# A Survey of Multi-Focus Image Fusion Methods
## 2 Fusion Methods and Analysis
### Multi-Focus Fusion Methods Based on Transform Domain
#### 2.1.1 Multi-Scale Decomposition (MSD)-Based Methods  
Multi-scale decomposition (MSD)-based methods have always been the mainstream of image fusion. Pyramid transform and wavelet transform are the first-used MSD methods in image fusion. In addition, the multi-scale geometric analysis method (the improved wavelet transform method) also achieves an excellent fusion effect in multi-focus image fusion, superior to pyramid transform and wavelet transform in feature representation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Mainstream Algorithm** \\ \hline Transformation domain & Laplacian pyramid (LP) [9]; gradient pyramid (GD) [10]; contrast pyramid (CP) [11]; region \\  & mosaicking on Laplacian pyramids (RMLP) [12]; fast discrete curvelet transform (F DCT) [5]; dual-tree complex wavelet transform (DT-CWT) [13]; nonsubsampled contourlet transform (NST) [14]; nonsubsampled shearlet transform (NSST) [15]; cross sparse representation (CSP) [16]; independent component analysis (ICA) [17]; discrete cosine transform (DCT) [18] \\ \hline Boundary segmentation & adaptive region-segmentation (ARS) [19]; morphology-based focus measure (MBFM) [20]; content adaptive blurring (CAB) [21]; robust principal component analysis (RPCA) [22]; Markov random field (MRF) [23]; optimal defocus estimation (ODE) [24] \\ \hline Deep learning & convolutional neural networks (CNN) [25]; CNN based [26]; PCNN-Pulse Coupled Neural Network (PCNN) [27]; PCNN based [28]; Generative Adversarial Networks (GAN) [29] \\ \hline Combination & CTD+SR [30]; NSCT+SR [31]; SF-PAPCNN+NSST+ ISML [32]; CNN+SR [33] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification and mainstream algorithms of multi-focus image fusion. Figure 4: The general schematic diagram of transform domain methods. (1) Pyramid transformation  
The Laplacian pyramid is the earliest multiscale decomposition method [9]. In this method, the absolute value of the decomposition coefficient is measured by its activity level, and the fusion coefficient is obtained by the choosing-Max rule. The greater the absolute value of the coefficient is, the more information it contains. In 2018, [PERSON] et al. [12] proposed a Region Mosaic (RMLP) method based on The Laplace pyramid to fuse microscopically captured multi-focus images. The method firstly used The Laplacian operator to measure the focus level of multi-focus images. Then, a density-based region growth algorithm was used to segment the focused region mask of each image. Finally, the mask was decomposed into a mask pyramid to supervise the regional stitching of the Laplacian pyramid. Due to the different forms of the tower structure, pyramid transformation can be divided into gradient pyramid [10], contrast pyramid [11], morphological pyramid [35], etc. The fusion method based on pyramid transformation has the advantages of high fusion efficiency while retaining sufficient original information. However, the decomposition method and the decomposition layer number have a great influence on the final result. The greater number of decomposition layers, the more blurred the fusion image boundary would be. (2) The wavelet transforms  
The wavelet transform can decompose the original image into high frequency coefficient and low frequency coefficient. The high frequency coefficient includes vertical, horizontal, and diagonal information. The fusion effect of wavelet transform is better than that of pyramid transform. However, the wavelet transform is not displacement invariant for the feature representation; thus, the fusion effect is not satisfactory for the image with poor registration. To solve this problem, many improved wavelet transform methods are proposed. [PERSON] et al. [5] introduced a multi-focus image fusion method based on fast discrete curve-wave transform (FDCT), which solved the problem of block effect in texture selection and spatial fusion. [PERSON] et al.