This section describes the various morphological structures used to represent images. We call morphological representation any complete decomposition which is invariant by (local or global) contrast changes. More precisely, if is the representation operator and c a contrast change function (that is, any non-decreasing real function), the contrast change invariance corresponds to the property (c(u)) = c((u)) for every image u. Exemples of such representations are based by level sets, level lines and connected components of level sets.
We begin our description with the Shape and Shapes structures. These are not the first developed in MegaWave2, but they are going to play an increasing role : they allow to handle level sets and connected components of level sets in a tree structure very useful to develop morphological shape-based applications. In addition, computation of these structures can be performed in a way faster than the traditional level set decomposition, using the Fast Level Set Transform (FLST in short). The FLST has been created by Pascal Monasse during its PhD thesis. The following description of the Shape and Shapes structures has been written with his help.