## 2 Materials and Methods
### Methods
#### 2.2.4 Image Fusion  
Image fusion is a technique in computer vision and image processing that merges multiple images into a single composite image that is more informative and suitable for further processing tasks. In this research, the main objective of image fusion was to integrate opposite-frequency components from MRA-DWT and Gaussian filtering or Difference of Gaussian to create new features that had better robustness against facial recognition system challenges than any original image. In general, according to the data integration phase, there are three types of image fusion: pixel-level fusion, feature-level fusion, and decision-level fusion [50]. In pixel-level fusion, the merging is directly performed on the input images. The essential features are extracted first from the image in feature-level fusion. Later, the process combines these features. Different from pixel-level and feature-level fusion, in decision-level fusion, the image analyses are performed separately until the final process to produce decisions, and these decisions are combined to create the final verdict. Figure 5: Results from Gaussian filtering and the Difference of Gaussian (from **left** to **right**): original image, Gaussian filtered image with \(\sigma_{1}\), Gaussian filtered image with \(\sigma_{2}\), Difference of Gaussian. In this research, we compared two different methods of image fusion, i.e., Laplacian pyramid image fusion (LP-IF) and discrete wavelet transform image fusion (DWT-IF). Both methods come from the transform domain image fusion [51]. The LP-IF and DWT/IDWT-IF processes are shown in the red block in Figure 2.  
* Laplacian pyramid image fusion (LP-IF)  
The Laplacian pyramid was first proposed by [PERSON] and [PERSON] [52]. It was then used to merge images [53]. The LP-IF creates a pyramid-like structure for the two source images using Gaussian filtering with decimation by a factor of two. This procedure is implemented until it reaches the desired level \(l\). The Laplacian is calculated by subtracting the filtered Gaussian from level \(l\) from the filtered Gaussian from level \(l+1\) that first undergoes a process of un-decimation by a factor of two. Using the popular fusion rule, we chose an averaging for the base low-pass and the highest absolute value for the fused high-pass coefficient. The final fused image is acquired by going through the inverse pyramid transformation. We used level \(l=4\). All LP-IF codes in this research were credited to the image fusion toolbox by [54]. * Discrete wavelet transform image fusion (DWT/IDWT-IF)  
Image fusion by DWT (DWT/IDWT-IF) was first introduced by [55] with a multi-resolution decomposition that shows the frequency and location where the frequency occurs. Like LP-IF, DWT-IF creates a multi-scale representation of the source images, producing four different sub-bands for each image: \(A\), \(H\), \(V\), and \(D\) (as explained in Section 2.2.2). The four sub-bands from each source image were fused using max-min, min-max, and mean-mean rules. The max-min rule indicates that the fusion takes the maximum absolute approximation value and minimum absolute value for details. In contrast, the min-max rule is the opposite of the max-min (minimum absolute value for approximation and maximum absolute value for details). The mean-mean rule means we take the mean value for approximation and details [33]. The final fused image is obtained through inverse DWT using the combined coefficients with different rules. After we acquired four sub-bands from MRA-DWT (\(A\), \(H\), \(V\), and \(D\)), the Gaussian filtered image (G1_1) from Equation (2), and the Difference of Gaussian (\(L\)) from Equation (4), we proposed to fuse these coefficients to produce an enhanced image. The fusion combined two opposite coefficients' frequencies, i.e., the low-pass coefficient (which lacks a high-frequency component) was combined with the high-pass coefficient (which lacks a low-frequency component), and vice versa. The idea was to combine the opposite frequencies to complement each other.