Incremental and efficient computation of families of component trees

Abstract

Component tree allows an image to be represented as a hierarchy of connected components. These components are directly related to the neighborhood chosen to obtain them and, in particular, a family of component trees built with increasing neighborhoods allows the linking of nodes of different trees according to their inclusion relation, adding a sense of scale as we travel along them. In this paper, we present a class of neighborhoods obtained from second-generation connectivities and show that this class is suited to the construction of a family of trees. Then, we provide an algorithm that benefits from the properties of this class, which reuses computation done in previously built tree in order to construct the entire family of component trees efficiently.