## 3 Methodology  
### Fusion Steps  
Figure 6 shows the fusion steps of a novel MS and PAN images fusion method based on weighted mean curvature filter (WMCF) decomposition, and the detailed fusion process is described below:  
Calculation the Intensity Component. The main purpose of this step is to fuse all bands of the MS image in accordance with a WLSF-based fusion method, thus generating an intensity component. If a simple averaging rule is used, some details and texture information contained in the original image will be dropped. Before performing the fusion operation, it is necessary  
Figure 6: The fusion steps of the proposed method. to weight the different regions in the image according to the importance of the information contained in the original image. The weighting factor size will directly affect the effect of fusion. Thus, a WLSF-based fusion method is utilized to fuse all the bands of a MS image to generate an intensity component \(IC\). More specific details about WLSF can be found in Section 2.4. An individual pixel fails to accurately represent all features within a local area. WLSF can make full use of the multiple pixels in a local area including horizontal, vertical, and eight neighborhoods in the primary and secondary diagonal directions. Different weights are assigned according to the Euclidean distance from the center pixel, and then participate in the weighted calculation. WLSF can be used as a quantitative index for important information such as details and textures. The pixels with larger WLSF values are more important for fusion and should be assigned with a larger weight, e.g., detail, texture, and other spatial detail information. Then, these pixels are given larger weights in the fusion process. Thus, we design a coefficient \(\omega_{d}\) for adaptive weighted averaging based on the WLSF value, as shown below:  
\[IC(i,j)=\sum\limits_{d=1}^{n}\frac{1}{\omega_{i}(i,j)}MS_{d}(i,j) \tag{26}\]  
\[\omega_{d}(i,j)=\frac{WLSF_{d}(i,j)}{\sum\limits_{d=1}^{n}WLSF_{d}} \tag{27}\]  
where \(n\) denotes the band number contained in the MS image. In the MS image, \(WLSF_{d}(i,j)\) denotes the WLSF value of the \(d\)-th band at the position \((i,j)\), \(MS_{d}(i,j)\) denotes the pixel value of the \(d\)-th band at the position \((i,j)\). \(\omega_{d}(i,j)\) denotes the weighting factor of the \(d\)-th band at the position \((i,j)\). \(IC(i,j)\) denotes the pixel value at the position \((i,j)\) in \(IC\). Spectral Estimation. The main purpose of this step is to extract the foreground and background colors in accordance with an image matting model, thus preserving the spectral information contained in the MS image. Setting \(IC\) as the original \(\alpha\) channel, a foreground image \(F\) and a background image \(B\) are obtained in accordance with Formula (2) in Section 2.1 to facilitate subsequent image reconstruction operations using \(F\) and \(B\). Multi-scale Decomposition. The main purpose of this step is to perform multi-scale decomposition for the PAN image on the basis of WMCF and Gaussian filter (GF), so as to sufficiently extract the spatial detail information contained in the PAN image. The multi-scale decomposition is based on WMCF and GF. By Formulas (30)-(34) in Section 3.2, a PAN image can be decomposed into three sub-images with different scales, which are a large scale image \(LS\), a small scale image \(SS\) and a basic image, respectively. More specific details about multi-scale decomposition can be found in Section 3.2. Component Fusion. The main purpose of this step is to fuse the primary spatial information contained in the MS and PAN images in accordance with a MSMDM-guided PAC-PCNN fusion strategy, thus improving the spatial resolution of the final fused image. The MSMDM value of the basic image and \(IC\) are used as the inputs of the PAC-PCNN model, respectively. All parameters in the PAC-PCNN model can be automatically calculated in accordance with the inputs with a fast convergence speed. In this paper, we set the maximum iteration number for the PAC-PCNN model to 2000.