Biomedical Engineering Reference
In-Depth Information
Finally, its level set representation is also given by replacing
g
col
(
·
) for
g
(
·
)in
(10.21):
R
·∇
φ.
φ
t
=
g
col
(
|∇
I
|
)(
κ
+
α
)
|∇
φ
|+∇
g
col
(
|∇
I
|
)
·∇
φ
−
β
(10.33)
10.7 The Mean Shift Algorithm
This section can be skipped without loss of continuity. Its topic is the process of
generating the image region segmentation map
S
which is then used as described
in Section 10.4.2. The reader can assume it is available and skip to the next
section.
An essential requisite for RAGS is a segmentation map of the image. This
means that RAGS is independent of any particular segmentation technique as
long as a region map is produced; however, it is dependent on its representational
quality. In this section, the mean shift algorithm is reviewed as a robust feature
space analysis method which is then applied to image segmentation. It provides
very reasonable segmentation maps and has extremely few parameters that
require tuning.
The concept underlying the nonparametric mean shift technique is to ana-
lyze the density of a feature space generated from some input data. It aims to
delineate dense regions in the feature space by determining the modes of the un-
known density, i.e. first the data is represented by local maxima of an empirical
probability density function in the feature space and then its modes are sought.
The denser regions are regarded as significant clusters. Comaniciu
et al.
[13, 20]
have recently provided a detailed analysis of the mean shift approach, including
the review below, and presented several applications of it in computer vision,
e.g. for color image segmentation.
We now briefly present the process of density gradient estimation. Consider
a set of
n
data points
{
x
i
}
i
=
1
,...,
n
in the
d
-dimensional Euclidean space
R
d
. Also
consider the Epanechnikov kernel, an optimum kernel yielding minimum mean
integrated square error:
2
Z
d
(
d
+
2)(1
−
x
T
x
)
,
1
if
x
T
x
<
1
K
(
x
)
=
(10.34)
otherwise
,
0
,
