## 5 Evaluation Strategies and Performance Metrics
Similar to the RMSE calculation, we can consider that the corrupting operation does not affect the pixel intensities or the features of the image remarkably. However, the correlation of the fused image to the original image was notably higher than the noisy one, indicating that the fusion managed to merge the valuable components of the sources. Segmentation (thresholding) as a preprocessing step made the fusion result have the highest correlation with the original images eventually. Fusion mutual information (FMI): This metric, based on the mutual information criterion, evaluates how much of the original images' features, such as the edge, detail or contrast, are inherited in the fused image [125]. The FMI computes the degree of dependency between the input images and the fused image [126]. Smaller values for the FMI indicate worse quality for the fused image. In our case, the original image features were firmly maintained in the corrupted image, with a notably higher FMI value than those of the noisy and fused ones. That aside, the fused one also had a relatively higher FMI value than the noisy one. The story was different when the intensity became deterministic (black and white segmented areas) in the threshold images (Figure 13). In such a case, the corrupted image had the lowest FMI value, and the fused one had the largest FMI value, confirming the benefit of even a simplified fusion operation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metrics** & **Corrupted** & **Noisy** & **Fused** \\ \hline RMSE & 12.960 & 30.910 & 16.607 \\ CC & 0.860 & 0.629 & 0.814 \\ FMI & 1.586 & 0.378 & 0.579 \\ SNR & 5.284 & 2.086 & 5.428 \\ PSNR & 15.165 & 11.940 & 15.310 \\ SSIM & 0.771 & 0.15 & 0.32 \\ \hline
**Thresholded** & & & \\ \hline RMSE & 0.164 & 0.192 & 0.148 \\ CC & 0.459 & 0.366 & 0.558 \\ FMI & 0.042 & 0.034 & 0.056 \\ SNR & 0.379 & \(-5.390\) & 0.822 \\ PSNR & 16.645 & 10.876 & 17.086 \\ SSIM & 0.846 & 0.406 & 0.745 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: A comparison of the evaluation metric values for the illustrative example for fusion metrics. _Signal-to-noise ratio (SNR)_: The SNR provides a metric of evaluating the quality of a signal quantitatively when comparing the fused and original signals [127], and it gives the proportion of signal power to noise power:  
\[SNR=10\log_{10}(Energy_{Signal})/(Energy_{Noise}) \tag{6}\]  
where \(Energy\) denotes the sum of the squares of the signal values for the estimated signal and the difference (error or noise) between the estimated and original signals. With the SNR measuring the ratio between the information and noise of the fused image, a higher value reveals a greater similarity between the fused and reference (original) images. In an example fusion of terahertz and thermal imaging, the larger SNR values contributing to the achievement of suppressing the background noise showed that the salient features were extracted successfully [102]. Another interesting quantitative assessment with the SNR demonstrated that although the fusion provided a higher contrast and resolution, the SNR value of the fused image was relatively lower [99]. This might be attributed to calculating the average SNR from the SNR values of different depths. Another closely relevant metric the peak signal-to-noise ratio (PSNR), indicates the ratio of effective information to noise using the maximum squared signal intensity. The SNR and PSNR values of our example evaluation application indicated that the fused image had the greatest values, demonstrating that a successful fusion can provide more evident marks by reducing the noise effects. This gave the same results after the thresholding application, demonstrating that the SNR and PSNR values were not affected by this preprocessing operation, contrary to other metrics. Moreover, the negative SNR value of the noisy segmented image might be attributed to the noise density of the image being heavier than the signal density [128].