Adaptive Morphological Operators Defined on Graphs

Adaptive mathematical morphology has recently become a popular topic in the mathematical morphology community. In particular, the construction of adaptive structuring elements that adjust their size and shape to the local image structures have increased a lot of attention in recent years. Apart from that, there is a growing interest for representation of digital objects as graph structures. This review aims to give an overview of the methods that have been used to define adaptive morphological operators on graphs. Among the methods discussed is the classical one that is a counterpart of the adaptive structuring elements often called morphological amoebas, while the other uses partial differential equations on graphs to describe morphological operators. The review concludes by assessing the prospectives of these two different approaches for adaptive morphology on graph spaces, and by identifying possible paths for future research.