![](bg7.png)
on experience. Nevertheless it makes sense to devise
an automatic parameter selection technique in a fu-
ture version of the system. Also as future work, we
plan to consider other types of video information such
as more sophisticated texture models and geometric
prior knowledge (such as object’s rigidity, height and
shape) in order to yield as most reliable vessel detec-
tion algorithm as possible.
ACKNOWLEDGEMENTS
Thanks to the French customs for funding.
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APPENDIX
Let us prove the claim we made in section 3. For sim-
plicity’s sake and without loss of generality, we con-
sider the following MAP based image segmentation
problem:
min
O
λPerim
O
+ βA
O
+
Z
O
g(z) (10)
where g(z) is a positive function as it corresponds
−log of a probability. Now, let us consider the Chan
& Vese image segmentation model
λPerim
O
+
Z
O
( f (z) − c
1
)
2
σ
2
1
+
Z
O
( f (z) − c
2
)
2
σ
2
2
(11)
One may rewrite model 11 equivalently (after throw-
ing away the constant term) as follows
λPerim
O
+
Z
O
( f (z) − c
1
)
2
σ
2
1
−
( f (z) − c
2
)
2
σ
2
2
)
=
(
λPerim
O
+
Z
O
f
2
(z)
1
σ
2
1
−
1
σ
2
2
− 2 f (z)
c
1
σ
2
1
−
c
2
σ
2
2
+
Z
O
c
2
1
σ
2
1
+
c
2
2
σ
2
2
= λPerim
O
+
Z
O
f
2
(z)
1
σ
2
1
−
1
σ
2
2
− 2 f (z)
c
1
σ
2
1
−
c
2
σ
2
2
+ K
+ (
c
2
1
σ
2
1
+
c
2
2
σ
2
2
− K + R
A(O)
where K is the smallest positive constant (perhaps 0)
which makes the integrand term
f
2
(z)
1
σ
2
1
−
1
σ
2
2
−
2 f (z)
c
1
σ
2
1
−
c
2
σ
2
2
+ K
always positive, whatever z.
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