# Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary

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## Abstract

**:**

## 1. Introduction

- The paper uses MSVD decomposition with a complementary structure and size for the first time, enhances the complementarity of the extracted image feature information and improves the ability to detect the focus area, in order to fully extract the structure and detailed information of the image.
- To fully extract the structure and details of the image, the complementary features extracted by different focus measures are developed as the external stimulus input of the PA-PCNN.
- Experiments are performed to verify the efficiency of the proposed method. The results show that the proposed method can effectively eliminate the pseudo edges caused by anisotropic blur or unregistration.

## 2. Proposed Multi-Focus Image Fusion Algorithm

#### 2.1. Multi-Scale Singular Value Decomposition of Multi-Focus Image

#### 2.1.1. Multi-Scale Singular Value Decomposition

#### 2.1.2. Decomposition of Multi-Focus Image

#### 2.2. Low-Frequency Component Fusion

#### 2.2.1. Quaternion

#### 2.2.2. Joint Bilateral Filter

#### 2.2.3. Low-Frequency Component Fusion Rule

- Select the pixel in the 3 × 3 domain of the target pixel to construct quaternion ${Q}_{\mathrm{I}}^{1},{Q}_{I}^{2}$, and calculate the local energy ${E}_{I}^{L}$ of the low-frequency component:$$\begin{array}{l}{E}_{I}^{L}(x,y)={Q}_{\mathrm{I}}^{1}{Q}_{\mathrm{I}}^{2}\ast {f}_{I}^{L}(x,y)\\ {Q}_{I}^{1}=f(x,y+1)+if(x,y-1)+jf(x-1,y)+kf(x+1,y)\\ {Q}_{I}^{2}=f(x+1,y+1)+if(x+1,y-1)+jf(x-1,y-1)+kf(x-1,y+1)\end{array}$$

- 2.
- JBF is used to process the local energy map ${E}_{I}^{L}$ of low frequency components to get the energy map ${S}_{I}^{L}$ of edge pixels:$${S}_{I}^{L}=JBF({E}_{I}^{L},{f}_{I}^{L},w,{\delta}_{s},{\delta}_{r})$$

- 3.
- According to the local energy ${E}_{I}^{L}$ and edge energy ${S}_{I}^{L}$ of the low-frequency component, the weight of the low-frequency component is calculated.$$\begin{array}{l}{d}_{A}^{L}=\left\{\begin{array}{l}1,{E}_{A}^{L}\cdot {S}_{A}^{L}\ge {E}_{B}^{L}\cdot {S}_{B}^{L},\\ 0,otherwise,\end{array}\right.\\ \hspace{1em}\hspace{1em}\hspace{1em}{d}_{B}^{L}=1-{d}_{A}^{L}.\end{array}$$
- 4.
- The fusion image of the low-frequency component is obtained by the following formula:$${f}_{F}^{L}={d}_{A}^{L}\cdot {f}_{A}^{L}+{d}_{B}^{L}\cdot {f}_{B}^{L}$$

#### 2.3. High-Frequency Component Fusion

#### 2.3.1. PA-PCNN

_{max}of the input image and the optimal histogram threshold ${S}^{\prime}$ jointly determine the value of $\beta {V}_{L}$. $\beta {V}_{L}$ and ${a}_{f}$ are combined to get ${V}_{E}$ and ${a}_{e}$. Figure 3 shows the PA-PCNN model used in the multi-focus image fusion method proposed in this paper.

#### 2.3.2. Space Frequency and Standard Deviation

#### 2.3.3. High-Frequency Component Fusion Rule

- In the first layer of decomposition, SF is used as the external stimulus input of PA-PCNN, and the number of ignitions of high-frequency components is obtained by$${T}_{S}^{1}[n]={T}_{S}^{1}[n-1]+{Y}_{S}^{1}[n],(S=A,B)$$
- Weight coefficient of high-frequency components is obtained by:$$\begin{array}{l}{d}_{A}^{H1}=\left\{\begin{array}{l}1,if{T}_{A}^{1}[n]{T}_{B}^{1}[n],\\ 0,otherwise,\end{array}\right.\\ \hspace{1em}\hspace{1em}\hspace{1em}{d}_{B}^{H1}=1-{d}_{A}^{H1}.\end{array}$$
- High-frequency components after fusion is obtained by:$${f}_{F}^{H1}={d}_{A}^{H1}\cdot {f}_{A}^{H1}+{d}_{B}^{H1}\cdot {f}_{B}^{H1}$$

#### 2.4. Non-Definite Focus Region Fusion

- Based on the two complementary decision maps, an initial decision map D
_{F}containing the definite focus region and the non-definite focus region is obtained.$$\begin{array}{ll}{D}_{F}=({D}_{1}+{D}_{2})\xb7/2& \\ {D}_{F}\left(i,j\right)\in {D}_{Iden},& & {D}_{F}\left(i,j\right)=1\mathrm{or}{D}_{F}\left(i,j\right)=0\\ {D}_{F}\left(i,j\right)\in {D}_{Uniden},& & {D}_{F}\left(i,j\right)=0.5\end{array}$$_{1}is the fusion decision map obtained by the first group of decomposition scheme (Figure 2c), D_{2}is the fusion decision map obtained by the second group of the decomposition scheme (Figure 2d), D_{F}is the initial decision map (Figure 2e). When ${D}_{F}(i,j)=1$ or ${D}_{F}(i,j)=0$, ${D}_{F}(i,j)$ belongs to the definite focus region D_{Iden}; when ${D}_{F}(i,j)=0.5$, ${D}_{F}(i,j)$ belongs to the definite focus region D_{Uniden}(the red region in Figure 2e). - The weight coefficient of the non-definite focus region is calculated by$${Q}_{U}^{Uniden}=\frac{1}{m\times n}{\displaystyle \sum _{m=0}^{w}{\displaystyle \sum _{n=0}^{w}(S{F}_{U}(i+m,j+n)\ast ST{D}_{U}(i+m,j+n)}}),U=(AorB)$$$$\begin{array}{cc}{d}_{A}^{Uniden}=& \left\{\begin{array}{ll}1,& if{Q}_{A}^{Uniden}\xb7{f}_{A}^{Uniden}{Q}_{B}^{Uniden}\xb7{f}_{B}^{Uniden},\\ 0,\hfill & otherwise,\hfill \end{array}\right.\hfill \\ & {d}_{B}^{Uniden}=1-{d}_{A}^{Uniden}.\hfill \end{array}$$
- The non-definite focus region fusion is calculated by$${f}_{F}^{Uniden}={d}_{A}^{Uniden}\u02b7{f}_{A}^{Uniden}+{d}_{B}^{Uniden}\xb7{f}_{B}^{Uniden}$$

#### 2.5. The Proposed Multi-Focus Image Fusion Method

_{1}and D

_{2}are obtained.

_{F}containing the definite focus region and the non-definite focus region is obtained. The non-definite focus region D

_{Uniden}in D

_{F}is the aliasing area at the boundary of the complementary decision maps. With the adoption of the proposed focus measurement method (in Section 2.4), the non-definite focus region D

_{Uniden}is transformed into the definite focus region, and the final fusion decision map D

_{FF}is obtained.

_{FF}obtained in Step 3, the final fusion image is obtained.

## 3. Experiments and Discussion

#### 3.1. Comparative Analysis of Fusion Results Based on Traditional Methods

#### 3.1.1. Subjective Analysis of Pre-Registered Image Fusion Results

#### 3.1.2. Subjective Analysis of Unregistered Images Fusion Results

#### 3.1.3. Subjective Analysis of More Image Fusion Results

#### 3.1.4. Objective Analysis of Fusion Results

_{AB/F}[25], the normalized mutual information metric Q

_{MI}[1], the phase congruency based fusion metric Q

_{PC}[33], and gradient-based fusion performance metric Q

_{G}[35] to evaluate the fusion results. For all four objective evaluation indicators, the larger the value, the better the fusion results. The highest value in the evaluation is bolded in all tables.

_{AB/F}value in the “newspaper”, and the proposed method fares the best in other evaluation indicators. The method obtains the largest values among the other objective evaluation indicators, which is consistent with the subjective visual effect of the fusion result.

_{AB/F}objective evaluation values of the fusion results of 10 pairs of source images with different methods. The proposed method fares the best in other evaluation indicators. The method gets the best fusion results in “book”, “craft”, “flower”, “girl”, “grass”, “lab”, “lytro”, and “hoed”. IFM and MWGF get the best fusion results in “clock” and “seascape”, respectively. This means that, in most cases, the proposed method can incorporate important edge information into the fusion image.

_{MI}objective evaluation of the fusion results of 10 pairs of source images with different methods. The proposed method obtains the best fusion results among the nine methods. Although the DCT_SVD method has the highest evaluation values in “flower” and “hoed”, the evaluation value of the proposed method is very close to it, and the variation is less than 0.04.

_{PC}objective evaluation values of the fusion results of 10 pairs of source images with different methods. Except for the MWGF method, to obtain the best fusion result in “seascape”, the proposed method has the highest values in other evaluation indicators. This means that the proposed method can well retain important source image feature information of the fused image.

_{G}objective evaluation of the fusion results of 10 pairs of source images with different methods. The IFM method achieves the best fusion results in “clock” and “craft”, and the DCT_SVD method in “hoed”. The proposed method fares the best in other evaluation indicators. These mean that the fused image obtained by the proposed method has high sharpness.

#### 3.1.5. Comparison of Computational Efficiency

#### 3.2. Comparative Analysis of Fusion Results Based on Deep Learning Methods

#### 3.2.1. Subjective Analysis of Image Fusion Results

#### 3.2.2. Objective Analysis of Image Fusion Results

_{AB/F}, the spatial frequency metric Q

_{SF}, the structural similarity metric Q

_{Y}, the feature contrast metric Q

_{CB}. For the above four evaluation metrics, the larger the value, the better the fusion results.

_{SF}and Q

_{CB}. Although the Q

_{AB/F}and Q

_{y}values of the proposed method are smaller than the other two, the difference between them is not greater than 0.015. In summary, the proposed method shows good performance in both visual perception and quantitative analysis.

#### 3.3. More Analysis

#### 3.3.1. Ablation Research

#### 3.3.2. Series Multi-Focus Image Fusion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Two groups of double-layer multi-scale singular value decomposition schemes with complementary structure and scale. In the two decomposition schemes, ${H}_{1-14}^{1}$ are the high-frequency components of the first layer after decomposition, ${H}_{1-5}^{2}$ are the high-frequency components of the second layer after decomposition, L is the low-frequency component of the second layer after decomposition. (

**a**) The first group of the decomposition scheme; (

**b**) the second group of the decomposition scheme.

**Figure 2.**(

**a**) the left focus source image; (

**b**) the right focus source image; (

**c**) fusion decision map obtained by the first group of the decomposition scheme; (

**d**) fusion decision map obtained by the second group of the decomposition scheme; (

**e**) the initial fusion decision map determined by (

**c**,

**d**), the black area corresponding to the decision value “0”, the white area corresponding to the decision value “1”, and the black and white areas are definite focus areas. The red area is the aliasing area of (

**c**,

**d**), which is the non-definite focus area.

**Figure 4.**Schematic diagram of the proposed method of multi-focus image fusion. D

_{1}is the first scheme decision map; D

_{2}is the second scheme decision map; the red region in the initial decision map D

_{F}is the non-definite focus region D

_{Uniden}. ${H}_{i}^{c}$ is the i-th high-frequency component in the c-th layer decom-position, where c = 1 or 2.

**Figure 5.**The source images of “wine” and the fusion results of different methods. (

**a**) Source image A, (

**b**) source image B, (

**c**) curvelet, (

**d**) DCT_SVD, (

**e**) DTCWT, (

**f**) IFM, (

**g**) LP, (

**h**) MSVD, (

**i**) MWGF, (

**j**) NSCT, (

**k**) proposed method.

**Figure 6.**The partial enlarged regions taken from Figure 5a–k. (

**a**) Source image A, (

**b**) source image B, (

**c**) curvelet, (

**d**) DCT_SVD (

**e**) DTCWT, (

**f**) IFM, (

**g**) LP, (

**h**) MSVD, (

**i**) MWGF, (

**j**) NSCT, (

**k**) proposed method.

**Figure 7.**The partial enlarged regions taken from Figure 5a–k. (

**a**) Source image A, (

**b**) source image B, (

**c**) curvelet, (

**d**) DCT_SVD (

**e**) DTCWT, (

**f**) IFM, (

**g**) LP, (

**h**) MSVD, (

**i**) MWGF, (

**j**) NSCT, (

**k**) proposed method.

**Figure 8.**The source image of “newspaper” and the fusion results of different methods. (

**a**) Source image A, (

**b**) source image B, (

**c**) curvelet, (

**d**) DCT_SVD (

**e**) DTCWT, (

**f**) IFM, (

**g**) LP, (

**h**) MSVD, (

**i**) MWGF, (

**j**) NSCT, (

**k**) proposed method.

**Figure 9.**The partial enlarged regions taken from Figure 8a–k. (

**a**) Source image A, (

**b**) source image B, (

**c**) curvelet, (

**d**) DCT_SVD (

**e**) DTCWT, (

**f**) IFM, (

**g**) LP, (

**h**) MSVD, (

**i**) MWGF, (

**j**) NSCT, (

**k**) proposed method.

**Figure 11.**The partial enlarged regions taken from Figure 10a–k. (

**a**) Source image A, (

**b**) Source image B, (

**c**) Curvelet, (

**d**) DCT_SVD (

**e**) DTCWT, (

**f**) IFM, (

**g**) LP, (

**h**) MSVD, (

**i**) MWGF (

**j**) NSCT (

**k**) Proposed method.

**Figure 14.**(

**a**–

**d**) show the score line graphs of the four image evaluation indicators (Q

_{AB/F}, Q

_{MI}, Q

_{PC}, and Q

_{G}) corresponding to Table 2,Table 3,Table 4,Table 5, respectively. In subfigures (

**a**–

**d**), the horizontal axis represents the image indices ranging from 1 to 10, and the vertical axis represents values of the image evaluation indicators.

**Figure 15.**The source images (

**a**,

**b**) are from the lytro dataset; (

**c**) is the fusion result of the CNN; (

**d**) is the fusion result of the FuseGAN; (

**e**) is the fusion result of the proposed method.

**Figure 16.**The partial enlarged regions taken from Figure 15a–e.

**Figure 17.**(

**a**,

**b**,

**e**,

**f**) show 16 pairs of source images; (

**c**,

**g**) are the fusion results of the FuseGAN; (

**d**,

**h**) are the fusion results of the proposed method.

**Figure 18.**Ablation experiment of the PCNN. (

**a**,

**b**) are source images; (

**c**) results with PCNN; (

**d**) results without PCNN.

**Figure 19.**An example of applying the proposed method to fuse three source images. (

**a**–

**c**) are source images, (

**d**) fusion results of the proposed method.

Images | Metrics | Curvelet | DCT_SVD | DTCWT | IFM | LP | MSVD | MWGF | NSCT | Proposed Method |
---|---|---|---|---|---|---|---|---|---|---|

wine | Q_{AB/F} | 0.6412 | 0.6942 | 0.6752 | 0.7111 | 0.6889 | 0.4467 | 0.6920 | 0.6290 | 0.7162 |

Q_{MI} | 5.2622 | 8.4875 | 5.6663 | 7.8042 | 6.5947 | 4.9732 | 6.4336 | 5.4534 | 8.6158 | |

Q_{PC} | 0.6299 | 0.6845 | 0.6649 | 0.7040 | 0.0004 | 0.4206 | 0.6901 | 0.6174 | 0.7087 | |

Q_{G} | 0.4809 | 0.6501 | 0.5303 | 0.6531 | 0.5679 | 0.3556 | 0.6251 | 0.4950 | 0.6682 | |

newspaper | Q_{AB/F} | 0.5244 | 0.6625 | 0.6270 | 0.6659 | 0.6369 | 0.3098 | 0.6766 | 0.4199 | 0.6751 |

Q_{MI} | 1.9036 | 6.4318 | 2.2117 | 5.8831 | 2.9815 | 1.7481 | 5.5151 | 1.9821 | 6.5558 | |

Q_{PC} | 0.5043 | 0.6533 | 0.6118 | 0.6568 | 0.0004 | 0.2827 | 0.6639 | 0.3999 | 0.6665 | |

Q_{G} | 0.4851 | 0.6382 | 0.5878 | 0.6425 | 0.6162 | 0.3349 | 0.6299 | 0.4266 | 0.6501 | |

temple | Q_{AB/F} | 0.5723 | 0.7512 | 0.6715 | 0.7582 | 0.7429 | 0.3474 | 0.6051 | 0.5369 | 0.7642 |

Q_{MI} | 2.9895 | 7.2276 | 3.0351 | 7.0355 | 5.1978 | 3.0224 | 3.2813 | 3.1448 | 7.3391 | |

Q_{PC} | 0.5832 | 0.7533 | 0.6795 | 0.7619 | 0.0005 | 0.3658 | 0.6047 | 0.5423 | 0.7676 | |

Q_{G} | 0.5109 | 0.7146 | 0.6089 | 0.7193 | 0.6891 | 0.3722 | 0.7124 | 0.4922 | 0.7203 |

Images | Curvelet | DCT_SVD | DTCWT | IFM | LP | MSVD | MWGF | NSCT | Proposed Method |
---|---|---|---|---|---|---|---|---|---|

book | 0.7335 | 0.7594 | 0.7504 | 0.7596 | 0.7532 | 0.6663 | 0.7227 | 0.7408 | 0.7628 |

clock | 0.6022 | 0.6713 | 0.6618 | 0.7025 | 0.6920 | 0.5658 | 0.5437 | 0.6190 | 0.7018 |

craft | 0.6605 | 0.7195 | 0.6891 | 0.7267 | 0.7086 | 0.6898 | 0.4401 | 0.6941 | 0.7346 |

flower | 0.6657 | 0.7098 | 0.7004 | 0.7125 | 0.6985 | 0.6679 | 0.3991 | 0.6848 | 0.7133 |

girl | 0.6146 | 0.6777 | 0.6528 | 0.6857 | 0.6696 | 0.5530 | 0.5836 | 0.5913 | 0.6919 |

grass | 0.5574 | 0.6459 | 0.6037 | 0.6694 | 0.6320 | 0.4120 | 0.4496 | 0.5502 | 0.6706 |

lab | 0.6183 | 0.7116 | 0.6892 | 0.7384 | 0.7194 | 0.5852 | 0.6859 | 0.6046 | 0.7394 |

lytro | 0.6233 | 0.7373 | 0.7013 | 0.7428 | 0.7334 | 0.5163 | 0.7101 | 0.6162 | 0.7445 |

seascape | 0.5358 | 0.6955 | 0.6231 | 0.7038 | 0.6333 | 0.4614 | 0.8794 | 0.4920 | 0.7060 |

hoed | 0.6619 | 0.8207 | 0.7473 | 0.8094 | 0.8074 | 0.5568 | 0.7379 | 0.6323 | 0.8212 |

Images | Curvelet | DCT_SVD | DTCWT | IFM | LP | MSVD | MWGF | NSCT | Proposed Method |
---|---|---|---|---|---|---|---|---|---|

book | 7.5469 | 9.2254 | 7.8636 | 9.2650 | 8.0568 | 7.0990 | 8.7403 | 7.5655 | 9.4974 |

clock | 6.5747 | 8.5643 | 6.6081 | 8.3289 | 7.2697 | 6.6358 | 6.5600 | 6.8297 | 8.5648 |

craft | 6.8147 | 8.5981 | 6.9386 | 8.8035 | 7.1822 | 7.2763 | 5.9810 | 7.4597 | 8.8691 |

flower | 5.2993 | 8.0569 | 5.8285 | 7.9184 | 6.4240 | 5.0763 | 3.8654 | 5.3363 | 8.0174 |

girl | 5.4226 | 8.8479 | 5.7647 | 8.8677 | 6.2546 | 5.3249 | 7.6408 | 5.5291 | 9.0835 |

grass | 4.8071 | 8.5131 | 4.9885 | 8.4649 | 5.8314 | 4.6484 | 4.9709 | 4.9466 | 8.9043 |

lab | 6.6219 | 8.5181 | 6.9902 | 8.5302 | 7.5773 | 6.9382 | 7.9229 | 7.0273 | 8.6211 |

lytro | 5.7419 | 8.1906 | 5.8921 | 8.0725 | 6.7115 | 5.7305 | 7.9050 | 5.9048 | 8.3023 |

seascape | 4.5815 | 7.9492 | 4.8031 | 7.7184 | 5.5810 | 4.6547 | 6.7174 | 4.8333 | 8.0761 |

hoed | 4.5654 | 8.3975 | 4.7390 | 7.9818 | 6.4462 | 4.5557 | 6.2599 | 4.6683 | 8.3834 |

Images | Curvelet | DCT_SVD | DTCWT | IFM | LP | MSVD | MWGF | NSCT | Proposed Method |
---|---|---|---|---|---|---|---|---|---|

book | 0.7254 | 0.7499 | 0.7416 | 0.7503 | 0.0005 | 0.6542 | 0.7081 | 0.7353 | 0.7535 |

clock | 0.6006 | 0.6718 | 0.6608 | 0.7059 | 0.0005 | 0.5644 | 0.5498 | 0.6190 | 0.7067 |

craft | 0.6195 | 0.6740 | 0.6547 | 0.6817 | 0.0004 | 0.6505 | 0.3123 | 0.6539 | 0.6910 |

flower | 0.6722 | 0.7141 | 0.7058 | 0.7179 | 0.0005 | 0.6861 | 0.4042 | 0.6962 | 0.7181 |

girl | 0.5967 | 0.6712 | 0.6389 | 0.6757 | 0.0004 | 0.5306 | 0.5737 | 0.5702 | 0.6827 |

grass | 0.5620 | 0.6452 | 0.6090 | 0.6692 | 0.0004 | 0.4238 | 0.4393 | 0.5527 | 0.6705 |

lab | 0.6307 | 0.7011 | 0.6992 | 0.7314 | 0.0005 | 0.5891 | 0.6794 | 0.6093 | 0.7320 |

lytro | 0.6094 | 0.7299 | 0.6928 | 0.7354 | 0.0005 | 0.4946 | 0.6973 | 0.6006 | 0.7374 |

seascape | 0.5402 | 0.6994 | 0.6261 | 0.7053 | 0.0004 | 0.4623 | 0.8893 | 0.4891 | 0.7064 |

hoed | 0.6792 | 0.8171 | 0.7538 | 0.8074 | 0.0005 | 0.5842 | 0.7582 | 0.6516 | 0.8174 |

Images | Curvelet | DCT_SVD | DTCWT | IFM | LP | MSVD | MWGF | NSCT | Proposed Method |
---|---|---|---|---|---|---|---|---|---|

book | 0.5636 | 0.6616 | 0.6142 | 0.6704 | 0.6249 | 0.5542 | 0.6482 | 0.6062 | 0.6733 |

clock | 0.4730 | 0.6538 | 0.5236 | 0.6700 | 0.5661 | 0.4861 | 0.6509 | 0.5194 | 0.6604 |

craft | 0.5124 | 0.6508 | 0.5619 | 0.6629 | 0.6070 | 0.5790 | 0.6507 | 0.5911 | 0.6494 |

flower | 0.5936 | 0.6831 | 0.6641 | 0.6863 | 0.6526 | 0.6068 | 0.6770 | 0.6200 | 0.6869 |

girl | 0.5924 | 0.6737 | 0.6443 | 0.6829 | 0.6628 | 0.5425 | 0.6826 | 0.5744 | 0.6859 |

grass | 0.5253 | 0.6435 | 0.5871 | 0.6696 | 0.6249 | 0.3950 | 0.6423 | 0.5300 | 0.6736 |

lab | 0.4604 | 0.7056 | 0.5463 | 0.6946 | 0.5788 | 0.4798 | 0.7153 | 0.4873 | 0.7167 |

lytro | 0.5552 | 0.6987 | 0.6465 | 0.7099 | 0.6879 | 0.5074 | 0.7068 | 0.5691 | 0.7101 |

seascape | 0.5332 | 0.6945 | 0.6295 | 0.6975 | 0.6687 | 0.4765 | 0.7032 | 0.5154 | 0.7116 |

hoed | 0.6216 | 0.7912 | 0.7090 | 0.7836 | 0.7748 | 0.5316 | 0.7806 | 0.5936 | 0.7896 |

Metric | Curvelet | DCT_SVD | DTCWT | IFM | LP | MSVD | MWGF | NSCT | Proposed Method |
---|---|---|---|---|---|---|---|---|---|

Time(Seconds) | 0.9757 | 1.1396 | 0.4036 | 2.2200 | 0.3072 | 0.3162 | 1.7036 | 0.7842 | 1.4473 |

Metric | Q_{Ab/F} | Q_{SF} | Q_{Y} | Q_{CB} | Time (Seconds) |
---|---|---|---|---|---|

FuseGAN | 0.7222 | 0.0211 | 0.9925 | 0.8032 | 0.53 |

CNN | 0.7177 | 0.0342 | 0.9901 | 0.8001 | 109.16 |

Proposed | 0.7162 | 0.07261 | 0.9776 | 0.8127 | 2.85 |

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## Share and Cite

**MDPI and ACS Style**

Wan, H.; Tang, X.; Zhu, Z.; Li, W.
Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary. *Entropy* **2021**, *23*, 1362.
https://doi.org/10.3390/e23101362

**AMA Style**

Wan H, Tang X, Zhu Z, Li W.
Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary. *Entropy*. 2021; 23(10):1362.
https://doi.org/10.3390/e23101362

**Chicago/Turabian Style**

Wan, Hui, Xianlun Tang, Zhiqin Zhu, and Weisheng Li.
2021. "Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary" *Entropy* 23, no. 10: 1362.
https://doi.org/10.3390/e23101362