Removal and contraction for n-dimensional generalized maps

In this paper we define removal and contraction operations in the generalized maps framework. These two operations are often used in graph theory to define images pyramids that allow multi-scale representation. However graphs don't represent the whole topological information of an image, even in the 2-dimensional case, contrary to generalized maps. We define here operations for removing or contracting cells of any dimension, in n-dimensional space. This work is the starting point for defining generalized map pyramids in any dimension. We prove in this paper the validity of these operations, and show that several different operations can be applied at the same time when some preconditions are satisfied.