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# Table 3 Main characters of the evaluation parameters

From: The application of multi-modality medical image fusion based method to cerebral infarction

Parameters | Definition | Formula | Evaluation criterion |
---|---|---|---|

Information entropy | 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 | 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 | 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. |

Space Frequency | 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. |