## 2 Proposed Fusion Scheme
\[TEM_{2}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{2}(m+2,n+2) \tag{16}\]

\[TEM_{3}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{3}(m+2,n+2) \tag{17}\]

\[TEM_{4}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{4}(m+2,n+2) \tag{18}\]

\[TEM_{5}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{5}(m+2,n+2) \tag{19}\]

\[TEM_{6}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{6}(m+2,n+2) \tag{20}\]

\[TEM_{7}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{7}(m+2,n+2) \tag{21}\]

\[TEM_{8}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{8}(m+2,n+2) \tag{22}\]

\[TEM_{9}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{9}(m+2,n+2) \tag{23}\]

Absolute values of \(TEM\)s are evaluated by using the following formula. Let the normalized \(TEM\)s be \(NTEMX_{1}\), \(NTEMX_{2}\), \(NTEMX_{3}\), \(NTEMX_{4}\), \(NTEMX_{5}\), \(NTEMX_{6}\), \(NTEMX_{7}\), \(NTEMX_{8}\), \(NTEMX_{9}\)

\[NTEMX_{i}=\text{normalized}\ (\left|TEMX_{i}\right|) \tag{24}\]Saliency of approximate sub-bands is calculated using Equation (25). \[TEM_{2}(r,c)=\sum_{m=-1}^{1}\sum_{m=-1}^{1}ASX(r+m,c+n)^{2}matrix_{2}(m+2,n+2) \tag{16}\]0

In a similar way, the saliency measure \(SASY\) is determined for the approximate sub-bands \(ASY\) of the original image \(Y\). The first fusion decision map (\(DM\)) is gathered by comparing the saliency values of the two source images at each position. Fusion decision maps for saliency measures are initially developed as

\[DM(r,\ c)=\{1_{0}^{1}\ \ \ \ \ \ \ \ \



Edge-Intensity (_EI_) [27], Gray-Mean-Value (_GM_) [29; 30], Image-Definition (_ID_) [29; 31], Percentage-Fit-Error (_PFE_) [24], and UIQI (_Q\({}^{0}\)_) [29; 32] are used to assess the interpretations of dissimilar fusion approaches quantitatively. ## 3 Experimental Results

A hybrid wavelet (_SWT_ and _DTCWT_) and _TEM_ are proposed in this paper. The proposed algorithm's quality was evaluated using quality metrics, including correlation-coefficient (_CC_), entropy (_E_(_F_)), total-fusion-performance (_Q\({}^{AB/F}\)_), average-gradient (_AG_), structural-similarity (_SSIM_), standard-deviation (_SD_), spatial-frequency (_SF_), weighted-fusion-quality (_Q\({}_{W}\)_), edge-dependent-fusion-quality (_Q\({}_{E}\)_), feature-mutual-information (_FMI_), root-mean-square-error (_RMSE_), fusion-loss (_L\({}^{AB/F}\)_), peak-signal-to-noise-ratio (_PSNR_), fusion-artifacts (_N\({}^{AB/F}\)_), edge-intensity (EI), gray-mean-value (_GM_), image-definition (_ID_), percentage-fit-error (_PFE_), and universal quality index (_Q\({}^{0}\)_). The proposed strategy is contrasted with previously published methods using these metrics. These criteria are used to assess the comparison and robustness of the fused images against distortions. Source images that are utilized for comparison are familiar with multi-focus image fusion. Numerous images from various datasets are used in experiments [33]. The proposed method produces successful outcomes for these images. However, the approaches that are contrasted with the proposed methodology do not yield results for these images, so they are not included in the publication. This paper compares approaches in the literature with [4; 18; 19; 20; 21; 22] using the desk, book, clock, flower, lab, leaf, flowerpot, Pepsi, balloon, grass, leopard, calendar, wine, craft, and remote sensing images. Additionally, the results of the proposed method for a few tested source images are shown. The images come in a range of sizes and quality. The proposed approach can be used with any multi-focus image, not just in this study. ### Outcomes of the Proposed Methodology for a Few Specified Images

Several kinds of grayscale images are utilized to apply the proposed method. Analyses such as _E_(_F_), _SD_, _AG_, _QE_, _CC_, _SSIM_, _Q\({}^{AB/F}\)_, _RMSE_, _PFE_, _PSNR_, and _SF_ are applied to these images. Many different kinds of images are used and analysed.