Nonlocal patch-based method on spatially-variant amoeba morphology for image restoration

In view of the selection of structuring elements problem in morphological filters, this paper presents a new method to generate structuring elements for spatially-variant morphology. This method takes the theory of amoeba morphology as a foundation and new amoeba distances to generate structuring elements for spatially-variant filters are defined. The proposed strategy essentially consists in an amoeba kernel is divided into two parts: one is the patch-based center; another is the pixel-based boundary, the two parts combining both nonlocal patch-based distance and local pixel-based distance. This nonlocal and local configurations make nonlocal patch-based processing method becomes local processing on amoeba structuring element. New amoeba kernels are less flexible at patch-based center than traditional amoebas and their shape is less affected by noises in pilot image. By designing new amoeba structuring element, a new family of morphological filters are derived that have better performance in removing the noise while adaptively preserving the main structures compared with traditional amoeba filters.