Digital Signal Processing Reference
In-Depth Information
Tabl e 5. 6
Rank one recognition performance for WVU Multimodal dataset [130]
SMBR-WE
SMBR-E
SLR-Sum
SLR-Major
SVM-Sum
SVM-Major
4 Fingerprints
97.9
97.6
96.3
74.2
90.0
73.0
2 Irises
76.5
78.2
72.7
64.2
62.8
49.3
Overall
98.7
98.6
97.6
84.4
94.9
81.3
on the sparse error, though the error may not be sparse in image domain. Further,
sum-based fusion shows a superior performance over voting-based methods. A
surprising result is the performance of SLR using all the modalities, which is lower
than its performance on the fingerprints. Due to the poor quality of iris images,
the performance of sum and voting based fusion techniques go down. However, by
jointly classifying all the modalities together, SMBR achieves a robust performance,
even though no weights based on quality has been assigned during testing.
5.5
Kernel Space Multimodal Recognition
The class identities in the multibiometric dataset may not be linearly separable.
Hence, one can also extend the sparse multimodal fusion framework to kernel space.
5.5.1
Multivariate Kernel Sparse Representation
Y
i
D
i
{
}
Considering the general case of
D
modalities with
as a set of
d
i
observa-
=
1
tions, the feature space representation can be written as:
Y
i
y
i
1
)
,
φ
(
y
i
2
)
,...,
φ
(
y
i
d
)]
Φ
(
)=[
φ
(
=
,···,
Similarly, the dictionary of training samples for modality
i
1
D
can be
represented in feature space as
X
i
X
i
1
)
,
φ
(
X
i
2
)
,···,
φ
(
X
i
C
)]
Φ
(
)=[
φ
(
As in the joint linear space representation, we have:
Y
i
X
i
i
Φ
(
)=
Φ
(
)
Γ
i
is the coefficient matrix associated with modality
i
. Incorporating
information from all the sensors, we seek to solve the following optimization
problem similar to the linear case:
where,
Γ
D
i
=
1
Φ
(
Y
i
1
2
ˆ
X
i
i
2
F
Γ
=
arg min
Γ
)
−
Φ
(
)
Γ
+
λ
Γ
1
,
q
(5.24)
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