# Image Fusion Algorithm Selection Based on Fusion Validity Distribution Combination of Difference Features

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Intuition-possible sets are built to model fusion validity of attributes of image difference features.
- (2)
- A novel construction method of fusion validity distribution based on intuition-possible sets is proposed, which can reflect the fusion validity change process of attributes of image difference features to algorithms.
- (3)
- This paper puts forward a distribution combination method based on intuition-possible set ordering to solve the optimal algorithm selection problem that has a relatively better effect on the fusion of the difference features according to the varied image feature attribute values, which provides the basis to algorithm classification and mimicry bionic fusion. The rest of this paper is organized as follows: Section 2 briefly analyses the type of difference feature for infrared polarization and intensity images. Section 3 determines intuition-possible set on fusion effect according to the distance of amplitudes of difference features, then proposes a fusion validity distribution construction method. A distribution combination method based on intuition possible set ordering is put forward. Experimental results and comparisons are given and analyzed. Conclusions are presented in Section 4.

## 2. Determination of the Type of Difference Feature

- Gray mean: In the grayscale image, the brightness information changes continuously from dark to bright. The difference gray mean value represents the absolute value of mean difference of all pixel intensity values of two types of images in the dual-mode infrared images, thus it can effectively reflect the change of the difference of brightness characteristics of images.
- Edge intensity: The edge information is the contour structural feature of the human eye recognition feature information, and the distributions of the two types of images are very different. The difference edge intensity represents the absolute value of the difference in the edge amplitude intensity of the two types of images. This paper selects the Sobel operator based on the commonly used edge extraction operators to extract the edge amplitude intensity information to characterize the edge feature difference change of the images.
- Standard deviation: The difference standard deviation can reflect the discrete situation of the gray scale of the dual mode infrared image compared to the average gray scale. The larger the difference standard deviation is, the more discrete the gray level distribution is, indicating the greater the contrast between the two kinds of images, the more information available, that is, the better the fusion effect.
- Spatial frequency: Difference spatial frequency can reflect the sharpness of pixel gray value changes in dual-mode infrared images, can effectively represent image texture feature information, and reflect the image’s ability to describe the contrast of small details. The greater the difference spatial frequency, the clearer the fused image. The above can be well described image information, so we adopt four difference features in this paper, labelled as T
_{1}, T_{2}, T_{3}and T_{4.}

## 3. Construction of Fusion Validity of Difference Feature Amplitude Based on Intuition Possible Sets

#### 3.1. Intuition Possible Sets

#### 3.2. Calculation of the Distance of the Amplitudes of Difference Feature between Fused Image and Source Images

_{1}, A

_{2}, A

_{3}, A

_{4}, A

_{5}, A

_{6}, A

_{7}, A

_{8}, A

_{9}, A

_{10}, A

_{11}and A

_{12}. Thus we can obtain fused images of different algorithms.

_{1}, T

_{2}, T

_{3}or T

_{4}.

_{5}) and source images are given as vertical axis.

#### 3.3. Distribution Construction

Algorithm 1: Distribution construction |

Input: Infrared polarization image, infrared intensity image and fused image Output: Fusion validity distribution Step 1: The amplitudes of difference feature // T _{1}, T_{2}, T_{3} and T_{4}. Step 2: Calculation of the distance of the amplitudes of difference feature using (5) Step 3: Building of Intuition possible sets on fusion effect Step 4: Construction of fusion validity distribution a. Determine the number of image blocks ${N}^{{X}_{k}}$ b. Initialize ${n}_{1}^{{X}_{k}}$,${n}_{2}^{{X}_{k}}$ and ${n}_{3}^{{X}_{k}}$ c. Update ${n}_{1}^{{X}_{k}}$, ${n}_{2}^{{X}_{k}}$ and ${n}_{3}^{{X}_{k}}$ using Equations (6)–(8) d. Calculate fusion validity |

- (1)
- For image blocks, if the distances of the amplitudes of difference feature between fused image and source images are in the interval $[0,\left|{\overline{X}}_{f}^{i}-\frac{{\overline{X}}_{P}^{i}+{\overline{X}}_{I}^{i}}{2}\right|)$, then fused images in these image blocks have better effect than those based on weighted average method. So in this case, there is definite possibility for the set of high fusion effect of difference feature to algorithms.
- (2)
- When the distances of the amplitudes of difference feature are in the interval $(\left|{\overline{X}}_{f}^{i}-\mathrm{min}({\overline{X}}_{P}^{i},{\overline{X}}_{I}^{i})\right|,1]$, difference features with high complementary have not been fused in fused image effectively, so there should be a definite possibility for the set of low fusion effect of difference feature to algorithms.
- (3)
- If the distance of the amplitudes of difference feature between fused image and source images are in the interval $[\left|{\overline{X}}_{f}^{i}-\frac{{\overline{X}}_{P}^{i}+{\overline{X}}_{I}^{i}}{2}\right|,\left|{\overline{X}}_{f}^{i}-\mathrm{min}({\overline{X}}_{P}^{i},{\overline{X}}_{I}^{i})\right|]$, we cannot determine the fusion validity to be high or low under this circumstance, i.e., medium state.

_{1}, A

_{2}, A

_{3}, A

_{4}, A

_{5}, A

_{6}, A

_{7}, A

_{8}, A

_{9}, A

_{10}, A

_{11}and A

_{12}. Take difference feature T

_{1}as an example, Figure 5 shows fusion validity distribution of difference feature T

_{1}to different algorithms.

#### 3.4. Combination of Fusion Validity Distribution Based on Intuition Possible Set Ordering

_{1}, fusion validity matrix F is given by:

_{1}to algorithm A

_{i}is expressed as follows:

- 1.
- If $m({\tilde{A}}_{i})>m({\tilde{A}}_{j})$, then ${\tilde{A}}_{i}$ is superior to ${\tilde{A}}_{j}$, denoted by ${\tilde{A}}_{i}>{\tilde{A}}_{j}$;
- 2.
- If $m({\tilde{A}}_{i})<m({\tilde{A}}_{j})$, then ${\tilde{A}}_{j}$ is superior to ${\tilde{A}}_{i}$, denoted by ${\tilde{A}}_{i}<{\tilde{A}}_{j}$;
- 3.
- If $m({\tilde{A}}_{i})=m({\tilde{A}}_{j})$, then,

- (1)
- If $\Delta ({\tilde{A}}_{i})>\Delta ({\tilde{A}}_{j})$, then ${\tilde{A}}_{i}$ is superior to ${\tilde{A}}_{j}$, denoted by ${\tilde{A}}_{i}>{\tilde{A}}_{j}$;
- (2)
- If $\Delta ({\tilde{A}}_{i})=\Delta ({\tilde{A}}_{j})$, then ${\tilde{A}}_{j}$ is equivalent to ${\tilde{A}}_{i}$, denoted by ${\tilde{A}}_{i}\text{~}{\tilde{A}}_{j}$
- (3)
- If $\Delta ({\tilde{A}}_{i})<\Delta ({\tilde{A}}_{j})$, then ${\tilde{A}}_{j}$ is superior to ${\tilde{A}}_{i}$, denoted by ${\tilde{A}}_{i}<{\tilde{A}}_{j}$.

_{1}to the 10th interval regarding fusion algorithm ${A}_{i}$, as shown in Table 2. Table 3 is score results ranging from the 11th amplitude interval of difference feature T

_{1}to the 20th interval.

_{1}, the nearer the score of algorithm approximates to 1, the better fusion effect this algorithm will have. The nearer the score of algorithm approximates to −1, the worse fusion effect the algorithm will have. Also, we can compute scores of each amplitude interval of the other three classes of difference features based on intuition possible set ordering. The advantage of such approach is that we can know the mapping between the amplitude of difference feature and fusion algorithms clearly. When the amplitude of difference feature changes, the fusion validity of each algorithm will also change accordingly. The total evaluation values of the amplitudes of difference features to algorithm ${A}_{i}$ are presented in Table 4 and pictorially depicted in Figure 6.

_{1}, the A

_{12}algorithm outperforms the other algorithms when source images contain T

_{2}, T

_{3}, and T

_{4}with the proposed intuition-possible set ordering method in this study. For difference feature T

_{2}, T

_{3}, and T

_{4}, the A

_{6}algorithm has obvious advantages in the fidelity of salient information (including contrast, edge feature and texture) and human visual effect.

_{i}of the fusion algorithm A

_{i}in the area and the average score value $\overline{{E}_{i}}$ are calculated. Because the values are both related to the performance of algorithm A

_{i}, the fusion index E

_{i}is constructed, as shown in Equation (11). The fusion index of different fusion algorithms synthesis of all the difference feature amplitudes is summed, and the fusion algorithm corresponding to the highest value is the optimal fusion algorithm:

#### 3.5. Experimental Results and Comparisons

_{i}for each group are shown in Table 5 and Table 6.

_{1}, A

_{6}and A

_{12}algorithms can retain the brightness of infrared intensity image, while the other fused images are dark as a whole. Under the premise of preserving the fused images with high brightness and contrast, algorithm A

_{6}has better texture detail and edge contour (particularly the box region of Figure 10) preservation performance, also it has better visual effects and resolution. For the box region with great difference of source image in Figure 11, algorithms A

_{5}and A

_{6}have better visual brightness, contrast, texture details and edge profile edge contour preservation performance than the other algorithms, particularly the A

_{5}algorithm, which preserves the texture details completely. The other fused images are dark, leading to poor human visual effect.

_{1}and T

_{2}, T

_{1}and T

_{3}, T

_{1}and T

_{4}, T

_{2}and T

_{3}, T

_{2}and T

_{4}), the fusion indicators of fusion algorithm A

_{6}are higher than other algorithms, and it is obvious that A

_{6}is much larger than other algorithms on the final calculation, so it is concluded that A

_{6}is the optimal fusion algorithm for the first group. In the same way, A

_{5}is the optimal fusion algorithm for the second group. In order to prove the effectiveness and advantages of this method in this study, based on the first set of images, a comparative analysis was made with the existing fusion effectiveness based on fuzzy theory. The fusion validity as follows:

_{6}> A

_{10}> A

_{11}> A

_{12}> A

_{1}> A

_{7}>A

_{5}>A

_{9}> A

_{3}> A

_{2}> A

_{8}> A

_{4}.

_{6}. It shows that the method proposed in this paper is effective.

_{j=1:8}(information entropy, Q

_{0}, Q

_{w}, Q

_{E}, VIFF, SSIM, mutual information, and average gradient). The fusion results of the 12 fusion algorithms corresponding to the two groups of source images are evaluated, we employ grade score R

_{i}(as shown in Formula (12)) to fully consider all evaluation indexes evaluate:

_{6}in the first group is significantly smaller than other fusion algorithms, which indicates that A

_{6}is the optimal fusion algorithm of the first group, with the strongest overall performance. With regard to the suboptimal algorithm A

_{1}, the X

_{2}and X

_{3}values are higher than the others, and the X

_{1}value is second highest, and the other values rank ahead. It is reasonable that A

_{1}is the suboptimal algorithm. Therefore, we can use the proposed method based on the intuitive possible sets to select the best fusion algorithm in dual mode infrared images.

_{5}algorithm is significantly better. For other fusion algorithms, it is consistent with the experimental results in Table 5 and Table 6, which verifies the correctness and effectiveness of the method in this paper. The algorithm with better fusion result by subjective and objective analysis are selected by the proposed fusion validity distribution construction and combination method, which shows that based on intuition possible set, it is feasible and effective to select the best fusion algorithm. According to multi-attributes (e.g., type and amplitude) of difference feature, the proposed method can select relatively better fusion algorithm specifically.

## 4. Conclusions

- (1)
- In this article, four difference features are used to select the best one of the twelve fusion algorithms. In further research, we should consider the recently published solutions for image fusion to choose the algorithm with better fusion effects.
- (2)
- Although the method proposed in this paper has great advantages in selecting the optimal fusion algorithm, there is still some room for improvement. We utilize a fuzzy operator to aggregate difference feature score results in this paper. It would be very interesting to apply some fuzzy weighted averaging operators to cope with fusion validity distribution combination of difference features, such as fuzzy ordered weighted averaging operator, and Pythagorean fuzzy averaging and geometric averaging operators, etc.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Discrete points figure of the distance of the four types of difference feature. (

**a**) difference feature T

_{1}; (

**b**) difference feature T

_{2}; (

**c**)difference feature T

_{3}; (

**d**)difference feature T

_{4}.

**Figure 4.**Fusion validity distribution of each difference feature to NSST algorithm. (

**a**) difference feature T

_{1}; (

**b**) difference feature T

_{2}; (

**c**) difference feature T

_{3}; (

**d**) difference feature T

_{4}.

Particular Terms | Description |
---|---|

Difference feature | The difference information of infrared polarization and intensity image. |

Diverse attribute | The type and amplitude of difference features. |

The type of difference features | The brightness, the edge and detailed features, including gray mean, standard deviation, edge intensity and spatial frequency. |

The amplitude of difference features | The absolute difference of the feature pixels intensity value of two types of image. |

Fusion validity | It is used to measure effective degree of fusing the features in fused images and the source images for the specific fusion algorithm. |

Fusion validity distribution | It can reflect fusion validity changing process of attributes of image difference features to algorithms. |

Intuition possible sets | It can realize quantitative description of fusion effect changing process of difference feature of images to algorithms. |

Relative better effect | From the comprehensive consideration of objective evaluation and subjective evaluation, this algorithm has the best fusion effect. |

Distribution construction | The changing process based on the new method (intuition possible sets) is constructed. |

**Table 2.**Score results in the range of the 1st of difference feature amplitude interval through the 10th interval.

Fusion Algorithm | Difference Feature Amplitude Interval | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

A_{1} | 0.2143 | 0.4742 | 0.6535 | 0.6526 | 0.8095 | 0.9182 | 0.8829 | 0.8962 | 0.9394 | 0.9167 |

A_{2} | 0.3571 | 0.3918 | 0.2970 | 0.2211 | 0.2143 | 0.1818 | 0.0450 | 0.0189 | 0.0101 | 0.0167 |

A_{3} | 0.0429 | 0.0206 | −0.0198 | 0.1474 | 0.1270 | 0.1091 | −0.0270 | −0.0094 | −0.0101 | −0.0500 |

A_{4} | −0.6286 | −0.4845 | −0.4356 | −0.2737 | −0.0635 | 0.0727 | 0 | 0 | −0.0101 | −0.0333 |

A_{5} | 0.3571 | 0.5464 | 0.6139 | 0.7053 | 0.7540 | 0.8273 | 0.8378 | 0.7264 | 0.6465 | 0.6167 |

A_{6} | 0.3857 | 0.5670 | 0.6733 | 0.6632 | 0.6190 | 0.7818 | 0.8108 | 0.6887 | 0.7374 | 0.6167 |

A_{7} | 0.2429 | 0.4124 | 0.5050 | 0.4947 | 0.5159 | 0.5818 | 0.6306 | 0.4906 | 0.5253 | 0.3833 |

A_{8} | 0.7000 | 0.7010 | 0.7228 | 0.5368 | 0.5794 | 0.5091 | 0.4865 | 0.5000 | 0.5859 | 0.5333 |

A_{9} | 1.0000 | 0.0515 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A_{10} | 0.7571 | 0.6392 | 0.3762 | 0.2842 | 0.2778 | 0.1455 | 0.0721 | 0.0943 | 0.0606 | 0.0500 |

A_{11} | 0.9143 | 0.1856 | 0.0198 | 0.0105 | 0 | 0 | 0 | 0 | 0 | 0 |

A_{12} | 0.1286 | 0.5670 | 0.7129 | 0.6737 | 0.8254 | 0.9182 | 0.8739 | 0.7642 | 0.8081 | 0.8167 |

**Table 3.**Score results in the range of the 11st of difference feature amplitude interval through the 20th interval.

Fusion Algorithm | Difference Feature Amplitude Interval | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |

A_{1} | 0.9310 | 0.9286 | 0.9245 | 0.9535 | 1.0000 | 0.9231 | 0.9167 | 1.0000 | 0 | 0 |

A_{2} | 0 | −0.1000 | −0.0755 | −0.1395 | −0.0870 | −0.1538 | −0.1667 | 0 | 0 | −1.0000 |

A_{3} | −0.0115 | −0.0429 | −0.0943 | −0.0233 | 0.2609 | 0.2308 | −0.3333 | −0.3333 | 0 | −1.0000 |

A_{4} | 0 | −0.0143 | −0.0377 | 0 | 0 | 0 | −0.2500 | −0.3333 | 0 | −1.0000 |

A_{5} | 0.7241 | 0.8286 | 0.7736 | 0.8372 | 0.8696 | 0.9231 | 1.0000 | 1.0000 | 0 | 0 |

A_{6} | 0.8161 | 0.8000 | 0.8491 | 0.8837 | 0.8696 | 0.9231 | 0.9167 | 1.0000 | 0 | −1.0000 |

A_{7} | 0.4943 | 0.6000 | 0.5660 | 0.6744 | 0.4783 | 0.3846 | 0.3333 | 0.3333 | 0 | −1.0000 |

A_{8} | 0.3678 | 0.0714 | 0.2453 | 0.0465 | −0.4783 | −0.5385 | −0.3333 | −0.3333 | 0 | 1.0000 |

A_{9} | 0 | 0 | −0.9623 | −1.0000 | −1.0000 | −1.0000 | −1.0000 | −1.0000 | 0 | −1.0000 |

A_{10} | 0.0460 | 0.0714 | 0.0189 | 0.0930 | −0.0870 | −0.1538 | −0.3333 | −0.3333 | 0 | −1.0000 |

A_{11} | 0 | −0.0429 | −0.7736 | −1.0000 | −1.0000 | −1.0000 | −1.0000 | −1.0000 | 0 | −1.0000 |

A_{12} | 0.8966 | 0.9429 | 0.9057 | 0.9767 | 1.0000 | 0.9231 | 1.0000 | 1.0000 | 0 | 1.0000 |

Fusion Algorithm | T_{1} | T_{2} | T_{3} | T_{4} |
---|---|---|---|---|

A_{1} | 0.7467 | 0.4579 | 0.3354 | 0.3260 |

A_{2} | 0.1738 | 0.1923 | 0.1901 | 0.2168 |

A_{3} | 0.1447 | 0.2418 | 0.1036 | 0.2181 |

A_{4} | 0.1819 | 0.1115 | 0.0817 | 0.1921 |

A_{5} | 0.6794 | 0.4127 | 0.2383 | 0.1781 |

A_{6} | 0.7301 | 0.5755 | 0.4967 | 0.4929 |

A_{7} | 0.4823 | 0.1355 | 0.1871 | 0.2020 |

A_{8} | 0.4635 | 0.3241 | 0.0651 | 0.0303 |

A_{9} | 0.4007 | 0.0912 | 0.2193 | 0.3080 |

A_{10} | 0.2447 | 0.2817 | 0.1657 | 0.1079 |

A_{11} | 0.3973 | 0.1899 | 0.1811 | 0.2653 |

A_{12} | 0.7867 | 0.5007 | 0.2744 | 0.3739 |

Difference Features | Index | Fusion Algorithm | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | A_{7} | A_{8} | A_{9} | A_{10} | A_{11} | A_{12} | ||

T_{1}, T_{2} | ${f}_{i}$ | 0.0207 | 0 | 0.0059 | 0 | 0.0237 | 0.6657 | 0.2219 | 0 | 0 | 0.0148 | 0.0059 | 0.0059 |

$\overline{{E}_{i}}$ | 0.2140 | 0 | 0.2031 | 0 | 0.3813 | 0.3439 | 0.2101 | 0 | 0 | 0.2226 | 0.2031 | 0.5980 | |

E_{i} | 0.0044 | 0 | 0.0012 | 0 | 0 | 0.2289 | 0.0466 | 0 | 0 | 0.0033 | 0.0012 | 0.0035 | |

T_{1}, T_{3} | ${f}_{i}$ | 0.1030 | 0 | 0 | 0 | 0.0258 | 0.4052 | 0.0585 | 0.1288 | 0.0081 | 0.0094 | 0 | 0.2646 |

$\overline{{E}_{i}}$ | 0.3341 | 0 | 0 | 0 | 0.3125 | 0.3118 | 0.1430 | 0.4267 | 0.1210 | 0.2688 | 0 | 0.3333 | |

E_{i} | 0.0344 | 0 | 0 | 0 | 0.0081 | 0.1263 | 0.0084 | 0.0550 | 0.0010 | 0.0025 | 0 | 0.0882 | |

T_{1}, T_{4} | ${f}_{i}$ | 0.1592 | 0.0100 | 0 | 0.0149 | 0.1194 | 0.3383 | 0.1741 | 0.0647 | 0 | 0.0697 | 0 | 0 |

$\overline{{E}_{i}}$ | 0.1818 | 0.2264 | 0 | 0.2814 | 0.5393 | 0.3561 | 0.1917 | 0.2691 | 0 | 0.2918 | 0 | 0 | |

E_{i} | 0.0289 | 0.0023 | 0 | 0.0042 | 0.0644 | 0.1205 | 0.0334 | 0.0174 | 0 | 0.0203 | 0 | 0 | |

T_{2}, T_{3} | ${f}_{i}$ | 0.1633 | 0 | 0 | 0 | 0.0854 | 0.4296 | 0.1985 | 0.0578 | 0 | 0.0226 | 0 | 0.0302 |

$\overline{{E}_{i}}$ | 0.3727 | 0 | 0 | 0 | 0.5650 | 0.5005 | 0.2120 | 0.3981 | 0 | 0.6550 | 0 | 0.5400 | |

E_{i} | 0.0609 | 0 | 0 | 0 | 0.0483 | 0.2151 | 0.0421 | 0.0230 | 0 | 0.0148 | 0 | 0.0163 | |

T_{2}, T_{4} | ${f}_{i}$ | 0.2111 | 0 | 0 | 0 | 0.0427 | 0.2563 | 0.1231 | 0 | 0 | 0.0427 | 0 | 0.2739 |

$\overline{{E}_{i}}$ | 0.2440 | 0 | 0 | 0 | 0.5755 | 0.4892 | 0.2553 | 0 | 0 | 0.6599 | 0 | 0.4480 | |

E_{i} | 0.0515 | 0 | 0 | 0 | 0.0246 | 0.1254 | 0.0314 | 0 | 0 | 0.0282 | 0 | 0.1227 | |

T_{3}, T_{4} | ${f}_{i}$ | 0.2601 | 0 | 0 | 0 | 0.0934 | 0.1086 | 0.1010 | 0.0985 | 0 | 0.0253 | 0 | 0.3131 |

$\overline{{E}_{i}}$ | 0.3210 | 0 | 0 | 0 | 0.6009 | 0.5951 | 0.1894 | 0.3213 | 0 | 0.7471 | 0 | 0.4510 | |

E_{i} | 0.0835 | 0 | 0 | 0 | 0.0561 | 0.0646 | 0.0191 | 0.0316 | 0 | 0.0189 | 0 | 0.1412 | |

sum | 0.2636 | 0.0023 | 0.0012 | 0.0042 | 0.2105 | 0.8808 | 0.1810 | 0.1270 | 0.0010 | 0.0880 | 0.0012 | 0.3719 | |

rank | 3 | 10 | 11 | 9 | 4 | 1 | 5 | 6 | 12 | 7 | 11 | 2 |

Difference Features | Index | Fusion Algorithm | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | A_{7} | A_{8} | A_{9} | A_{10} | A_{11} | A_{12} | ||

T_{1}, T_{2} | ${f}_{i}$ | 0 | 0.2553 | 0.0184 | 0 | 0.3289 | 0.0474 | 0.1263 | 0.0184 | 0.0145 | 0.0094 | 0 | 0.1158 |

$\overline{{E}_{i}}$ | 0 | 0.6891 | 0.8492 | 0 | 0.6361 | 0.8124 | 0.7805 | 0.8492 | 0.6549 | 0.0851 | 0 | 0.6876 | |

E_{i} | 0 | 0.1759 | 0.0156 | 0 | 0.2092 | 0.0385 | 0.0986 | 0.0156 | 0.0095 | 0.0008 | 0 | 0.0796 | |

T_{1}, T_{3} | ${f}_{i}$ | 0.0797 | 0.1087 | 0 | 0 | 0.5966 | 0.1522 | 0 | 0 | 0 | 0 | 0.0338 | 0.0072 |

$\overline{{E}_{i}}$ | 0.7975 | 0.6974 | 0 | 0 | 0.6790 | 0.7858 | 0 | 0 | 0 | 0 | 0.7048 | 0.7717 | |

E_{i} | 0.0636 | 0.0758 | 0 | 0 | 0.4051 | 0.1196 | 0 | 0 | 0 | 0 | 0.0238 | 0.0056 | |

T_{1}, T_{4} | ${f}_{i}$ | 0 | 0.2746 | 0.0405 | 0 | 0.2197 | 0.1069 | 0.1012 | 0.0405 | 0.0825 | 0 | 0 | 0.2572 |

$\overline{{E}_{i}}$ | 0 | 0.6857 | 0.6456 | 0 | 0.5714 | 0.8249 | 0.7746 | 0.6456 | 0.2839 | 0 | 0 | 0.6969 | |

E_{i} | 0 | 0.1883 | 0.0261 | 0 | 0.1255 | 0.0882 | 0.0784 | 0.0261 | 0.0234 | 0 | 0 | 0.1793 | |

T_{2}, T_{3} | ${f}_{i}$ | 0.0150 | 0 | 0 | 0 | 0.6675 | 0.1925 | 0.0425 | 0 | 0.1457 | 0.0246 | 0 | 0 |

$\overline{{E}_{i}}$ | 0.5056 | 0 | 0 | 0 | 0.2652 | 0.4916 | 0.4146 | 0 | 0.4015 | 0.0285 | 0 | 0 | |

E_{i} | 0.0076 | 0 | 0 | 0 | 0.1770 | 0.0946 | 0.0176 | 0 | 0.0585 | 0.0007 | 0 | 0 | |

T_{2}, T_{4} | ${f}_{i}$ | 0 | 0 | 0 | 0.0025 | 0.4347 | 0.0779 | 0.1382 | 0 | 0.0023 | 0 | 0.0553 | 0.1457 |

$\overline{{E}_{i}}$ | 0 | 0 | 0 | 0.3074 | 0.1668 | 0.4844 | 0.4525 | 0 | 0.6105 | 0 | 0.3465 | 0.2850 | |

E_{i} | 0 | 0 | 0 | 0.0008 | 0.0725 | 0.0377 | 0.0625 | 0 | 0.0014 | 0 | 0.0192 | 0.0415 | |

T_{3}, T_{4} | ${f}_{i}$ | 0.0090 | 0 | 0 | 0.0045 | 0.6014 | 0.2545 | 0.0383 | 0 | 0 | 0 | 0.0180 | 0.0721 |

$\overline{{E}_{i}}$ | 0.7382 | 0 | 0 | 0.2611 | 0.1995 | 0.4321 | 0.3799 | 0 | 0 | 0 | 0.3426 | 0.3236 | |

E_{i} | 0.0067 | 0 | 0 | 0.0012 | 0.1200 | 0.1100 | 0.0145 | 0 | 0 | 0 | 0.0062 | 0.0233 | |

sum | 0.0778 | 0.4400 | 0.0418 | 0.0019 | 1.1094 | 0.4886 | 0.2716 | 0.0049 | 0.1705 | 0.0015 | 0.0492 | 0.3293 | |

rank | 7 | 3 | 9 | 11 | 1 | 2 | 5 | 10 | 6 | 12 | 8 | 4 |

Group | Method | Evaluation Index | R | Rank | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

X_{1} | X_{2} | X_{3} | X_{4} | X_{5} | X_{6} | X_{7} | X_{8} | ||||

1 | A_{1} | 0.5791 | 0.4356 | 0.7113 | 0.3051 | 0.5886 | 0.4116 | 3.1011 | 0.0534 | 36 | 2 |

A_{2} | 0.3698 | 0.3807 | 0.5591 | 0.2022 | 0.6174 | 0.3445 | 4.3507 | 0.0637 | 64 | 10 | |

A_{3} | 0.5734 | 0.4118 | 0.7060 | 0.2878 | 0.4635 | 0.3886 | 2.8213 | 0.0556 | 58 | 8 | |

A_{4} | 0.4056 | 0.3777 | 0.5651 | 0.1905 | 0.4327 | 0.3432 | 3.1173 | 0.0376 | 82 | 12 | |

A_{5} | 0.5587 | 0.4005 | 0.6697 | 0.2745 | 0.5100 | 0.3693 | 3.0407 | 0.0485 | 55 | 7 | |

A_{6} | 0.5873 | 0.4663 | 0.6353 | 0.2743 | 0.8514 | 0.4385 | 7.1886 | 0.0686 | 21 | 1 | |

A_{7} | 0.4721 | 0.3851 | 0.5955 | 0.2101 | 0.6797 | 0.3510 | 6.3275 | 0.0597 | 51 | 6 | |

A_{8} | 0.3651 | 0.3095 | 0.6639 | 0.2452 | 0.4863 | 0.2724 | 3.3568 | 0.0487 | 72 | 11 | |

A_{9} | 0.3621 | 0.4446 | 0.6110 | 0.2366 | 0.5029 | 0.4141 | 3.4465 | 0.0313 | 62 | 9 | |

A_{10} | 0.4007 | 0.4531 | 0.5648 | 0.2173 | 0.7542 | 0.4633 | 4.0854 | 0.0418 | 50 | 5 | |

A_{11} | 0.4587 | 0.4214 | 0.6708 | 0.2751 | 0.6502 | 0.3978 | 3.0044 | 0.0668 | 41 | 4 | |

A_{12} | 0.4511 | 0.5241 | 0.5441 | 0.2582 | 0.5451 | 0.5197 | 7.4121 | 0.0558 | 40 | 3 | |

2 | A_{1} | 0.4536 | 0.3853 | 0.5386 | 0.3719 | 0.1691 | 4.5003 | 0.0605 | 0.1259 | 53 | 7 |

A_{2} | 0.4849 | 0.3779 | 0.657 | 0.374 | 0.31 | 1.9077 | 0.0538 | 0.2986 | 37 | 3 | |

A_{3} | 0.4895 | 0.3549 | 0.6488 | 0.3458 | 0.1678 | 1.5654 | 0.0459 | 0.2517 | 64 | 10 | |

A_{4} | 0.4319 | 0.3421 | 0.5639 | 0.3305 | 0.159 | 2.7579 | 0.043 | 0.1568 | 77 | 11 | |

A_{5} | 0.4921 | 0.4368 | 0.6406 | 0.4851 | 0.2989 | 8.0634 | 0.0657 | 0.3351 | 17 | 1 | |

A_{6} | 0.4663 | 0.3883 | 0.6753 | 0.3824 | 0.268 | 1.9236 | 0.066 | 0.2915 | 32 | 2 | |

A_{7} | 0.4377 | 0.3666 | 0.6813 | 0.3546 | 0.2708 | 1.6754 | 0.0659 | 0.2613 | 50 | 5 | |

A_{8} | 0.4398 | 0.3846 | 0.5538 | 0.3676 | 0.1829 | 4.4382 | 0.0654 | 0.1175 | 57 | 9 | |

A_{9} | 0.4477 | 0.377 | 0.5654 | 0.3211 | 0.2021 | 5.2334 | 0.0489 | 0.322 | 51 | 6 | |

A_{10} | 0.2843 | 0.0524 | 0.0652 | 0.0244 | 0.0255 | 4.6624 | 0.0354 | 0.0203 | 88 | 12 | |

A_{11} | 0.4442 | 0.3704 | 0.6375 | 0.3619 | 0.2823 | 2.2638 | 0.0504 | 0.227 | 54 | 8 | |

A_{12} | 0.5028 | 0.4665 | 0.5359 | 0.4711 | 0.1699 | 6.3297 | 0.048 | 0.1505 | 43 | 4 |

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## Share and Cite

**MDPI and ACS Style**

Ji, L.; Yang, F.; Guo, X.
Image Fusion Algorithm Selection Based on Fusion Validity Distribution Combination of Difference Features. *Electronics* **2021**, *10*, 1752.
https://doi.org/10.3390/electronics10151752

**AMA Style**

Ji L, Yang F, Guo X.
Image Fusion Algorithm Selection Based on Fusion Validity Distribution Combination of Difference Features. *Electronics*. 2021; 10(15):1752.
https://doi.org/10.3390/electronics10151752

**Chicago/Turabian Style**

Ji, Linna, Fengbao Yang, and Xiaoming Guo.
2021. "Image Fusion Algorithm Selection Based on Fusion Validity Distribution Combination of Difference Features" *Electronics* 10, no. 15: 1752.
https://doi.org/10.3390/electronics10151752