thermore, the complexity of the process of evaluation
of a segmentation algorithm depends directly on the
number of parameters that need to be specified (Wirth
et al., 2006). Thus, reducing the number of param-
eters not only makes the methodology easier to use
and more adaptive, it facilitates the evaluation of the
approach.
In this paper, an extension of the BNN methodol-
ogy is proposed to incorporate automatic selection of
the appropriate kernel width. The proposed enhanced
BNNs do not suffer from the above mentioned short-
comings of the fixed-kernel-width BNNs and achieve
comparable segmentation performance.
The rest of the paper is organized as follows: Sec-
tion 2 provides a survey of related published work.
Section 3 contains a short description of BNNs. The
proposed enhancement of the BNNs is described in
Section 4. Section 5 is dedicated to the presentation
of experimental evaluation results. Section 6 contains
the conclusions.
2 RELATED WORK
Early foreground segmentation methods dealing with
non-stationary background are based on a model of
background created by applying some kind of low-
pass filter on the background frames. The high-
frequency changes in intensity or color of a pixel are
filtered out using different filtering techniques such
as Kalman filters (Karmann and von Brandt, 1990) to
create an approximation of background in the form of
an image (reference frame). The reference frame is
updated with each new frame in the input sequence,
and used to segment the foreground objects by sub-
tracting the reference frame from the observed frame
(Rosin, 1998). These methods are based on the most
restrictive assumption that observe pixel changes due
to the background are much slower than those due
to the objects to be segmented. Therefore they are
not particularly effective for sequences with high-
frequency background changes, such as natural scene
and outdoor sequences.
Probabilistic techniques achieve superior results
in case of such complex-background sequences.
These methods rely on an explicit probabilistic model
of the background, and a decision framework allow-
ing for foreground segmentation. A Gaussian-based
statistical model whose parameters are recursively up-
dated in order to follow gradual background changes
within the video sequence is proposed in(Boult et al.,
1999). More recently, Gaussian-based modelling was
significantly improved by employing a Mixture of
Gaussians (MoG) as a model for the probability den-
sity functions (PDFs) related to the distribution of
pixel values. Multiple Gaussian distributions, usu-
ally 3-5, are used to approximate the PDFs (Ellis and
Xu, 2001)(Stauffer and Grimson, 2000). The param-
eters of each Gaussian curve are updated with each
observed pixel value. If an observed pixel value is
within the 2.5 standard deviations (σ) from the mean
(µ) of a Gaussian, the pixel value matches the Gaus-
sian (Stauffer and Grimson, 2000). The parameters
are updated only for Gaussians matching the observed
pixel value, based on the following Equations:
µ
t
= (1−ρ)∗µ
t−1
+ ρ ∗X
t
(1)
σ
2
t
= (1−ρ) ∗σ
2
t−1
+ ρ ∗(X
t
−µ
t
)
T
∗(X
t
−µ
t
) (2)
where
ρ = ℵ(X
t
, µ
t−1
, σ
t−1
) (3)
and ℵ is a Gaussian function and X
t
is a pixel value
observed at time t. Equations 1 - 3 express a causal
low-pass filter applied to the mean and variance of the
Gaussian.
Using a small number of Gaussians leads to
a rough approaximation of the PDFs involved.
Due to this fact, MoG achieves weaker results
for video sequences containing non-periodical back-
ground changes (e.g. due to waves and water sur-
face illumination, cloud shadows, and similar phe-
nomena), as was reported in (Li et al., 2004). The
Gaussian-based models are parametric in the sense
that they incorporate underlying assumptions about
the probability density functions (PDFs) they are try-
ing to estimate.
In 2003, Li et al. proposed a method for fore-
ground object detection employing a Bayes decision
framework (Li et al., 2004). The method has shown
promising experimental object segmentation results
even for the sequences containing complex variations
and non-periodical movements in the background.
The primary model of the background used by Li
et al. is a background image obtained through low
pass filtering. However, the authors use a probabilis-
tic model for the pixel values detected as foreground
through frame-differencing between the current frame
and the reference background image. The probabilis-
tic model is used to enhance the results of primary
foreground detection. The probabilistic model is non-
parametric since it does not impose any specific shape
to the PDFs learned. However, for reasons of effi-
ciency and improving results the authors applied bin-
ning of the features and assigned single probability to
each bin, leading to a discrete representation of PDFs.
The representation is equivalent to a kernel-based es-
timate with quadratic kernel. The width of the kernel
used was determined empirically and remained fixed
in all the reported experiments(Li et al., 2004). The