Digital Signal Processing Reference
In-Depth Information
Table 12.3
Summary of LDA Algorithms
Methods
Authors—Dates
Direct LDA (DLDA)
Yu et al. (2001) [
60
]
Parameterized Direct LDA (PD-LDA)
Song et al. (2007) [
61
]
Weighted LDA (WLDA)
Loog et al. (2001) [
62
]
Direct Weighted LDA (DW-LDA)
Zhou et al. (2004) [
63
]
Null Space LDA
Chen et al. and Liu et al. (2000, 2004)
[
64
,
65
]
Dual Space LDA
Wang et al. and Zheng et al. (2004,
2009) [
66
,
67
]
Regularized LDA
Pima et al. (2004) [
68
]
Generalized Singular Value Decomposi-
tion
Howland et al. and Ye et al. (2004,
2004) [
69
,
70
]
Direct Fractional Step LDA
Lu et al. (2003) [
71
]
Boosting LDA
Lu et al. (2003) [
72
]
Discriminant Local Feature Analysis
Yang et al. and Hwang et al. (2003,
2005) [
73
,
74
]
Kernel LDA
Liu et al. (2002) [
75
]
Kernel Scatter Difference Based Discrimi-
nant Analysis
Liu et al. (2004) [
76
]
2D-LDA
Li et al. (2005) [
77
]
Fourier LDA
Jing et al. (2005) [
78
]
Gabor LDA
Pang et al. (2004) [
79
]
Block LDA
Nhat et al. (2005) [
80
]
Enhanced
Fisher
Linear
Discriminant
Zhou et al. (2004) [
81
]
(EFLD)
Component-based cascade LDA
Zhang et al. (2004) [
82
]
Incremental LDA
Zhao et al. (2008) [
83
]
image sequence, the uncertainty that Gaussian model approximates the target state
is reasonable, and the use of the Kalman filter can gain better tracking [
86
,
87
].
In many situations of interest, the assumptions of linear and Gaussian do not
hold. The Kalman filter cannot, therefore, be used in some practical situations-
approximations are necessary. Particle filtering algorithm addresses these two issues.
The key idea is to represent the required posterior density function by a set of random
samples with associated weights and to compute estimates based on these samples
and weights.
Particle filter also known as sequential Monte Carlo method, has become a stan-
dard tool for non-parametric estimation in visual tracking applications. According to
the Bayesian theorem, estimating the object states is equivalent to determining the
posterior probabilistic density
p
n
x
(
x
k
|
y
1
:
k
)
of the object state variable where
x
k
∈
is a state vector,
y
k
is system observations and
k
is discrete time.
The basic idea of particle filter is to represent
p
(
x
k
|
y
1
:
k
)
using a set of weighed
x
(
i
)
k
i
N
i
particles (samples)
k
is
particle weight to evaluate the importance of a particle [
88
]. The main steps of par-
{
,w
k
}
i
=
1
, where
N
is the number of particles used,
w
