**Experimental results** (more experiments were conducted in the research
report)

**About initialization**

We first need to initialize each level set function
defined in (4). We have
chosen to initialize the 's with circular signed distance
function. We use 2 methods for selecting the initial 's. The
first one is completely manually handled : we manually select initial
circular level sets.

The second one is automatic and we called it "**seed
initialization**". This method consists of cutting the
data image of *u*_{0} into *N* windows
of predefined size. We compute the average *m*_{l} of *u*_{0} on each window
*W*_{l}. We then select the index *k* such that
.
And we initialize the corresponding circular signed
distance function
on each *W*_{l}. Windows are not overlapping and
each of them is supporting one and only one function ,
therefore we
avoid overlapping of initial 's. The size of the windows is
related to the smallest details we expect to detect. The major avantages of this
simple initialization method are : it is automatic (only the size of
the windows has to be fixed), it accelerates the speed of convergence
(the smaller the windows, the faster the convergence), and it is less
sensitive to noise (in the sense that we compute the average *m*_{l} of *u*_{0}over each window before selecting the function
whose mean is the closest one to *m*_{l}).