Gaussian of Differences: A Simple and Efficient General Image Fusion Method
<p>Proposed general image fusion method based on pixel-based linear weighting using the Gaussian of differences (GD).</p> "> Figure 2
<p>Sample input images (<span class="html-italic">I</span><sub>1</sub> and <span class="html-italic">I</span><sub>2</sub>) [<a href="#B54-entropy-25-01215" class="html-bibr">54</a>] and their column and row differences.</p> "> Figure 3
<p>Combined difference images (<span class="html-italic">D</span>) of the input images.</p> "> Figure 4
<p>Gaussian of differences (<span class="html-italic">GD</span>) of the input images.</p> "> Figure 5
<p>Weighting factors (<span class="html-italic">fw</span>) for the input images.</p> "> Figure 6
<p>Fused image (<span class="html-italic">F</span>).</p> "> Figure 7
<p>Gaussian kernel (<span class="html-italic">w</span>) for <span class="html-italic">s</span> = 3 and <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 8
<p>Optimization of the parameters of the proposed GD fusion method.</p> "> Figure 9
<p>Multi-modal medical images used in the experiments.</p> "> Figure 10
<p>Multi-sensor infrared and visible images used in the experiments.</p> "> Figure 11
<p>Multi-focus images used in the experiments.</p> "> Figure 12
<p>Multi-exposure images used in the experiments.</p> "> Figure 13
<p>Medical image set M#2 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 14
<p>Medical image set M#5 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 15
<p>Infrared and visible image set IV#4 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 16
<p>Infrared and visible image set IV#5 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 17
<p>Multi-focus image set F#11 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 18
<p>Multi-focus image set F#15 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 19
<p>Multi-exposure image set E#5 (Images A and B) and their fusion image results, obtained using comparison methods.</p> "> Figure 20
<p>Multi-exposure image set E#6 (Images A and B) and their fusion image results, obtained using comparison methods.</p> ">
Abstract
:1. Introduction
1.1. Related Work
1.2. Contributions of This Study and Advantages of the Proposed Method
- The proposed algorithm does not use any transformations and works directly in the pixel domain. Also, it is based on basic image convolution and linear weighting, which makes it simple and efficient. It can be implemented on real-time systems and is suitable for parallel processing.
- The method enhances the high-frequency components of each input image using simple first-order derivative edge detection. It then uses a Gaussian filter to weight the contributions of neighboring pixels to the center pixel, with the weight decreasing with distance.
- The proposed GD method has only two control parameters: the size of the filter and the standard deviation of the distribution. In addition to making use of predefined parameters, an optimal solution using the pattern search (PS) algorithm is also proposed to investigate the adaptability capability of the GD method.
- The method is a general-purpose image fusion algorithm that can be used in a variety of applications, including multi-modal medical image fusion, infrared and visible image fusion for enhanced night vision or remote sensing, multi-focus image fusion for extending the depth of field, and multi-exposure image fusion for high dynamic range imaging.
- It can combine single-band (gray-level), color (RGB), multi-spectral, and hyperspectral images due to its generalized structure.
2. Proposed Method
- Edge information is generally related with the information content of an image. The first-order derivation (difference of adjacent pixels) of an image simply emphasizes the edges. The column and row differences of each input image are calculated:
- 2.
- Column and row differences emphasize the edges along vertical and horizontal axes, respectively. To combine them into a single representation (D), the Euclidian distance is used, and features related with each pixel based on the edge content are calculated (visualized in Figure 3):
- 3.
- Linear weighting is a well-known approach used to determine the information transfer of each input image to the output fused image. To determine the contributions of neighbors of pixels in each image at different input images to the information content of the respective pixel, the differences are filtered (i.e., weighted) using a 2D Gaussian filter and the Gaussian of the Differences is obtained (GD), which is visualized in Figure 4. This representation will be used to calculate the weighting factor of each pixel:
- 4.
- Weighting factors (fw) are determined for the pixels in each input image using GD proportional to their values, as visualized in Figure 5. Therefore, the sum of the weighting coefficients of a specific pixel is always equal to one, regardless of how many input images exist:
- 5.
- The fused image (F), as demonstrated in Figure 6, is created with the linear weighting method using weighting factors. Assume that there are two input images in an application, and for a specific pixel, let the fws be 0.4 and 0.6, respectively. The fusion result of that specific pixel is summation of 40% of the first input image’s pixel value ) and 60% of the second input image ).
Optimization of GD Parameters
- Define the maximum iteration number of PS and set the initial values of GD parameters.
- Evaluate the initial solution and calculate its fitness value (overall quality of the fused image):
- a.
- Apply all steps of the proposed GD fusion method explained in the previous section (Equations (1)–(6)).
- b.
- Calculate the fused image quality using an image metric (see Section 3.3).
- 3.
- Apply the operators of PS to find a better GD parameter solution that maximizes the fused image quality.
- 4.
- Repeat Steps 2 and 3 until the maximum iteration number or a predefined stopping condition is reached.
3. Experimental Results
- First, a predefined parameter set for GD was used. s values of 5, 10, and 15 values, named GD5, GD10, and GD15, respectively, were evaluated. In this case, the second parameter was defined according to the value of the filter size, .
- Second, the parameters of GD were adaptively determined by using the pattern search optimization algorithm to maximize the image quality. Unreported intensive experiments have shown that using Qabf, Qcb, and Qcv as fitness functions generates the best results. Therefore, the versions of this case were named GDPSQABF, GDPSQCB, and GDPSQCV, respectively.
3.1. Image Dataset
3.2. Experimental Setup
3.3. Objective Quality Metrics
3.4. Medical Image Fusion
3.5. Infrared and Visible Image Fusion
3.6. Multi-Focus Image Fusion
3.7. Multi-Exposure Image Fusion
3.8. Overall Comparison
4. Conclusions
- It is based on basic image convolution and linear weighting. Thus, the main algorithm is very simple and can be implemented on embedded systems and PCs and easily parallelized on multiple CPU or GPU cores.
- It is a pixel-based image fusion method, and the method does not utilize an image transform. Moreover, it does not require a training phase. Therefore, the proposed method is pretty fast compared to state-of-the-art fusion methods.
- The method relies on transferring information from each input image by enhancing the high-frequency components using simple, first-order derivative edge detection. Neighboring pixels also contribute to the center pixel’s weighting, proportional to their distance, using a Gaussian filter.
- The method has only two control parameters. In this paper, we define some predefined parameter sets and explore their performance. And a simple optimal solution to determine the adaptively control parameters is also proposed and compared.
- It can be used in any kind of image fusion application, such as multi-modal medical image fusion, infrared and visible image fusion for enhanced night vision, multi-focus image fusion for extending the depth of field, and multi-exposure image fusion for high-dynamic-range imaging.
- It can fuse more than two input images with the help of its generalized structure. Therefore, it can be used in future studies to fuse multi-spectral and hyperspectral images with 10–200 input images corresponding to different wavelengths in the visible and non-visible spectrum.
Supplementary Materials
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
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Application | Images in Dataset | Image Type | Resolution |
---|---|---|---|
Multi-modal medical | 8 | Graylevel TIF | 256 × 256 |
Multi-sensor infrared and visible | 14 | Graylevel PNG | 360 × 270, 430 × 340, 512 × 512, 632 × 496 |
Multi-focus | 20 | RGB JPG | 520 × 520 |
Multi-exposure | 6 | RGB JPG | 340 × 230, 230 × 340, 752 × 500 |
Total | 48 | - | - |
Environmental Feature | Description |
---|---|
Operating system | Windows 10 Pro |
CPU | Intel i7-4790K @ 4 GHz |
GPU | Nvidia GeForce GTX 760 |
RAM | 16 GB |
Programming language | MATLAB 2023a |
Fusion Method | Configuration Parameters |
---|---|
ADF | num_iter = 10, delta_t = 0.15, kappa = 30, option = 1 |
CBF | cov_wsize = 5, sigmas = 1.8, sigmar = 25, ksize = 11 |
FPDE | n = 15, dt = 0.9, k = 4 |
GFCE | nLevel = 4, sigma = 2, k = 2, r0 = 2, eps0 = 0.1, l = 2 |
GTF | adapt_epsR = 1, epsR_cutoff = 0.01, adapt_epsF = 1, epsF_cutoff = 0.05, pcgtol_ini = 1 × 10−4, loops = 5, pcgtol_ini = 1 × 10−2, adaptPCGtol = 1, |
HMSD | nLevel = 4, lambda = 30, sigma = 2.0, sigma_r = 0.05, k = 2, |
IFEVIP | QuadNormDim = 512, QuadMinDim = 32, GaussScale = 9, MaxRatio = 0.001, StdRatio = 0.8, |
MSVD | - |
VSMWLS | sigma_s = 2, sigma_r = 0.05 |
CNN | type = siamese network, weights_b1_1 = 9 ∗ 64, weights_b1_2 = 64 ∗ 9 ∗ 128, weights_b1_3 = 128 ∗ 9 ∗ 256, weights_output= 512 ∗ 64 ∗ 2 |
Proposed GD5 | s = 5, σ = 1.6 |
Proposed GD10 | s = 10, σ = 3.3 |
Proposed GD15 | s = 15, σ = 5 |
Proposed GDPSQABF | optimizer = pattern search, algorithm = classic, init_sol = [10; 3.3], lb = [5; 1], ub = [80; 100], max_iter = 20, fit_fun = −1 ∗ Qabf |
Proposed GDPSQCB | optimizer = pattern search, algorithm = classic, init_sol = [10; 3.3], lb = [5; 1], ub = [80; 100], max_iter = 20, fit_fun = −1 ∗ Qcb |
Proposed GDPSQCV | optimizer = pattern search, algorithm = classic, init_sol = [10; 3.3], lb = [5; 1], ub = [80; 100], max_iter = 20, fit_fun = Qcv |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 4.783 | 2.308 | 59.298 | 0.467 | 1.498 | 0.363 | 1.281 | 0.076 | 858.898 |
CBF | 5.015 | 2.494 | 58.979 | 0.531 | 1.496 | 0.407 | 1.198 | 0.082 | 858.355 |
FPDE | 4.836 | 2.339 | 59.397 | 0.433 | 1.505 | 0.348 | 1.190 | 0.075 | 840.941 |
GFCE | 7.615 | 2.190 | 53.849 | 0.474 | 0.463 | 0.389 | 4.502 | 0.268 | 1643.875 |
GTF | 4.813 | 2.248 | 58.770 | 0.574 | 1.486 | 0.637 | 0.831 | 0.086 | 1154.964 |
HMSD | 4.831 | 2.286 | 58.628 | 0.550 | 1.488 | 0.442 | 0.852 | 0.089 | 999.258 |
IFEVIP | 5.153 | 2.457 | 57.528 | 0.484 | 1.495 | 0.365 | 1.352 | 0.115 | 1242.540 |
MSVD | 4.823 | 2.368 | 57.327 | 0.471 | 0.690 | 0.201 | 5.933 | 0.120 | 813.834 |
VSMWLS | 5.024 | 2.352 | 59.033 | 0.529 | 1.530 | 0.469 | 0.667 | 0.081 | 964.498 |
CNN | 4.932 | 2.337 | 58.484 | 0.554 | 1.505 | 0.603 | 0.705 | 0.092 | 1016.499 |
GD5 | 4.901 | 2.478 | 59.209 | 0.506 | 1.519 | 0.389 | 1.247 | 0.078 | 805.711 |
GD10 | 4.854 | 2.463 | 59.300 | 0.479 | 1.522 | 0.393 | 1.220 | 0.076 | 780.445 |
GD15 | 4.819 | 2.452 | 59.342 | 0.464 | 1.522 | 0.391 | 1.208 | 0.076 | 773.312 |
GDPSQABF | 4.934 | 2.471 | 59.145 | 0.516 | 1.514 | 0.386 | 1.236 | 0.079 | 841.810 |
GDPSQCB | 4.862 | 2.472 | 59.280 | 0.485 | 1.521 | 0.390 | 1.240 | 0.077 | 785.127 |
GDPSQCV | 4.796 | 2.443 | 59.369 | 0.456 | 1.524 | 0.392 | 1.145 | 0.075 | 781.420 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 5.975 | 2.288 | 56.459 | 0.408 | 1.170 | 0.503 | 0.329 | 0.147 | 845.674 |
CBF | 5.962 | 2.571 | 56.592 | 0.512 | 1.289 | 0.511 | 0.293 | 0.143 | 523.914 |
FPDE | 6.408 | 2.122 | 56.007 | 0.305 | 1.019 | 0.475 | 0.404 | 0.163 | 896.311 |
GFCE | 7.311 | 2.382 | 54.953 | 0.447 | 0.964 | 0.492 | 2.920 | 0.208 | 751.841 |
GTF | 6.006 | 2.386 | 55.932 | 0.404 | 1.275 | 0.431 | 0.287 | 0.166 | 1677.168 |
HMSD | 6.400 | 2.435 | 56.376 | 0.513 | 1.324 | 0.519 | 0.564 | 0.150 | 549.287 |
IFEVIP | 6.348 | 2.554 | 55.266 | 0.528 | 1.338 | 0.508 | 0.798 | 0.193 | 628.882 |
MSVD | 5.752 | 2.405 | 56.837 | 0.404 | 1.183 | 0.386 | 3.935 | 0.135 | 694.471 |
VSMWLS | 6.170 | 2.659 | 56.588 | 0.512 | 1.355 | 0.524 | 0.344 | 0.143 | 495.160 |
CNN | 6.913 | 2.585 | 56.001 | 0.571 | 1.277 | 0.533 | 1.427 | 0.163 | 449.774 |
GD5 | 5.822 | 2.557 | 56.906 | 0.473 | 1.352 | 0.467 | 0.329 | 0.133 | 500.209 |
GD10 | 5.791 | 2.574 | 56.966 | 0.453 | 1.371 | 0.479 | 0.338 | 0.131 | 454.096 |
GD15 | 5.776 | 2.562 | 56.997 | 0.436 | 1.374 | 0.470 | 0.340 | 0.130 | 454.362 |
GDPSQABF | 5.820 | 2.553 | 56.901 | 0.474 | 1.349 | 0.483 | 0.327 | 0.133 | 511.725 |
GDPSQCB | 5.796 | 2.564 | 56.954 | 0.457 | 1.367 | 0.481 | 0.331 | 0.131 | 455.932 |
GDPSQCV | 5.782 | 2.568 | 56.983 | 0.444 | 1.373 | 0.474 | 0.339 | 0.130 | 452.181 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 6.132 | 1.468 | 60.947 | 0.470 | 1.045 | 0.434 | 0.790 | 0.052 | 118.387 |
CBF | 6.730 | 1.919 | 59.715 | 0.632 | 1.102 | 0.473 | 0.782 | 0.069 | 211.646 |
FPDE | 6.159 | 1.325 | 60.930 | 0.481 | 1.027 | 0.434 | 0.740 | 0.052 | 119.226 |
GFCE | 7.644 | 1.231 | 55.427 | 0.391 | 0.465 | 0.393 | 2.065 | 0.186 | 646.551 |
GTF | 6.161 | 1.016 | 60.122 | 0.311 | 0.863 | 0.310 | 0.575 | 0.063 | 160.482 |
HMSD | 6.070 | 1.485 | 60.356 | 0.579 | 0.998 | 0.462 | 0.391 | 0.060 | 165.976 |
IFEVIP | 6.869 | 2.143 | 59.503 | 0.670 | 1.129 | 0.469 | 0.891 | 0.073 | 206.815 |
MSVD | 6.024 | 1.578 | 60.779 | 0.309 | 0.944 | 0.339 | 5.285 | 0.054 | 154.207 |
VSMWLS | 6.297 | 1.403 | 60.621 | 0.617 | 1.072 | 0.437 | 0.494 | 0.056 | 145.077 |
CNN | 5.735 | 1.350 | 60.244 | 0.562 | 0.956 | 0.424 | 0.282 | 0.061 | 178.710 |
GD5 | 6.672 | 1.791 | 60.006 | 0.628 | 1.135 | 0.469 | 0.812 | 0.065 | 152.836 |
GD10 | 6.670 | 1.761 | 60.027 | 0.632 | 1.148 | 0.470 | 0.798 | 0.065 | 146.837 |
GD15 | 6.665 | 1.723 | 60.052 | 0.629 | 1.151 | 0.469 | 0.787 | 0.064 | 135.276 |
GDPSQABF | 6.671 | 1.769 | 60.023 | 0.632 | 1.147 | 0.469 | 0.802 | 0.065 | 148.808 |
GDPSQCB | 6.672 | 1.763 | 60.029 | 0.630 | 1.146 | 0.470 | 0.796 | 0.065 | 145.011 |
GDPSQCV | 6.495 | 1.479 | 60.470 | 0.564 | 1.127 | 0.463 | 0.763 | 0.058 | 78.475 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 5.981 | 2.091 | 58.438 | 0.588 | 1.422 | 0.415 | 3.677 | 0.093 | 649.629 |
CBF | 6.896 | 2.822 | 57.178 | 0.600 | 1.227 | 0.492 | 2.157 | 0.125 | 639.983 |
FPDE | 5.972 | 2.149 | 58.439 | 0.559 | 1.422 | 0.418 | 3.275 | 0.093 | 625.309 |
GFCE | 7.230 | 2.124 | 57.075 | 0.558 | 1.327 | 0.375 | 3.706 | 0.128 | 80.675 |
GTF | 5.520 | 1.997 | 58.210 | 0.183 | 1.380 | 0.323 | 2.877 | 0.098 | 2764.969 |
HMSD | 6.722 | 2.092 | 58.250 | 0.613 | 1.412 | 0.368 | 1.318 | 0.097 | 237.620 |
IFEVIP | 6.409 | 3.898 | 57.700 | 0.551 | 1.362 | 0.366 | 0.918 | 0.110 | 246.528 |
MSVD | 6.870 | 2.735 | 58.210 | 0.625 | 1.334 | 0.459 | 3.007 | 0.098 | 609.813 |
VSMWLS | 6.129 | 1.800 | 58.400 | 0.647 | 1.408 | 0.403 | 5.896 | 0.094 | 667.889 |
CNN | 6.781 | 2.059 | 57.686 | 0.743 | 1.345 | 0.411 | 4.080 | 0.111 | 256.092 |
GD5 | 6.738 | 2.334 | 57.497 | 0.567 | 1.285 | 0.497 | 3.769 | 0.116 | 524.444 |
GD10 | 6.693 | 2.349 | 57.528 | 0.625 | 1.351 | 0.519 | 3.983 | 0.115 | 503.300 |
GD15 | 6.677 | 2.303 | 57.559 | 0.652 | 1.370 | 0.541 | 1.177 | 0.114 | 496.323 |
GDPSQABF | 6.647 | 2.169 | 57.616 | 0.658 | 1.383 | 0.543 | 1.307 | 0.113 | 492.907 |
GDPSQCB | 6.395 | 1.502 | 57.954 | 0.618 | 1.421 | 0.535 | 1.852 | 0.104 | 729.452 |
GDPSQCV | 6.677 | 2.312 | 57.546 | 0.630 | 1.360 | 0.536 | 4.001 | 0.114 | 487.171 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 7.669 | 4.513 | 63.818 | 0.610 | 1.654 | 0.643 | 0.017 | 0.027 | 101.099 |
CBF | 7.681 | 5.319 | 63.383 | 0.752 | 1.647 | 0.758 | 0.019 | 0.030 | 20.292 |
FPDE | 7.661 | 4.401 | 63.914 | 0.570 | 1.663 | 0.622 | 0.021 | 0.026 | 91.789 |
GFCE | 6.962 | 2.861 | 58.590 | 0.600 | 1.419 | 0.527 | 0.543 | 0.090 | 130.958 |
GTF | 7.670 | 4.585 | 63.464 | 0.708 | 1.637 | 0.660 | 0.019 | 0.029 | 65.129 |
HMSD | 7.650 | 4.999 | 63.173 | 0.738 | 1.642 | 0.742 | 0.020 | 0.031 | 15.926 |
IFEVIP | 7.019 | 2.661 | 59.720 | 0.449 | 1.500 | 0.505 | 0.361 | 0.069 | 321.098 |
MSVD | 7.669 | 4.149 | 63.421 | 0.427 | 1.633 | 0.616 | 0.020 | 0.030 | 94.007 |
VSMWLS | 7.666 | 4.424 | 63.498 | 0.674 | 1.655 | 0.664 | 0.015 | 0.029 | 39.009 |
CNN | 7.668 | 5.404 | 63.106 | 0.757 | 1.635 | 0.769 | 0.030 | 0.032 | 14.200 |
GD5 | 7.688 | 4.754 | 63.655 | 0.724 | 1.665 | 0.710 | 0.023 | 0.028 | 32.352 |
GD10 | 7.685 | 4.747 | 63.696 | 0.723 | 1.667 | 0.712 | 0.022 | 0.028 | 27.732 |
GD15 | 7.684 | 4.745 | 63.714 | 0.722 | 1.667 | 0.713 | 0.022 | 0.028 | 26.936 |
GDPSQABF | 7.688 | 4.756 | 63.651 | 0.725 | 1.665 | 0.709 | 0.023 | 0.028 | 33.095 |
GDPSQCB | 7.685 | 4.747 | 63.696 | 0.722 | 1.667 | 0.712 | 0.022 | 0.028 | 27.694 |
GDPSQCV | 7.683 | 4.709 | 63.781 | 0.714 | 1.669 | 0.707 | 0.022 | 0.027 | 26.191 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 7.611 | 5.753 | 68.864 | 0.748 | 1.856 | 0.755 | 0.009 | 0.008 | 3.640 |
CBF | 7.628 | 6.445 | 68.394 | 0.805 | 1.840 | 0.815 | 0.011 | 0.009 | 3.873 |
FPDE | 7.614 | 5.617 | 68.806 | 0.744 | 1.854 | 0.725 | 0.013 | 0.009 | 3.734 |
GFCE | 7.636 | 3.140 | 57.958 | 0.610 | 1.396 | 0.625 | 0.971 | 0.105 | 94.969 |
GTF | 7.623 | 6.540 | 69.036 | 0.791 | 1.837 | 0.786 | 0.011 | 0.008 | 5.307 |
HMSD | 7.628 | 5.958 | 68.060 | 0.789 | 1.836 | 0.779 | 0.012 | 0.010 | 4.031 |
IFEVIP | 7.632 | 3.663 | 60.891 | 0.627 | 1.674 | 0.616 | 0.321 | 0.053 | 158.223 |
MSVD | 7.579 | 4.972 | 66.507 | 0.520 | 1.784 | 0.711 | 0.010 | 0.015 | 6.843 |
VSMWLS | 7.626 | 5.828 | 68.217 | 0.787 | 1.838 | 0.751 | 0.012 | 0.010 | 3.528 |
CNN | 7.626 | 6.829 | 68.088 | 0.811 | 1.837 | 0.829 | 0.011 | 0.010 | 3.618 |
GD5 | 7.624 | 5.941 | 68.613 | 0.789 | 1.847 | 0.784 | 0.010 | 0.009 | 3.195 |
GD10 | 7.623 | 5.940 | 68.629 | 0.787 | 1.848 | 0.786 | 0.010 | 0.009 | 3.211 |
GD15 | 7.623 | 5.937 | 68.636 | 0.787 | 1.848 | 0.787 | 0.010 | 0.009 | 3.225 |
GDPSQABF | 7.624 | 5.938 | 68.609 | 0.789 | 1.847 | 0.783 | 0.010 | 0.009 | 3.194 |
GDPSQCB | 7.624 | 5.940 | 68.617 | 0.789 | 1.847 | 0.785 | 0.010 | 0.009 | 3.194 |
GDPSQCV | 7.624 | 5.939 | 68.613 | 0.789 | 1.847 | 0.784 | 0.010 | 0.009 | 3.207 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 6.530 | 3.440 | 58.730 | 0.700 | 1.719 | 0.578 | 0.544 | 0.087 | 69.401 |
CBF | 6.704 | 3.064 | 58.370 | 0.674 | 1.641 | 0.593 | 0.537 | 0.095 | 99.078 |
FPDE | 6.498 | 3.433 | 58.732 | 0.697 | 1.720 | 0.576 | 0.547 | 0.087 | 69.466 |
GFCE | 5.133 | 2.764 | 57.641 | 0.569 | 1.607 | 0.469 | 1.615 | 0.112 | 165.118 |
GTF | 6.027 | 2.950 | 58.222 | 0.638 | 1.670 | 0.509 | 0.592 | 0.098 | 112.981 |
HMSD | 6.683 | 3.317 | 58.387 | 0.703 | 1.656 | 0.675 | 0.669 | 0.094 | 98.335 |
IFEVIP | 5.534 | 2.471 | 57.822 | 0.551 | 1.601 | 0.477 | 0.993 | 0.108 | 188.610 |
MSVD | 6.524 | 3.329 | 58.690 | 0.691 | 1.701 | 0.582 | 0.555 | 0.088 | 70.008 |
VSMWLS | 6.541 | 3.278 | 58.663 | 0.703 | 1.700 | 0.607 | 0.593 | 0.089 | 74.676 |
CNN | 6.539 | 2.893 | 58.400 | 0.702 | 1.690 | 0.618 | 1.241 | 0.094 | 92.188 |
GD5 | 6.676 | 3.342 | 58.618 | 0.713 | 1.693 | 0.600 | 0.532 | 0.089 | 76.043 |
GD10 | 6.665 | 3.334 | 58.636 | 0.716 | 1.699 | 0.617 | 0.536 | 0.089 | 73.182 |
GD15 | 6.655 | 3.328 | 58.647 | 0.716 | 1.703 | 0.622 | 0.539 | 0.089 | 72.057 |
GDPSQABF | 6.643 | 3.349 | 58.676 | 0.714 | 1.708 | 0.617 | 0.547 | 0.088 | 71.193 |
GDPSQCB | 6.655 | 3.316 | 58.647 | 0.715 | 1.702 | 0.624 | 0.539 | 0.089 | 72.086 |
GDPSQCV | 6.606 | 3.439 | 58.716 | 0.707 | 1.716 | 0.608 | 0.533 | 0.087 | 68.797 |
EN | MI | PSNR | Qabf | SSIM | Qcb | CE | RMSE | Qcv | |
---|---|---|---|---|---|---|---|---|---|
ADF | 6.382 | 3.912 | 57.541 | 0.660 | 1.510 | 0.520 | 0.792 | 0.115 | 88.447 |
CBF | 6.674 | 3.308 | 56.844 | 0.680 | 1.377 | 0.550 | 0.881 | 0.135 | 168.641 |
FPDE | 6.381 | 3.904 | 57.541 | 0.659 | 1.509 | 0.523 | 0.868 | 0.115 | 88.193 |
GFCE | 6.749 | 2.497 | 54.457 | 0.644 | 1.123 | 0.510 | 3.677 | 0.233 | 241.984 |
GTF | 5.664 | 3.065 | 57.035 | 0.594 | 1.431 | 0.555 | 0.609 | 0.129 | 201.843 |
HMSD | 6.661 | 3.289 | 57.130 | 0.691 | 1.461 | 0.521 | 1.065 | 0.126 | 132.652 |
IFEVIP | 6.100 | 3.716 | 57.112 | 0.619 | 1.458 | 0.468 | 1.409 | 0.126 | 126.541 |
MSVD | 6.385 | 3.829 | 57.518 | 0.637 | 1.498 | 0.521 | 0.800 | 0.115 | 89.599 |
VSMWLS | 6.469 | 3.650 | 57.467 | 0.669 | 1.477 | 0.540 | 0.899 | 0.117 | 88.157 |
CNN | 6.372 | 3.141 | 57.094 | 0.704 | 1.449 | 0.538 | 1.912 | 0.127 | 125.477 |
GD5 | 6.597 | 3.442 | 57.200 | 0.709 | 1.452 | 0.550 | 0.902 | 0.124 | 119.147 |
GD10 | 6.608 | 3.489 | 57.232 | 0.716 | 1.475 | 0.567 | 0.924 | 0.123 | 114.830 |
GD15 | 6.613 | 3.492 | 57.263 | 0.716 | 1.485 | 0.570 | 0.829 | 0.122 | 111.714 |
GDPSQABF | 6.616 | 3.486 | 57.294 | 0.715 | 1.490 | 0.566 | 0.851 | 0.121 | 108.474 |
GDPSQCB | 6.619 | 3.488 | 57.277 | 0.717 | 1.488 | 0.570 | 0.837 | 0.122 | 110.358 |
GDPSQCV | 6.487 | 3.619 | 57.466 | 0.687 | 1.510 | 0.536 | 0.903 | 0.117 | 95.170 |
ADF | CBF | FPDE | GFCE | GTF | HMSD | IFEVIP | MSVD | VSMWLS | CNN | GD5 | GD10 | GD15 | GDPSQABF | GDPSQCB | GDPSQCV | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Img. M#1 Rank. | 8.78 | 7.00 | 7.78 | 12.89 | 11.44 | 6.78 | 9.00 | 10.44 | 7.22 | 8.78 | 8.00 | 7.11 | 7.78 | 8.00 | 6.78 | 8.22 |
Img. M#2 Rank. | 11.00 | 6.78 | 8.33 | 13.00 | 9.33 | 9.44 | 11.00 | 12.89 | 5.78 | 8.00 | 7.11 | 5.89 | 6.67 | 7.56 | 6.67 | 6.56 |
Img. M#3 Rank. | 6.78 | 9.56 | 7.56 | 11.56 | 12.22 | 7.56 | 7.33 | 15.22 | 8.22 | 6.56 | 8.89 | 6.44 | 7.00 | 6.78 | 6.56 | 7.78 |
Img. M#4 Rank. | 7.67 | 6.89 | 8.67 | 13.78 | 11.67 | 5.00 | 8.22 | 13.33 | 9.67 | 7.89 | 8.67 | 6.89 | 6.89 | 7.33 | 6.67 | 6.78 |
Img. M#5 Rank. | 10.56 | 6.56 | 12.33 | 12.00 | 11.78 | 8.22 | 9.22 | 12.67 | 5.78 | 6.44 | 7.33 | 6.00 | 7.00 | 7.22 | 6.44 | 6.44 |
Img. M#6 Rank. | 15.22 | 8.22 | 10.11 | 11.56 | 10.11 | 6.00 | 5.44 | 9.78 | 5.56 | 8.11 | 8.11 | 7.56 | 6.89 | 7.44 | 8.78 | 7.11 |
Img. M#7 Rank. | 9.56 | 7.00 | 9.33 | 13.56 | 12.44 | 8.44 | 9.89 | 12.56 | 5.67 | 7.56 | 7.33 | 6.44 | 5.67 | 7.44 | 6.33 | 6.78 |
Img. M#8 Rank. | 7.33 | 10.22 | 9.67 | 13.56 | 12.22 | 6.11 | 7.33 | 13.67 | 6.11 | 7.89 | 9.56 | 7.11 | 5.89 | 7.11 | 5.67 | 6.56 |
Avg. Ranking | 9.61 | 7.78 | 9.22 | 12.74 | 11.40 | 7.19 | 8.43 | 12.57 | 6.75 | 7.65 | 8.13 | 6.68 | 6.72 | 7.36 | 6.74 | 7.03 |
Infrared and Visible Images | ADF | CBF | FPDE | GFCE | GTF | HMSD | IFEVIP | MSVD | VSMWLS | CNN | GD5 | GD10 | GD15 | GDPSQABF | GDPSQCB | GDPSQCV |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Img. IV#1 Rank. | 5.67 | 11.33 | 7.11 | 11.11 | 10.00 | 5.56 | 10.33 | 10.11 | 7.22 | 5.67 | 10.33 | 8.67 | 8.44 | 9.11 | 7.44 | 7.89 |
Img. IV#2 Rank. | 8.00 | 11.22 | 8.33 | 10.22 | 10.56 | 5.78 | 10.11 | 8.78 | 7.33 | 6.22 | 10.89 | 9.33 | 7.89 | 7.22 | 7.33 | 6.78 |
Img. IV#3 Rank. | 6.11 | 11.67 | 7.11 | 10.44 | 10.89 | 5.33 | 11.00 | 10.00 | 6.44 | 5.67 | 10.11 | 8.56 | 8.00 | 9.00 | 8.11 | 7.56 |
Img. IV#4 Rank. | 7.89 | 7.33 | 8.11 | 13.67 | 11.56 | 8.78 | 8.33 | 11.11 | 7.33 | 10.44 | 8.22 | 6.78 | 6.22 | 7.33 | 6.11 | 6.78 |
Img. IV#5 Rank. | 8.33 | 9.44 | 7.78 | 10.67 | 11.33 | 6.44 | 7.89 | 7.11 | 9.44 | 8.67 | 10.22 | 8.89 | 6.67 | 6.22 | 8.56 | 8.33 |
Img. IV#6 Rank. | 8.78 | 9.89 | 7.22 | 8.22 | 9.78 | 6.33 | 9.33 | 9.00 | 7.56 | 9.78 | 10.00 | 8.56 | 6.89 | 6.67 | 11.22 | 6.78 |
Img. IV#7 Rank. | 7.11 | 11.56 | 7.44 | 9.00 | 12.22 | 5.22 | 9.22 | 8.67 | 9.89 | 5.00 | 11.56 | 10.00 | 8.56 | 6.00 | 9.11 | 5.44 |
Img. IV#8 Rank. | 8.67 | 10.56 | 10.78 | 10.89 | 10.78 | 6.22 | 8.44 | 10.11 | 6.78 | 6.33 | 10.00 | 9.00 | 8.00 | 6.67 | 6.56 | 6.22 |
Img. IV#9 Rank. | 7.89 | 10.11 | 7.11 | 11.22 | 15.00 | 7.33 | 10.67 | 7.89 | 5.78 | 6.44 | 10.56 | 7.67 | 7.00 | 7.00 | 6.67 | 7.67 |
Img. IV#10 Rank. | 7.56 | 11.22 | 8.33 | 8.78 | 9.33 | 8.56 | 9.22 | 11.78 | 7.00 | 7.56 | 11.22 | 9.56 | 8.00 | 5.33 | 6.22 | 6.33 |
Img. IV#11 Rank. | 8.11 | 11.33 | 8.11 | 12.78 | 7.56 | 9.67 | 6.78 | 6.67 | 5.33 | 6.78 | 10.44 | 9.78 | 8.33 | 6.11 | 11.33 | 6.89 |
Img. IV#12 Rank. | 10.44 | 8.33 | 10.11 | 12.00 | 12.11 | 7.11 | 10.11 | 9.22 | 9.89 | 7.22 | 9.44 | 6.89 | 6.00 | 6.56 | 5.56 | 5.00 |
Img. IV#13 Rank. | 7.78 | 12.33 | 7.89 | 7.89 | 13.00 | 7.11 | 5.89 | 9.00 | 6.44 | 6.44 | 10.11 | 8.78 | 7.89 | 7.56 | 10.89 | 7.00 |
Img. IV#14 Rank. | 8.11 | 12.11 | 8.11 | 7.89 | 11.22 | 5.67 | 5.33 | 9.89 | 6.22 | 7.22 | 10.11 | 8.89 | 8.67 | 7.89 | 10.67 | 8.00 |
Avg. Ranking | 7.89 | 10.60 | 8.11 | 10.34 | 11.10 | 6.79 | 8.76 | 9.24 | 7.33 | 7.10 | 10.23 | 8.67 | 7.61 | 7.05 | 8.27 | 6.91 |
Multi-Focus Images | ADF | CBF | FPDE | GFCE | GTF | HMSD | IFEVIP | MSVD | VSMWLS | CNN | GD5 | GD10 | GD15 | GDPSQABF | GDPSQCB | GDPSQCV |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Img. F#1 Rank. | 9.44 | 5.67 | 8.89 | 11.67 | 9.89 | 6.89 | 14.11 | 12.89 | 8.11 | 6.22 | 7.56 | 6.89 | 7.44 | 6.67 | 6.89 | 6.78 |
Img. F#2 Rank. | 7.78 | 6.89 | 9.78 | 13.56 | 9.33 | 7.44 | 13.89 | 9.56 | 7.89 | 6.78 | 7.11 | 7.22 | 6.44 | 7.00 | 7.56 | 7.78 |
Img. F#3 Rank. | 9.44 | 6.56 | 9.78 | 13.78 | 10.89 | 7.00 | 13.44 | 9.56 | 7.89 | 7.89 | 7.67 | 6.67 | 5.89 | 7.00 | 6.33 | 6.22 |
Img. F#4 Rank. | 8.11 | 5.78 | 9.22 | 15.44 | 11.78 | 10.11 | 13.67 | 10.56 | 7.44 | 7.11 | 7.11 | 5.67 | 5.56 | 6.33 | 6.11 | 6.00 |
Img. F#5 Rank. | 7.11 | 6.33 | 10.00 | 14.89 | 9.67 | 7.67 | 15.89 | 9.56 | 9.33 | 7.00 | 6.44 | 5.78 | 6.22 | 7.44 | 6.67 | 6.00 |
Img. F#6 Rank. | 7.67 | 6.89 | 9.78 | 13.78 | 9.56 | 8.00 | 13.44 | 9.00 | 8.67 | 8.11 | 7.44 | 6.78 | 6.44 | 7.22 | 6.56 | 6.67 |
Img. F#7 Rank. | 9.11 | 6.78 | 9.44 | 15.22 | 10.56 | 7.44 | 14.22 | 8.67 | 7.33 | 7.00 | 7.56 | 6.22 | 5.67 | 8.44 | 7.11 | 5.22 |
Img. F#8 Rank. | 8.89 | 6.22 | 9.44 | 14.00 | 7.33 | 9.56 | 13.78 | 12.44 | 8.44 | 6.33 | 6.67 | 7.22 | 5.89 | 6.89 | 6.89 | 6.00 |
Img. F#9 Rank. | 9.00 | 6.78 | 9.89 | 12.67 | 9.89 | 7.11 | 13.44 | 8.89 | 9.33 | 8.22 | 8.00 | 6.78 | 6.33 | 7.00 | 6.11 | 6.56 |
Img. F#10 Rank. | 8.11 | 6.78 | 9.22 | 14.22 | 10.11 | 6.89 | 13.44 | 13.22 | 6.67 | 6.89 | 7.22 | 6.67 | 6.00 | 7.56 | 6.44 | 6.56 |
Img. F#11 Rank. | 8.22 | 6.00 | 9.00 | 15.33 | 9.44 | 7.44 | 15.33 | 12.00 | 9.11 | 7.78 | 6.56 | 5.78 | 5.67 | 6.67 | 5.89 | 5.78 |
Img. F#12 Rank. | 8.00 | 6.11 | 8.67 | 15.33 | 9.78 | 8.33 | 13.78 | 10.22 | 8.78 | 7.89 | 7.89 | 6.11 | 5.44 | 7.56 | 6.33 | 5.78 |
Img. F#13 Rank. | 8.67 | 7.56 | 9.89 | 13.67 | 9.00 | 8.11 | 13.78 | 10.22 | 9.22 | 8.22 | 7.56 | 6.11 | 5.56 | 6.00 | 6.78 | 5.67 |
Img. F#14 Rank. | 9.00 | 6.22 | 9.67 | 15.33 | 8.78 | 6.89 | 14.67 | 10.44 | 9.11 | 7.56 | 7.22 | 6.33 | 6.33 | 6.56 | 6.11 | 5.78 |
Img. F#15 Rank. | 7.22 | 6.78 | 9.44 | 14.00 | 6.56 | 9.44 | 13.67 | 13.22 | 10.00 | 6.67 | 6.56 | 6.33 | 6.22 | 7.11 | 5.78 | 7.00 |
Img. F#16 Rank. | 7.22 | 7.89 | 8.33 | 15.22 | 9.67 | 9.89 | 15.44 | 8.44 | 7.44 | 9.44 | 7.11 | 5.44 | 5.78 | 6.67 | 6.11 | 5.89 |
Img. F#17 Rank. | 9.11 | 6.67 | 9.56 | 14.44 | 9.89 | 7.22 | 15.56 | 9.56 | 9.22 | 6.78 | 7.78 | 5.67 | 6.22 | 6.44 | 5.78 | 6.11 |
Img. F#18 Rank. | 7.78 | 7.78 | 9.56 | 14.33 | 9.33 | 10.11 | 13.56 | 8.22 | 7.33 | 7.11 | 6.67 | 6.67 | 6.56 | 8.11 | 6.56 | 6.33 |
Img. F#19 Rank. | 8.67 | 6.22 | 9.67 | 14.11 | 9.89 | 7.11 | 15.44 | 10.78 | 9.11 | 7.22 | 7.67 | 6.22 | 5.00 | 6.56 | 5.56 | 6.78 |
Img. F#20 Rank. | 8.89 | 5.67 | 10.22 | 15.33 | 10.22 | 7.11 | 13.78 | 8.67 | 7.67 | 6.67 | 7.67 | 6.33 | 6.67 | 7.11 | 6.67 | 7.33 |
Avg. Ranking | 8.37 | 6.58 | 9.47 | 14.32 | 9.58 | 7.99 | 14.22 | 10.31 | 8.40 | 7.34 | 7.27 | 6.34 | 6.07 | 7.02 | 6.41 | 6.31 |
Multi-Exposure Images | ADF | CBF | FPDE | GFCE | GTF | HMSD | IFEVIP | MSVD | VSMWLS | CNN | GD5 | GD10 | GD15 | GDPSQABF | GDPSQCB | GDPSQCV |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Img. E#1 Rank. | 6.11 | 14.00 | 5.78 | 13.78 | 12.44 | 7.44 | 10.56 | 8.00 | 7.22 | 7.89 | 11.11 | 8.56 | 6.78 | 4.78 | 6.33 | 5.22 |
Img. E#2 Rank. | 5.33 | 10.44 | 5.44 | 13.22 | 11.56 | 10.78 | 15.89 | 7.67 | 6.56 | 9.56 | 8.67 | 7.67 | 6.89 | 5.33 | 6.33 | 4.67 |
Img. E#3 Rank. | 6.33 | 13.22 | 6.78 | 11.11 | 10.44 | 8.33 | 9.89 | 6.00 | 7.22 | 10.33 | 11.67 | 8.89 | 8.11 | 5.56 | 7.33 | 4.78 |
Img. E#4 Rank. | 5.00 | 13.67 | 5.11 | 13.56 | 11.22 | 6.11 | 9.11 | 7.11 | 9.00 | 7.56 | 12.33 | 9.89 | 8.33 | 6.33 | 6.67 | 5.00 |
Img. E#5 Rank. | 5.44 | 10.33 | 6.00 | 15.56 | 13.33 | 9.00 | 15.33 | 7.89 | 8.56 | 10.67 | 7.00 | 6.00 | 5.33 | 5.44 | 6.22 | 3.89 |
Img. E#6 Rank. | 5.44 | 10.78 | 5.78 | 13.89 | 12.22 | 10.44 | 12.33 | 6.33 | 6.56 | 12.00 | 9.11 | 7.67 | 5.67 | 5.78 | 5.33 | 6.67 |
Avg. Ranking | 5.61 | 12.07 | 5.82 | 13.52 | 11.87 | 8.68 | 12.19 | 7.17 | 7.52 | 9.67 | 9.98 | 8.11 | 6.85 | 5.54 | 6.37 | 5.04 |
All Images | ADF | CBF | FPDE | GFCE | GTF | HMSD | IFEVIP | MSVD | VSMWLS | CNN | GD5 | GD10 | GD15 | GDPSQABF | GDPSQCB | GDPSQCV |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Avg. Ranking | 8.09 | 8.64 | 8.58 | 12.79 | 10.61 | 7.59 | 11.41 | 9.98 | 7.71 | 7.62 | 8.62 | 7.30 | 6.72 | 6.90 | 7.00 | 6.44 |
Avg. CPU Time | 0.56 | 14.08 | 1.76 | 1.46 | 5.63 | 6.28 | 0.15 | 0.57 | 2.30 | 22.99 | 0.16 | 0.18 | 0.20 | 19.65 | 15.40 | 21.72 |
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Kurban, R. Gaussian of Differences: A Simple and Efficient General Image Fusion Method. Entropy 2023, 25, 1215. https://doi.org/10.3390/e25081215
Kurban R. Gaussian of Differences: A Simple and Efficient General Image Fusion Method. Entropy. 2023; 25(8):1215. https://doi.org/10.3390/e25081215
Chicago/Turabian StyleKurban, Rifat. 2023. "Gaussian of Differences: A Simple and Efficient General Image Fusion Method" Entropy 25, no. 8: 1215. https://doi.org/10.3390/e25081215