sults are obtained with real clinical images.
ACKNOWLEDGEMENTS
This work has been partially supported by FIS
projects PI04/0857, PI05/1953 and by the Greece-
Spain Integrated Action HG2004-0014.
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APPENDIX
In algorithm 3 we need to calculate the quantities
E[x
j
]
q
k
(x)
, E[log(π
c
p
G
(x
j
| β
c
,α
c
))]
q
k+1
(x),q
k+1
(β),q
k
(π)
,
E[1/β
c
]
q
k+1
(β)
and E[logA
i, j
x
j
]
q
k+1
(x)
.
To calculate E[x
j
]
q
k
(x)
we note that (see Eq. 8)
E[x
j
]
p
G
(x
j
|u
j
,v
j
)
= v
j
(61)
To calculate E[1/β
c
]
q
k+1
(β)
we observe with the use of
Eq. 13 that
E
1
β
c
q(β
c
|r
c
,s
c
)
=
=
β
c
((r
c
− 1)s
c
)
r
c
Γ(r
c
)
β
−(r
c
+1)−1
c
e
−(r
c
−1)s
c
/β
c
dβ
c
=
((r
c
−1)s
c
)
r
c
Γ(r
c
)
Γ(r
c
+ 1)
((r
c
−1)s
c
)
r
c
+1
=
r
c
(r
c
−1)s
c
(62)
VISAPP 2007 - International Conference on Computer Vision Theory and Applications
172