Level lines in the ideal case

Disjoint Jordan curves: notion of interior and exterior
Shape = level line $\cup$ its interior
$\Rightarrow$ Inclusion tree of shapes

But it is not a realistic model
[Kronrod 50] considers isolevel sets, whose cc's constitute a topological tree (connected, locally connected set, without any subset homeomorphic to $\mathbb {S}^1$)

Summer School on Mathematical Problems in Image Processing, Trieste, Italy, September 4th-18th 2000