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4. Update R with the rectangle set with the highest quality bound in Q .
5. Stop and return R if R contains only one rectangle R . Otherwise go to Step 2.
The quality bound f for a rectangle set R should satisfy the following conditions:
f
(
)
(
)
1.
R
max R R f
R
f
2.
if R is the only element in R
Critical for the branch-and-bound scheme is to find the quality bound f .Giventhe
proven performance of the Gaussianized vector representation in classification tasks
shown in previous work [11, 13, 15, 12], we are motivated to design a quality bound
based on this representation, to enable localization based on this representation.
(
R
)=
f
(
R
) ,
4.2
Quality Function
For the Gaussianized vector representation, the binary classification score in Equa-
tion 9 informs the confidence that the evaluated image subarea contains the object
instead of pure background. Therefore, we can use this score as the quality function
for the Gaussianized vector representation.
In particular, according to Equation 8 and Equation 9, the quality function f can
be defined as follows,
)= t α t φ ( Z ) φ ( Z t ) b ,
f
(
Z
)=
g
(
Z
(13)
which can be expanded using Equation 7,
w c
2 Σ
K
k = 1
2
)= t α t
f
(
Z
μ k
c
w k
2
1
2
i
k
Σ
μ
b
c
K
k = 1
w k
= t α t
2 Σ 1
t
k
μ k μ
b
.
k
(14)
According to Equation 3, the adapted mean of an image-specifc GMM is the sum of
the feature vectors in the image, weighted by the corresponding posterior. Therefore,
K
k = 1
H
j = 1 Pr ( k | z j ) z j μ
w k
2
1
n k
)= t α t
Σ 1
k
t
k
f
(
Z
b
.
K
k = 1
H
j = 1
1
n k Pr
w k
2 Σ 1
t α t μ
t
k
=
(
k
|
z j )
z j
b
.
k
(15)
 
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