Digital Signal Processing Reference
In-Depth Information
In this paper, we successfully introduce the spatial-temporal constraints into the
T2-FGMM by the MRF framework to achieve superior modeling performance for
dynamic backgrounds. Different to [5], this work can deal with dynamic scenes well
since the fuzzy method is used. Firstly, the output of T2-FGMM is regarded as the
initial labeling field of the MRF. Then, the local energy of the labeling field is ele-
gantly combined with that of the observation by a Bayesian framework. The Iterated
Conditional Modes (ICM) algorithm, due to its calculation efficiency, is employed to
obtain the maximum a posterior probability (MAP). The contribution of this paper is
that we successfully combine the spatial-temporal prior and the observation of the
T2-FGMM to achieve satisfactory performance for dynamic backgrounds. The expe-
riment results show that the designed method behaves better than GMM and
T2-FGMM in such typical dynamic backgrounds as waving trees and water rippling.
The rest of the paper is organized as follows: state of the art and some recent works
are reviewed briefly in Section 2. Section 3 is the basic principle of T2-FGMM. Sec-
tion 4 gives the details of the designed background modeling approach. Experiment
results are shown in Section 5, and the conclusion is provided in Section 6.
2
Related Works
The common approach for background subtraction is to give an appropriate back-
ground model, which aims to deal with the challenges such as illumination variant,
dynamic backgrounds, camouflage, shadows, etc. Wren
et al.
[11] model the back-
ground as a single Gaussian in the system called “Pfinder”, which aims to detect
people indoors. But this method cannot handle the outdoor scenes well, since the dis-
tribution of gray-level value outdoors is multimodal. Stauffer and Grimson [4] model
the background as a Gaussian Mixture Model, which can deal with the multimodal
background well. But the update of GMM's parameters cannot accommodate with the
rapidly changing scenes, such as sudden illumination changes, dynamic backgrounds,
etc. Non-parametric methods are proposed in [12, 13], which are more flexible for the
rapid variation of the background at the price of heavy computation. Compared with
the model-based methods above, the data-based methods have lower computation
complexity, and can handle part of the background challenges with the well-designed
processes of initialization and update like Vibe [14]. The self-organizing approach for
background subtraction proposed by Maddalena
et al
. [15]
may be one of best me-
thods for the moment, which learns background motion in a self-organizing manner
through the technique of the neural network. Other recent works using fuzzy
approaches can be found in [16].
3
Type-2 Fuzzy Gaussian Mixture Model
T2-FGMM [10] consisting of
K
components of multivariate Gaussian with an uncer-
K
tain mean vector is described as:
p
()
x
=
ωη
(; , ,
x
μ
Σ
where
ω
denotes the
k
k
k
k
k
=
1
