Multi-focus image fusion based on nonsubsampled compactly supported shearlet transform

Multi-focus image fusion, which aims to combine multi-focus images of a scene to construct an all-in-focus image, has become a major topic in image processing. Different methods have been proposed in spatial or transform domain. But many methods usually suffer from fusion quality degradations, such as contrast reduction, artificial edges, and discontinuous phenomena at boundaries of focused regions, which may cause issues when going for further processing. In order to overcome these problems, we introduce a nonsubsampled compactly supported shearlet transform (NSCSST), which possesses multi-scale, multi-direction, translation invariance and spatial localization characteristics that are very important for image fusion in transform domain. The transform can be implemented sequentially by the shear transform and the separable anisotropic nonsubsampled wavelet transform (SANSWT). Furthermore, we propose a new image fusion method based on NSCSST. It consists of two aspects: multi-direction fusion and transform domain fusion, which respectively correspond to the shear transform and the SANSWT of NSCSST. For each sheared image pair, the SANSWT coefficients are firstly fused by the transform domain fusion rules. And then, the final fused image is obtained by the multi-direction fusion rules, ranging from the simple averaging method to the proposed complex genetic algorithm based method. Experimental results show that our method outperforms some other methods, such as the method based on bilateral gradient, the method based on nonsubsampled contourlet transform, the method based on simultaneous empirical wavelet transform, and the method based on guided filtering.