## 4 Proposed Methodology  
The proposed method for embedding the watermark image into the host image is illustrated by Figure 3. It is not an embedding operation of a direct substitution. Rather, we have performed different levels of DWT and SVD operation on both host and watermark images before the embedding operation. At first, the Arnold map is used for encrypting the watermark image to ensure the security of the system. We have applied SVD twice both for LL4 and ew for increasing robustness and security. Watermark embedding with different SVD levels resists the geometric attacks more effectively. Therefore, two-level (2L) SVD is applied to LL4 to extract S components. The method applies 4L DWT to the host image and extracts the LL4 sub-band. After that, 2L SVD is applied to that sub-band and S components are extracted. Then, the method embeds the watermark image's S components into the host image's S components with a scaling factor \(\alpha\) that is chosen manually to obtain the best value so that there maintains a better trade-off between the imperceptibility and robustness of the system. In this study, we have used \(\alpha=0.07\). After that, the LL4 sub-band is rebuilt and the inverse DWT (IDWT) is applied to obtain the watermarked image. Watermark extraction is conducted in a reverse way which is shown by Figure 4. Initially, 4L DWT is applied to the watermarked image to extract LL4 wmv. Then, 2L SVD is applied to it to extract the Sw component. After that, inverse SVD (ISVD) is applied to Sw to extract the encrypted watermark, ew. Finally, the system applies the inverse Arnold map to ew to obtain the watermark image. We have encrypted the watermark with Arnold mapping; our main focus is to extract the watermark image from the watermarked image. However, this section describes proposed algorithms for watermark embedding and extraction in Algorithm 1 and Algorithm 2, respectively. Figure 3: Proposed method for watermark embedding. ```
Input: Watermark image, \(w\), and host image, \(I\), both of size \(512\times 512\) pixels Output: Watermarked image, \(WI\) Apply 4L DWT to host image; \(DWT(I)=[LL1,HL1,LH1,HH1]\); \(DWT(LL1)=[LL2,HL2,LH2,HH2]\); \(DWT(LL2)=[LL3,HL3,LH3,HH3]\); \(DWT(LL3)=[LL4,HL4,LH4,HH4]\); Apply 2L SVD on \(LL4\); \(SVD(LL4)=[Uly,Sy,Vy]\); \(SVD(Sy)=[U1y,S1y,V1y]\); Resize the watermark image, \(w\), to the size of \(LL4\) (\(32\times 32\) pixels);  Apply the Arnold map to encrypt the watermark image: \(ev=ArnoldMap(w)\);  Apply 2L SVD to \(ev\); \(SVD(ew)=[Ulaw,Sw,Vw]\); \(SVD(Sw)=[U1w,S1w,V1w]\); Insert \(S\) components of the watermark image into the \(S\) components of the host image with a scaling factor \(\alpha\). The embedding equation is: \(Smark=S1y+\alpha\times 51w\); Rebuild the sub-band; \(LL4_{1}=Uy\times Smark\times V_{y}^{T}\); Apply inverse DWT (IDWT) to obtain \(WI\); \(LL3_{1}=IDWT(LL4_{1},HI4,LH4,HH4)\); \(LL2_{1}=IDWT(LL3_{1},HL3,LH3_{3},HH3)\); \(LL1_{1}=IDWT(LL2_{1},HI2,LH2,HH2)\); \(WI=IDWT(LL1_{1},H1L,LH1,HH1)\);
```  
**Algorithm 1** Watermark Embedding Algorithm  
Insert \(S\) components of the watermark image into the \(S\) components of the host image with a scaling factor \(\alpha\). The embedding equation is: \(Smark=S1y+\alpha\times 51w\); Rebuild the sub-band; \(LL4_{1}=Uy\times Smark\times V_{y}^{T}\); Apply inverse DWT (IDWT) to obtain \(WI\); \(LL3_{1}=IDWT(LL4_{1},HI4,LH4,HH4)\); \(LL2_{1}=IDWT(LL3_{1},HL3,LH3_{3},HH3)\); \(LL1_{1}=IDWT(LL2_{1},HI2,LH2,HH2)\); \(WI=IDWT(LL1_{1},H1L,LH1,HH1)\);  
``` Input: Watermarked image,



## 5 Experimental Results and Analysis

The suggested algorithm was carried out through MATLAB R2016a software. We validated the imperceptibility and robustness of the proposed watermarking through rigorous experimentation with different groups of images like miscellaneous, texture, medical, and underwater images. Our main novelty is the dynamic-sized watermark image that maintains a balanced visual impression.