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. 2026 May 29;16:24669. doi: 10.1038/s41598-026-52181-8

Table 5.

Performance indicator metrics.

SN PEM Expressions in mathematics
1 EN EN = −Inline graphic;where p(i) is the probability of occurrence of intensity i in the image.
2 SF

SF= Inline graphic,where

RF =Inline graphic

CF = Inline graphic

where m= rows, n = columns, x(i, j) is the intensity value at ith row and jth column pixel.

3 SSIM SSIM (x, y) = Inline graphic; where Inline graphic is the sample mean, Inline graphic is the variance and Inline graphic is the covariance of image x and image, c1 and c2 are two constants.
4 MSE MSE =Inline graphic; where FO (i, j) is a fused output and S (i, j) is a reference image.
5 MSSIM MSSIM= Inline graphic |Inline graphic); where FO is a fused output and S is a source image, k is the number of local windows in the image.
6 RMSE RMSE = Inline graphic; where m= rows, n = columns, FO (i, j) is a fused output image and S (i, j) is a reference image.
7 PSNR PSNR = 10*Inline graphic; where MAX is the maximum intensity value of an image.
8 NMI

NMI = Inline graphic, where FO is a fused image and S is a source image, MI is the mutual information

\:MI(FO;S) = EN (FO)–EN (FO | S); where EN is an entropy.

9 VIF VIF = Inline graphic; where Inline graphic is the covariance of source image and output image in the bth block at the kth sub-band, Inline graphic is the scalar gain field.
10 FSIM FSIM = Inline graphic;SL is similarity at location x; PCm is maximum phase congruency.