Infrared Image Fusion Algorithm Selection Based on Joint Drop Shadow of Possibility Distributions

T-module operator	Correlation of x, y	$p_{x, y}$
$T_{1} (x, y) = m a x (0, x + y - 1)$	Extremely negative correlation	$[- 1, - 0.5)$
$T_{2} (x, y) = m a x (0, (x^{0.5} + y^{0.5} {- 1))}^{2}$	Negative correlation	$[- 0.5,0)$
$T_{3} (x, y) = x \cdot y$	Irrelevant	$[0,0.2)$
$T_{4} (x, y) = (x^{- 0.5} + y^{- 0.5} {C 1)}^{- 0.5}$	Weak positive correlation	$[0.2,0.4)$
$T_{5} (x, y) = (x^{- 1} + y^{- 1} {- 1)}^{- 1}$	Positive correlation	$[0.4,0.6)$
$T_{6} (x, y) = m i n (x, y)$	Extremely positive correlation	$[0.6,1)$

Table 2. The first group of heterogeneous difference feature weight function synthesis rules
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Table 2. The first group of heterogeneous difference feature weight function synthesis rules
Feature weight function Q₁、Q₂ Q₂、Q₃ Q₃、Q₄ Q₄、Q₁ Q₂、Q₄ Q₁、Q₃
T-module operator T₃ T₃ T₃ T₆ T₆ T₆

Table 3. The second group of heterogeneous difference feature weight function synthesis rules
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Table 3. The second group of heterogeneous difference feature weight function synthesis rules
Feature weight function Q₁、Q₂ Q₂、Q₃ Q₃、Q₄ Q₄、Q₁ Q₂、Q₄ Q₁、Q₃
T-module operator T₄ T₄ T₄ T₆ T₆ T₆

Table 4. D_iof different fusion algorithms of the first group

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Table 4. D_iof different fusion algorithms of the first group

Difference features	Index	Fusion algorithm
Difference features	Index	A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉	A₁₀	A₁₁
Q₁、Q₂	$f_{i}$	0.014 8	0	0	0.023 7	0.005 9	0.020 7	0.221 9	0.665 7	0	0.005 9	0.041 4
	$\bar{E_{i}}$	0.222 6	0	0	0.381 3	0.598 0	0.214 0	0.210 1	0.343 9	0	0.203 1	0.266 5
	D_i	0.003 3	0	0	0.009 0	0.0035	0.004 4	0.046 6	0.228 9	0	0.001 2	0.011 0
Q₁、Q₃	$f_{i}$	0.009 4	0	0.128 8	0.025 8	0.264 6	0.103 0	0.058 5	0.405 2	0	0	0.004 7
	$\bar{E_{i}}$	0.268 8	0	0.426 7	0.312 5	0.333 3	0.334 1	0.143 0	0.311 8	0	0	0.228 2
	D_i	0.002 5	0	0.055 0	0.008 1	0.088 2	0.034 4	0.008 4	0.126 3	0	0	0.001 1
Q₁、Q₄	$f_{i}$	0.069 7	0.014 9	0.064 7	0.119 4	0	0.159 2	0.174 1	0.338 3	0.010 0	0	0.049 8
	$\bar{E_{i}}$	0.291 8	0.281 4	0.269 1	0.539 3	0	0.181 8	0.191 7	0.356 1	0.226 4	0	0.205 6
	D_i	0.020 3	0.004 2	0.017 4	0.064 4	0	0.028 9	0.033 4	0.120 5	0.002 3	0	0.010 2
Q₂、Q₃	$f_{i}$	0.022 6	0	0.057 8	0.085 4	0.030 2	0.163 3	0.198 5	0.429 6	0	0	0.012 6
	$\bar{E_{i}}$	0.655 0	0	0.398 1	0.565 0	0.540 0	0.372 7	0.212 0	0.500 5	0	0	0.665 1
	D_i	0.014 8	0	0.023 0	0.048 3	0.016 3	0.060 9	0.042 1	0.215 1	0	0	0.008 4
Q₂、Q₄	$f_{i}$	0.042 7	0	0	0.042 7	0.273 9	0.211 1	0.123 1	0.256 3	0	0	0.050 3
	$\bar{E_{i}}$	0.659 9	0	0	0.575 5	0.448 0	0.244 0	0.255 3	0.489 2	0	0	0.722 6
	D_i	0.028 2	0	0	0.024 6	0.122 7	0.051 5	0.031 4	0.125 4	0	0	0.036 3
Q₃、Q₄	$f_{i}$	0.025 3	0	0.098 5	0.093 4	0.313 1	0.260 1	0.101 0	0.108 6	0	0	0
	$\bar{E_{i}}$	0.747 1	0	0.321 3	0.600 9	0.451 0	0.321 0	0.189 4	0.595 1	0	0	0
	D_i	0.018 9	0	0.031 6	0.056 1	0.141 2	0.083 5	0.019 1	0.064 6	0	0	0
Sum		0.088 0	0.004 2	0.127 0	0.210 5	0.371 9	0.263 6	0.181 0	0.880 8	0.002 3	0.001 2	0.067 0
Rank		7	9	6	4	2	3	5	1	10	11	8

Table 5. D_iof different fusion algorithms of the second group

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Table 5. D_iof different fusion algorithms of the second group

Difference features	Index	Fusion algorithm
Difference features	Index	A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉	A₁₀	A₁₁
Q₁、Q₂	$f_{i}$	0	0.115 8	0	0.126 3	0	0	0.255 3	0.047 4	0.018 4	0.328 9	0.107 9
	$\bar{E_{i}}$	0	0.687 6	0	0.780 5	0	0	0.689 1	0.812 4	0.849 2	0.636 1	0.719 8
	D_i	0	0.079 6	0	0.098 6	0	0	0.175 9	0.038 5	0.015 6	0.209 2	0.077 7
Q₁、Q₃	$f_{i}$	0.007 2	0.007 2	0	0	0.033 8	0.079 7	0.108 7	0.152 2	0	0.596 6	0.014 5
	$\bar{E_{i}}$	0.675 5	0.771 7	0	0	0.704 8	0.797 5	0.697 4	0.785 8	0	0.679 0	0.654 9
	D_i	0.004 9	0.005 6	0	0	0.023 8	0.063 6	0.075 8	0.119 6	0	0.405 1	0.009 5
Q₁、Q₄	$f_{i}$	0	0.257 2	0	0.101 2	0	0	0.274 6	0.106 9	0.040 5	0.219 7	0
	$\bar{E_{i}}$	0	0.696 9	0	0.774 6	0	0	0.685 7	0.824 9	0.645 6	0.571 4	0
	D_i	0	0.179 3	0	0.078 4	0	0	0.188 3	0.088 2	0.026 1	0.125 5	0
Q₂、Q₃	$f_{i}$	0	0	0	0.042 5	0	0.015 0	0	0.192 5	0	0.667 5	0.082 5
	$\bar{E_{i}}$	0	0	0	0.414 6	0	0.505 6	0	0.491 6	0	0.265 2	0.283 9
	D_i	0	0	0	0.017 6	0	0.007 6	0	0.094 6	0	0.177 0	0.023 4
Q₂、Q₄	$f_{i}$	0	0.145 7	0.002 5	0.138 2	0.055 3	0	0	0.077 9	0	0.434 7	0.145 7
	$\bar{E_{i}}$	0	0.285 0	0.307 4	0.452 5	0.346 5	0	0	0.484 4	0	0.166 8	0.401 5
	D_i	0	0.041 5	0.000 8	0.062 5	0.019 2	0	0	0.037 7	0	0.072 5	0.058 5
Q₃、Q₄	$f_{i}$	0	0.072 1	0.004 5	0.038 3	0.018 0	0.009 0	0	0.254 5	0	0.601 4	0.002 3
	$\bar{E_{i}}$	0	0.323 6	0.261 1	0.379 9	0.342 6	0.738 2	0	0.432 1	0	0.199 5	0.610 5
	D_i	0	0.023 3	0.001 2	0.014 5	0.006 2	0.006 7	0	0.110 0	0	0.120 0	0.001 4
Sum		0.004 9	0.329 3	0.001 9	0.271 6	0.049 2	0.077 8	0.440 0	0.488 6	0.041 8	1.109 4	0.170 5
Rank		10	4	11	5	8	7	3	2	9	1	6

Table 6. Evaluation index of different fusion algorithms of images

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Table 6. Evaluation index of different fusion algorithms of images

Image	Method	Evaluation index								R_i	Rank
Image	Method	X₁	X₂	X₃	X₄	X₅	X₆	X₇	X₈	R_i	Rank
1	A₁	0.534 2	0.454 7	0.563 1	0.224 1	0.186 4	0.447 7	0.354 4	0.066 9	37	3
	A₂	0.391 2	0.394 0	0.612 7	0.136 2	0.252 9	0.387 3	0.242 1	0.057 1	70	10
	A₃	0.419 0	0.434 3	0.613 9	0.181 6	0.473 0	0.416 0	0.364 5	0.081 5	45	5
	A₄	0.541 5	0.435 4	0.634 4	0.247 7	0.462 7	0.495 5	0.693 9	0.067 2	30	2
	A₅	0.410 7	0.434 1	0.625 2	0.173 0	0.471 6	0.412 6	0.364 2	0.079 1	50	7
	A₆	0.560 3	0.495 0	0.473 0	0.222 9	0.330 2	0.495 1	0.835 1	0.057 6	39	4
	A₇	0.045 9	0.001 4	0.003 5	0.000 1	0.004 4	0.000 7	0.100 4	0.060 9	77	11
	A₈	0.7028	0.485 8	0.669 0	0.222 0	0.477 0	0.449 8	0.776 6	0.082 3	20	1
	A₉	0.452 5	0.429 1	0.648 2	0.158 4	0.383 3	0.418 0	0.275 4	0.083 3	48	6
	A₁₀	0.360 0	0.437 9	0.617 1	0.134 6	0.391 2	0.428 4	0.294 8	0.061 4	58	9
	A₁₁	0.421 5	0.398 8	0.660 0	0.145 4	0.383 5	0.390 9	0.252 5	0.082 7	54	8
2	A₁	0.455 5	0.466 7	0.715 8	0.261 0	0.454 2	0.452 2	0.418 1	0.020 6	46	5
	A₂	0.542 4	0.396 1	0.770 5	0.294 4	0.438 3	0.384 6	0.275 4	0.030 7	50	7
	A₃	0.468 4	0.423 2	0.673 3	0.265 7	0.442 8	0.393 7	0.420 1	0.033 1	51	8
	A₄	0.535 2	0.502 6	0.539 1	0.281 5	0.442 0	0.494 6	0.709 9	0.035 3	37	3
	A₅	0.403 0	0.402 0	0.618 2	0.239 5	0.413 2	0.370 2	0.418 7	0.030 5	68	11
	A₆	0.524 2	0.523 7	0.537 0	0.249 5	0.343 6	0.516 2	0.777 4	0.020 2	51	9
	A₇	0.522 7	0.420 8	0.748 3	0.286 0	0.567 9	0.402 2	0.301 5	0.028 3	45	4
	A₈	0.502 9	0.402 0	0.734 0	0.233 6	0.409 9	0.382 9	0.350 6	0.025 6	67	10
	A₉	0.545 4	0.430 1	0.780 0	0.285 6	0.522 0	0.410 5	0.309 5	0.034 3	35	2
	A₁₀	0.571 5	0.527 3	0.536 3	0.295 6	0.549 9	0.493 1	0.739 5	0.024 8	31	1
	A₁₁	0.524 7	0.388 9	0.785 8	0.285 7	0.548 7	0.380 6	0.272 7	0.036 2	47	6

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Linna JI, Xiaoming GUO, Fengbao YANG, Yaling ZHANG. Infrared Image Fusion Algorithm Selection Based on Joint Drop Shadow of Possibility Distributions[J]. Acta Photonica Sinica, 2021, 50(4): 228

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