## 1 Introduction  
Atomic force acoustic microscopy (AFAM) [1] is an imaging technology combining acoustic detection and atomic force microscopy (AFM), which can image nondestructively the internal structures, as well as the surface topography of the samples in high resolution. In AFAM, the transducer of the pedestal emits sound echo to the sample as the probe scans on the sample. The probe response signal is collected by the light spot detector mounted on the cantilever of the probe and analyzed during the scan. The morphology and phase images were obtained simultaneously after the scanning of the sample in 2D. When AFAM is applied to image cells, the morphology images could only show cytoplasmic regions, while their phase images showed the cytoplasmic internal structures, but without the cell boundaries clearly [1]. To see the cells in detail, image fusion is needed to fuse both images so that the fused image can contain both information of the morphology contour and the internal structures of the cell. To our knowledge, there is no such research on AFAM image fusion yet.  
Image fusion is a process combining two or more source images of the same scene to obtain a single fused image which is more suitable for human visual perception or computer vision processing. The fused image requires to dig the duplicate Supplementary Materials in the source images and remove the redundant information. The selection of source image information is critical in image fusion. One of the important methods in image fusion is to separate the information in the source images and then fuse different types of information separately. For instance, the fusion method based on multi-scale transformation decomposes the source images at different scales to obtain the information, such as edges, details, and base contours, and applies suitable fusion rules to different kinds of information to obtain a better fused image.  
Multi-scale transform (MST) is an important tool in image fusion, and many MSTs have been proposed, such as wavelet transform [2], contourlet transform [3], curvelet transform [4], shearlet transform [5], and the nonsubsampled contourlet transform (NSCT) [6; 7]. Non-subsampled shearlet transform (NSST) [8; 9] is an improved multi-scale geometric analysis tool based on shearlet transform, which has the advantages of simple calculation and less Gibbs effect, and therefore, is widely used in multi-scale image fusion [10; 11; 12]. NSST can separate image information, such as edges and base layers, so that different fusion rules can be applied to different kinds of information. [PERSON] et al. [11] presented a multi-focus image fusion method based on NSST and the human vision system. [PERSON] et al. proposed a variable coefficient Meyer window for constructing a shearing filter, which is used for image fusion [12]. However, these methods only work well for certain types of image fusion, such as optical images with an inconsistent focus in the same scene.  
Contrast limited adaptive histogram equalization (CLAHE) can effectively enhance the local contrast of images, and the variance reflects the local information richness of the image, which is an effective indicator for information selection in image fusion [13; 14]. Because the local variance of an image by CLAHE could reflect the local image information efficiently, therefore, it is used in our image fusion to preserve more information of low-contrast images.  
In this paper, a cell image fusion method with AFAM based on the local variance in the NSST domain is proposed. The proposed method decomposes the image into low-frequency sub-band and a series of high-frequency sub-bands using NSST and fuses the low-frequency and high-frequency sub-bands using a weight map based on CLAHE-enhanced variance and maximum rule, respectively. The results of the experiments showed that the proposed method can effectively protect both edge and geometric structures by combining the morphology and phase images.