## 4 Results
### Comparison with Other Methods  
In this subsection, the proposed method is compared with the selected state-of-the-art (SOTA) methods mentioned earlier in the literature review. In order to make the comparison, the obtained MSE results were converted into the PSNR coefficient according to the following formula [47]:  
\[\text{PSNR}=10\log_{10}\!\left(\frac{\left(2^{M}-1\right)^{2}}{\text{MSE}}\right) \tag{20}\]  
where PSNR stands for peak signal-to-noise ratio given in dB, \(M\) is the number of bits needed to define the range of values that a pixel can take, and MSE is an abbreviation for the mean square error. It should be noted that the MSE given in the previous tables was calculated for the floating-point values at the encoder input and output because neural networks usually take values in the range \(\left\langle 0;\ 1\right\rangle\) due to the normalization process. In the comparison with other methods, these values will be compared with MSE values in the range \(\left\langle 0;\ 255\right\rangle\). Figure 11: The absolute accuracy of the hidden message (number of correctly recovered characters). Figure 9: Mean squared error of the watermarked image relative to the original image. To ensure the comparability of the methods in the experiment, the selected compression value for HEVC is 16. The results of the method comparison are presented in Table 12.  
Each method uses a different way to embed a watermark. The first method [15] presents an intra-drift-free watermarking algorithm, which uses a multi-coefficient modification method. This method embeds the watermark into intra prediction residual pixels of 4 \(\times\) 4 luminance transform blocks in the spatial domain. In the second method [16], initially, a spatial texture analysis is performed based on the number of non-zero transform coefficients of embedding blocks. Then, suitable candidate blocks for watermark embedding are selected. In the next step, the grouping of intra prediction modes is performed. Each group is represented by two bits of watermark sequence. The embedding process is performed by altering the prediction modes of selected 4 \(\times\) 4 intra prediction blocks to the representative mode of the group denoted by the watermark bit pair. The third method [43] uses the BCH syndrome code technique. In this method, groups of the prediction directions are provided to limit the intra-frame distortion drift. The encoded data are embedded into the multi-coefficients of the selected 4 \(\times\) 4 luminance discrete sine transform blocks as required by pre-defined groups. A detailed description of the proposed method of high-capacity and transparent watermarking based on the usage of DNNs with the adjustable subsquares properties algorithm is presented in Section 3. The average PSNR for the proposed method and the compared methods is greater than 40 dB, which provides an acceptable visual experience. The time needed to compute the proposed method is much greater compared to that required by the other methods; this is due to the fact that the ANN structure is not optimized for real-time processing. The currently proposed ANN structure is a research structure and is only applicable for offline watermark embedding. The embedding time for the proposed method also includes the time taken to remove the edge effect described in Section 3.4, which doubles the watermarking time. An additional factor that increased the computation time was the need to encode 8 areas of 128 \(\times\) 128 in order to embed a watermark on the entire image with a size of 416 \(\times\) 240. It is worth noting that watermark repeats were embedded, while other watermark combinations could be embedded by creating sequences of watermarks to compose one larger watermark. In order to accelerate the computation, the structures of the ANNs proposed in this paper should be reduced. The compared methods [15; 16; 43] have a watermark capacity of 100 bits on the test sets, with the smallest image size being 416 \(\times\) 240.