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2. An outer iteration to
find the joint con
guration of the component set
f
X
i
;
i
¼
0
;
1
; ...;
N
1
g
by a belief propagation (BP) based inference [
7
].
The inner iteration and outer iteration are described as follows:
Algorithm I Inner iteration to
nd the con
guration X
i
of Vi,
i
For an object V
i
and its con
guration parameters Xi
i
gurations of Vi,
i
, X
i
;
1. Randomly generate a set of K con
k
¼
0
;
1
; ...;
1.
2. Compute the belief of each con
K
X
i
Þ
guration as
x
i
/
p
ð
I
j
based on the
component observation model as de
ned in Eq. (
1
), (
2
) and (
3
). Obviously
gurations of Vi,
i
, X
i
;
the K con
k
¼
0
;
1
; ...;
K
1 with their correspon-
dent beliefs
x
i
;
1 can be regarded as a particle based
non-parametric representation of the distribution p
ð
I
j
X
i
Þ
3. Resample from the distribution p
k
¼
0
;
1
; ...;
K
ð
I
j
X
i
Þ
to obtain new samples of the
guration of Vi,
i
, X
i
;
new
;
k
¼
con
1., which can be approxi-
mated by drawing samples from the distribution density
0
;
1
; ...;
K
fx
i
g
with the
guration X
i
correspondent con
followed by a random perturbation of the
guration X
i
.
4. Repeat 2
con
3 until the procedure converges.
-
Algorithm II Outer iteration (BP) to compute the joint distribution p
ð
X
j
I
Þ
the samples X
i
;
Given all
i
¼
0
;
1
; ...;
N
1
;
k
¼
0
;
1
; ...;
K
1
g
of
f
V
i
;
i
¼
0
;
1
; ...;
N
1} and the correspondent beliefs
fx
i
;
i
¼
0
;
1
; ...;
N
1
;
k
¼
0
;
1
; ...;
K
1}
f
X
i
g
1. Taking the randomly generated con
figurations
as candidate con-
as local beliefs, run a
(loopy) belief propagation on the graphical model as shown in Fig.
1
to
approximate the joint distribution p X
figurations of each component and the beliefs
fx
i
g
.
2. Compute the marginal distribution of each component as
ðÞ
j
I
fx
i
g
, which can
be obtained from the distribution p X
ðÞ
j
I
.
The basic concept of our optimization algorithm is to combine the inner and
outer iterations as shown in Algorithm III.
