## 2 Proposed Fusion Scheme  
In this work, _TEM_ laws [15] are used to predict the features of the image. The input image data is passed through with _SWT_[4; 5], which quantifies the information into approximate and detailed bands. Subsequently, the approximate information is put into detailed and approximate bands again. Further, _TEM_ laws are applied on the low contrast part of the approximate bands, and the absolute-maximum fusion rule is implemented on approximate bands of _DTCWT_[6; 7; 8; 9]. Further, the inverse _DTCWT_ procedure is applied to the output of the low contrast part and absolute maximum fusion rule. The absolute-maximum fusion rule is implemented in the case of _SWT_ detailed bands. Further, inverse _SWT_ is applied on the output of detailed sub-bands of _SWT_ and output of _IDTCWT_ to generate the final image, as shown in Algorithm 1. The proposed method can provide both good shift invariance and directional selectivity, enhances the resolution of fused images, eliminates additive noise, and reduces distortion, all of which increase image quality. Figure 1 represents the fusion scheme of the proposed method. ``` Input: Multi-focus Images Output: Features Extracted Image Steps:
1. Apply _SWT_ to generate sub-band images of given multi-focus images. 2. Apply _DTCWT_ for LL sub-bands of multi-focus images. 3. TEM laws are applied on the low contrast part of the approximate bands, and the absolute-maximum fusion rule is implemented on approximate bands of _DTCWT_. 4. Apply inverse _DTCWT_ procedure on the output of low contrast part and absolute-maximum fusion rule. 5. The absolute-maximum fusion rule is implemented in the case of _SWT_ detailed bands. 6. Apply inverse _SWT_ on the output of detailed sub-bands of _SWT_ and output of _IDTCWT_ to generate the final image, i.e., features extracted image. The following significant steps of the proposed scheme involve \(SWT\) decomposition, \(DTCWT\) decomposition, and implementation of \(TEM\), which are discussed in the following subsections. ### Decomposition Procedure Using SWT

Down-sampling and up-sampling of two primary operations proposed in wavelet transformations. Regarding other wavelet transformations, \(SWT\)[4, 5] implements an up-sampling procedure that up-samples the filters at each level of decomposition. Instead of down-sampling, it removes odd values. With this procedure, sub-bands are created. The sub-bands of the \(SWT\) wavelet have the same size as the source. The second degree of \(SWT\) sub-bands is represented by four levels: LL (low-low), LH (low-high), HL (high-low), and HH (high-high). Here, LL is referred to as approximation sub-bands and others are detailed sub-bands. The flow diagram of \(SWT\) is represented in Figure 2.

The source image is processed to low and high-pass extracts with \(SWT\) to get approximation and detailed coefficients. Ref. [23] illustrates the \(SWT\) at the jth level for the source image (M, N). \[\text{Low\_Low\_Low\_K+1}(\text{r}+\text{c}) =\sum_{\text{P}}\sum_{\text{q}}\text{low}_{\text{P}}^{\text{k}} \text{low}_{\text{q}}^{\text{k}}\text{Low\_Low\_K}(\text{r}+\text{p},\text{c}+ \text{q}) \tag{1}\] \[\text{Low\_High\_K+1}(\text{r}+\text{c}) =\sum_{\text{P}}\sum_{\text{q}}\text{high}_{\text{P}}^{\text{k}} \text{low}_{\text{q}}^{\text{k}}\text{Low\_Low\_K}(\text{r}+\text{p},\text{c}+ \text{q})\] (2) \[\text{High\_Low\_K+1}(\text{r}+\text{c}) =\sum_{\text{P}}\sum_{\text{q}}\text{low}_{\text{P}}^{\text{k}} \text{high}_{\text{q}}^{\text{k}}\text{Low\_Low\_K}(\text{r}+\text{p},\text{c}+ \text{q})\] (3) \[\text{High\_High\_High\_K+1}(\text{r}+\text{c}) =\sum_{\text{P}}\sum_{\text{q}}\text{high}_{\text{P}}^{\text{k}} \text{high}_{\text{q}}^{\text{k}}\text{Low\_Low\_K}(\text{r}+\text{p},\text{c}+ \text{q}) \tag{4}\]

where r equals 1, 2, 3, 4,... M and c equals 1, 2, 3, 4,... N and the low and high values indicate the low-pass and high-pass extracts.