Laplacian Pyramid and Dempster-Shafer with Alpha Stable Distance in Multi-Focus Image Fusion

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