Insertion and Expansion Operations for n -Dimensional Generalized Maps

Hierarchical representations, such as irregular pyramids, are the bases of several applications in the field of discrete imagery. So, ndimensional ”bottom-up” irregular pyramids can be defined as stacks of successively reduced n-dimensional generalized maps (n-G-maps) [11], each n-G-map being defined from the previous level by using removal and contraction operations defined in [8]. Our goal is to build a theoretical framework for defining and handling n-dimensional ”top-down” irregular pyramids. To do so, we propose in this paper to study the definition of both insertion and expansion operations that allow to conceive these kinds of pyramids.