A general framework for tree-based morphology and its applications to self-dual filtering

This paper presents a tree-based framework for producing self-dual morphological operators, based on a tree-representation complete inf-semilattice (CISL). The idea is to use a self-dual tree transform to map a given image into the above CISL, perform one or more morphological operations there, and map the result back to the image domain using the inverse tree transform. We also present a particular case of this general framework, involving a new tree transform, the Extrema-Watershed Tree (EWT). The operators obtained by using the EWT in the above framework behave like classical morphological operators, but in addition are self-dual. Some application examples are provided: pre-processing for OCR and dust and scratch removal algorithms, and image denoising. We also explore first steps towards obtaining tree transforms that induce a CISL on the image domain as well.