (SVD) approach, augmented with Firefly Algorithm (FA). To make the approach blind, the proposed technique uses Hu’s invariant moments which are invariant against rotation, scaling and translation (RST) attack over the image. In the resulting watermarked image, the watermark is imperceptible, which make it suitable for a large class of watermarking applications. In the proposed approach, a given colour image is subjected to 2 Level DWT for decomposing into sub-bands, namely LL, LH, HL and HH bands. These coefficients of HH band are fed as input for HD. The output is operated for SVD for obtain U, S and V matrices. The Hu’s invariant moments are scaled and mapped to binary string using logarithm scaling. The binary matrix, corresponding to binary watermark, is XoRed with the invariant moments, in a repeated manner, to obtain a new binary matrix, of the same dimension as count of 2X2 partitions of S. The watermark is embedded by changing the orthogonal V matrices. The magnitude of the change is computed with Firefly algorithm considering the robustness and imperceptibility as the trade-off parameters. The firefly algorithm is one of the nature inspired optimization algorithm. The proposed watermarking approach is capable of withstanding JPEG compression attack, filtering attacks and noise. PSNR and SSIM are used as the quality metric for accessing the watermarked image quality. It turns out that the proposed watermarking technique gives a considerable improvement over robustness and imperceptibility as compared to the benchmark approaches. The performance of the proposed approach as compared to the benchmark approach, increases in linear manner with the dimension of the image under consideration, reaching from 1 percent to 4 percent for image dimensions ranging from 400X400 to 1200X1200 pixels.

Cite This Paper

Sachin Sharma, Shikha Choudhary, Vijay Kumar Sharma, Ankur Goyal, Meena Malik Balihar, "Image Watermarking in Frequency Domain using Hu's Invariant Moments and Firefly Algorithm", International Journal of Image, Graphics and Signal Processing(IJIGSP), Vol.14, No.2, pp. 1-15, 2022. DOI: 10.5815/ijigsp.2022.02.01


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