## 4 Experimental Results and Discussion
### Comparative Study
The scheme proposed in [23] has a higher embedding rate at the cost of lower imperceptibility, robustness and security. Even though the embedding rate of the proposed scheme is lower than [23], still, in comparison to the state-of-the-art schemes, the proposed scheme shows higher imperceptibility, robustness and security for different image modalities. Security comparison: Schemes proposed in [27; 31] have paid less attention to watermark security, whereas schemes in [18; 32] use Arnold maps for watermark security, which can be easily cracked and thus provide low security. Generating a chaotic map scheme [23] ensures security but suffers from hyper tuning issues. Using two-level adaptive embedding and symmetric cryptographic approaches security is achieved in the proposed scheme. First, the watermark is partitioned into two parts and then encrypted using a pseudo random key. By the use of mathematical theory and the algorithm, the proposed scheme generates a Pseudo random key. It is difficult to predict the Pseudo random key generated by the proposed scheme by an attacker. Secondly, encrypted watermark is embedded at a random position selected by using BBS in low entropy blocks. This further makes the fort strong and non-invadable. When compared to other schemes in [18; 23; 32], the proposed scheme has a highly secured encryption approach. From the above discussion, it can be claimed that the proposed scheme provides higher watermark security than all other comparative schemes [18; 23; 31; 32]. Fitness function: Designing a proper fitness function for NIO algorithms is very important. To demonstrate the effectiveness of the proposed fitness function, imperceptibility and robustness performance comparison are done with the scheme proposed in [28] where scaling factor \((\alpha)\) is optimized by using ABC [18]. Minimized fitness function derived from watermarking characteristics (PSNR, SSIM, NC, and BER) is used in [28] as shown in Equation (17):  
Figure 15:0  
where scaling factor\((\alpha)\) is an initial random value, whereas, in the proposed scheme, maximized fitness function is used as shown in the following equation:  
Figure 15:1  
where scaling factor \((\alpha)\) is the initial seed value generated adaptively from the image. Since \((\alpha)\) is image dependent, the maximized fitness function is used. The maximum fitness value is used to achieve high watermarking characteristics. Imperceptibility performance of the proposed scheme is compared with the scheme in [28] by optimizing scaling factor \((\alpha)\) using ABC and GA in Figure 15:2 Here, it can be observed that, for all images, the proposed scheme has higher PSNR and SSIM than the scheme in [28] for ABC and GA. For all color images, remarkable improvement can be observed by the proposed scheme over [28] with ABC as well as GA from Figure 15:3 Hence, it can be claimed that the proposed scheme has higher imperceptibility as compared to [28]. Robustness of the proposed scheme and the scheme in [28] with optimized scaling factor using ABC and GA is also compared and presented in Table 12 in terms of NC and BER under zero attack. From Table 12, it can be studied that, for grayscale images, the performance of both schemes are at par for ABC and GA. However, for the color images, the proposed scheme has a higher NC value and lower BER value than [28], indicating that  
Using NIO algorithms for ISF optimization further improves performance of watermarking characteristics. The proposed scheme is also free from FPE due to Pseudo random key and two-level adaptive embedding. The simulation results show that the proposed scheme provides higher watermarking characteristics and is able to sustain the majority of image processing attacks. Furthermore, comparative study with state-of-the-art schemes exhibits that the proposed scheme shows higher imperceptibility, robustness, security and embedding rate than state-of-the-art schemes. The fitness function proposed in the scheme is also more fitting.