Multi-focal image fusion occupies a place in image processing research. It allows, from several images of the same scene with different blurred regions, to give a fused image without blur. This allows fusing photos taken by drones at different heights by zooming in each image a different object. Several methods are developed in the literature but which are made independently of the nature of the images. The aim of our work is to propose a method adapted essentially to images of significant fluctuations (of very large variance) considered as an alpha stable signal. For these images, we propose a method consisting of combining the Laplacian pyramid and Dumpster-Shafer theory using the alpha stable distance as a selection rule. Indeed, we decompose the multifocal images into several pyramidal levels, and apply the Dumpster Shafer method with the alpha stable distance at each level of the pyramid. The motivation of this work is to exploit the power of the dumpster Shafer fusion method and that of the Laplacian pyramidal decomposition and the fineness of the alpha stable distance. This kind of image-specific method gives better fusion because it uses a metric more suited to the nature of the data. This work was applied to some experimental images and it provides a comparison, using statistical tests, between our method and other known methods in the field of image fusion. We deduce that this method gives good fusions and that it is significantly better.