## 3 Proposed Technique
### Watermark Extraction Process  
The following section outlines the methodology employed for the extraction of watermarks. The process of extracting the watermark is illustrated in Figure 4. The technique for incorporating the watermark is described in detail in Algorithm 3 which takes the colour medical image \((H^{\prime})\) as an input and returns the extracted watermark. In the first stage, the watermarked image's colour channels are separated into red, green, and blue. In the second stage, the extracted green channel of the watermarked image is transformed using the LWT transform to acquire low-frequency sub-bands \((LL)\). In the third stage, the low-frequency sub-band is divided into \(3\times 3\) blocks. Each of these blocks is chosen in a zigzag pattern. In the fourth stage, Hessenberg decomposition is used to acquire the \(Q\) matrix containing the watermark bits. In the sixth phase, the watermark bits are extracted. In the sixth stage, the extracted watermark is obtained by scrambling the watermark bits. ```
1 Algorithm3.WatermarkExtractionProcess
2 Input:WatermarkedColourMedicalImage(\(H^{\prime}\))
3 Output:ExtractedWatermark
4 BEGIN:
5\(\left[H^{\prime}_{i}H^{\prime}_{g}H^{\prime}_{h}\right]=\left[red(H^{\prime}), green(H^{\prime}), blue(H^{\prime})\right]\)
6\(\left[LL^{\prime},LH^{\prime},HL^{\prime},HH^{\prime}\right]=\left[lat(H^{ \prime}_{g})\right]\)
7\(b^{\prime}_{i}=getBlock(LL^{\prime},blockNumber)\)
8\(\left[Q^{\prime},H,Q^{T}\right]=Hberg(b^{\prime}_{i})\)
9\(W^{\prime}=\left\{ \begin{array}{ll}1,&if\ Q^{\prime}+\Delta\leq\lambda\\ 0,&Otherwise\end{array} \right.\)
10\(W^{\prime}=W^{\prime}\oplus k\)
11 Obtainextracted watermark as (W'')
12 END

Figure 3: Zig-Zag Block Selection Diagram. ### Role of PSO in Finding Optimal Scaling Factor

The efficiency of watermarking is influenced by a number of characteristics, with imperceptibility and robustness being two of the most crucial. On the contrary, these two concepts are irreconcilable. Therefore, it is important to examine the trade-off between robustness and imperceptibility while developing a watermarking scheme [45]. PSO has some natural advantages over other intelligent optimization algorithms, such as theoretical simplicity, a lower number of parameters to adjust, and the ability to escape the local optimal condition through the integration of local and global information, particularly in multidimensional and nonlinear situations. These appealing qualities have contributed to the widespread use of PSO. In recent years, the PSO method has been successfully used to solve search and optimization problems. It has been demonstrated that PSO can achieve better optimization solutions in a faster and less expensive manner than many other methods. As a result, it can efficiently identify the optimal global (or near globally optimum) solution in multidimensional search spaces. This is a primary reason for utilising PSO at work. Furthermore, the classic PSO algorithm's global convergence cannot always be ensured because swarm diversity decreases as evolution progresses. To address this issue, this research employs a multi-objective PSO variation to reduce flaws. Since the majority of multi-objective PSO variant algorithms [53; 54] utilise an external archive to preserve a collection of Pareto optimal solutions that approximate the actual Pareto front. Certain variations of multi-objective PSO [55] operate under the assumption of an infinite archive size, whereas the majority of other variants employ a fixed archive size. The exponential increase in non-dominated solutions for multi-objective PSO algorithms results in a significant expense when updating the archive set, should an unlimited archive size be employed. Therefore, it cannot be deemed a cost-effective solution for archive maintenance. In the case of an archive with a fixed size, it is necessary to establish regulations for managing instances of overflow within the archive.