Table 3 Main characters of the evaluation parameters

The information entropy can be described as the capability of the detail-performance.

\( IE=\sum_{m=0}^{255}H\left({P}_m\right)=-\sum_{m=0}^{255}{P}_m\cdot \log \left({P}_m\right) \) (where m and P_m stand for the gray-scale value and the probability that the pixel appears in the image.)

The larger the entropy is, the richer the details are, and the better the quality of the fused image is.

Mutual information is a measurement of statistical correlation between two random variables.

\( MI\left(A,B\right)=\sum_{m=0}^{255}{P}_{AB}(m)\log \frac{P_{AB}(m)}{P_A(m)\cdot {P}_B(m)} \) (where P_A(m), P_B(m), and P_AB(m), respectively, show the probability of m-gray-scale among image A, image B, and the united of images A and B.)

The higher the MI is, the much information fused images can extract from the original image, and the better the fusion results are.

Mean grads, also called clarity, which reflects the changes of image gray-scale.

\( MG=\frac{1}{M\times N}\sum_{i=1}^M\sum_{j=1}^N\sqrt{\varDelta xF{\left(i,j\right)}^2+\varDelta yF{\left(i,j\right)}^2} \) (where ΔxF(i, j) and ΔyF(i, j) denote the difference of F along X and Y directions.)

The higher the mean grads is, the richer the image gray-scale can express, and the more clearly the image is.

The spatial frequency of images measures the degree of the richness of image detail information images

\( SF=\sqrt{RF^2+{CF}^2} \)

(where RF and CF stand for the row-frequency and column-frequency, respectively)

The higher the spatial frequency is, the richer the image levels are, the higher the contrast is. Consequently, the better the fusion result is.