This paper proposes a novel adaptive circular watermarking framework based on the human visual system that resolves this fundamental trade-off through methodological synthesis. We integrate a pre-trained backpropagation neural network, used to calculate the localized just noticeable difference in the discrete cosine transform domain, with a geometric circular constraint embedding strategy. Our core contribution is the dynamic modulation of the circular detection radius; instead of using a fixed parameter, we set the circular detection radius as a function of the backpropagation neural network output just noticeable difference. This dynamic approach ensures that the constraint region expands where the block can perceptually mask stronger changes (textured areas), maximizing robustness, and contracts where the image is visually sensitive (smooth areas), maximizing imperceptibility. Experimental results rigorously demonstrate the superiority of the adaptive circular watermarking framework. Against both a pure artificial neural network additive baseline and a static-constraint baseline, the proposed adaptive circular watermarking method achieved significantly higher peak signal-to-noise ratio in smooth image regions proving better imperceptibility while simultaneously achieving similarity of extracted watermark values, particularly against aggressive JPEG compression, proving enhanced robustness. The adaptive circular watermarking scheme sets a new benchmark for creating structurally resilient and visually intelligent watermarks.
Taheri, A. and Golzade Gervi, E. (2025). Adaptive circular watermarking based on modulating discrete cosine transform region constraints via neural network human visual system modeling. Journal of Statistical Modelling: Theory and Applications, 6(2), 89-100. doi: 10.22034/jsmta.2026.24215.1209
MLA
Taheri, A. , and Golzade Gervi, E. . "Adaptive circular watermarking based on modulating discrete cosine transform region constraints via neural network human visual system modeling", Journal of Statistical Modelling: Theory and Applications, 6, 2, 2025, 89-100. doi: 10.22034/jsmta.2026.24215.1209
HARVARD
Taheri, A., Golzade Gervi, E. (2025). 'Adaptive circular watermarking based on modulating discrete cosine transform region constraints via neural network human visual system modeling', Journal of Statistical Modelling: Theory and Applications, 6(2), pp. 89-100. doi: 10.22034/jsmta.2026.24215.1209
CHICAGO
A. Taheri and E. Golzade Gervi, "Adaptive circular watermarking based on modulating discrete cosine transform region constraints via neural network human visual system modeling," Journal of Statistical Modelling: Theory and Applications, 6 2 (2025): 89-100, doi: 10.22034/jsmta.2026.24215.1209
VANCOUVER
Taheri, A., Golzade Gervi, E. Adaptive circular watermarking based on modulating discrete cosine transform region constraints via neural network human visual system modeling. Journal of Statistical Modelling: Theory and Applications, 2025; 6(2): 89-100. doi: 10.22034/jsmta.2026.24215.1209
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