## 7 Robustness
### BOSSBase Dataset: Cropping, Scaling, and Rotation  
Similar to [PERSON] et al. (2016), the proposed approach omits the use of error correction codes. In contrast to methods such as [PERSON] et al. (2016), robust performance is achieved  
Figure 5: Disk Image JPEG-106 \(\times\) 160 pixel robustness results. The plots display watermark performance metrics after JPEG-70 compression and 0.9 resize factor attacks. Left: DCT and DWT accuracy across different sample images. Center: NC (Normalised Correlation) values showing watermark similarity. Right: BER (Bit Error Rate) measurements demonstrating error resilience. Higher NC and lower BER values indicate better watermark recovery after attacks.  
without scaling images to a fixed resolution during testing. As previously outlined, a 64-bit watermark was embedded in all images in the dataset, regardless of size. For this evaluation, testing was conducted on 256 \(\times\) 256 and 512 \(\times\) 512 greyscale images sourced from the BOSSBase dataset.  
[PERSON] et al. [23] employed different watermark lengths: 32 bits for both their proposed method and that of [PERSON] et al. [82], 64-bits for [PERSON] et al. [83] and [PERSON] et al. [84], and 128 bits for [PERSON] et al. [23]. The use of a 64-bit watermark in this study enables a direct comparison with previous work and offers twice the capacity of the 32-bit approaches.  
This study shows strong robustness against geometric attacks, such as rotation and scaling. In rotation, we achieve perfect watermark recovery (Bit Error Quality, BEQ = 0) for 1\({}^{\circ}\), 5\({}^{\circ}\), and 90\({}^{\circ}\) on the datasets. For scaling, this study achieved perfect recovery (BEQ = 0) from scale factors of 0.6 to 1.5, with minimal BEQ values (0.0359 for 256 \(\times\) 256 and 0.0484 for 512 \(\times\) 512) at 0.5.  
This study demonstrates resilience even under a heavy cropping test. It maintains consistent results, with BEQ values between 0.2438 and 0.4063 for 256 \(\times\) 256 images and 0.3843 to 0.4844 for 512 \(\times\) 512 images. The method performs better on smaller images (256 \(\times\) 256) and shows consistent robustness without error-correcting codes or scaling adjustments.  
Although some methods, such as [PERSON] et al.'s [23], perform better due to fixed resolution scaling, the method preserves the original resolution. This approach offers a more realistic evaluation, particularly in evidence management, where scaling is not feasible. This study aligns with the goals of practicality and adaptability emphasised by [PERSON] et al. [23] and is more adaptable to real-world attack conditions.  
To quantify the specific benefits of our dual-domain approach, we performed a comparative analysis against single-domain implementations. Table 8 presents performance metrics across identical datasets, clearly demonstrating the superiority of the combined DCT+DWT method over either transform used individually.  
The results show that while DWT alone provides better rotation resilience (BER = 0.012 at 90\({}^{\circ}\) rotation) than DCT alone (BER = 0.118), the combined approach achieves perfect watermark recovery (BER = 0) under both compression and geometric attacks while simultaneously doubling the payload capacity to 128 bits. Additionally, the dual domain technique improves image quality by approximately 1 dB compared to either single-domain method.