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.

- Shape

- Shapes

- Point with a type field

- Horizontal segment

- Morpho set

- Chain of morpho sets

- Morpho line

- Morpho line in the continuous plane

- Morphological image