In the field of infrared technology, the fusion of infrared and visible images is important. To obtain infrared and visible fusion images with clear targets and rich details, this paper proposes an infrared and visible image fusion method based on an improved two-dimensional Kaniadakis entropy segmentation method and fast guided filtering. First, a simplified two-dimensional Kaniadakis entropy segmentation algorithm (S2DKan) is used to fully extract the target from the infrared image. Then, the non-subsampled shearlet transform (NSST) is performed on the infrared and visible images to obtain the low- and high-frequency sub-bands, and fast guided filtering is applied to the obtained high-frequency components to retain rich visible image details. The low-frequency fusion coefficient is obtained from the extracted target image and the infrared and visible low-frequency components using the low-frequency fusion rule. The high-frequency fusion coefficient is obtained from the enhanced high-frequency sub-band components using the dual-channel spiking cortical model (DCSCM). Finally, the fused image is obtained using the inverse NSST transform. Experimental results show that the fusion image obtained by the proposed algorithm has clear targets and background information and that the algorithm’s effect is stable.