Digital Signal Processing Reference
In-Depth Information
setting various parameters including sigma, which is used to smooth the input image
and the threshold
. Some experimental results and the source code can be referred
to
http://people.cs.uchicago.edu/pff/segment/
.
θ
1.2.2
Nonparametric Clustering-Based Segmentation
Mean shift analysis is a nonparametric, iterative procedure introduced by Fukunaga
[
31
] for seeking the mode of a density function represented by local samples, which
was generalized by Cheng for the image analysis [
33
]. More specifically, mean shift
estimates the local density gradient of similar pixels via finding the peaks in the local
density. It is proved that mean shift procedure is a quadratic bound maximization
both for stationary and evolving sample sets [
32
]. Comaniciu and Meer extended
this algorithm to the color image segmentation application [
34
].
Given
n
data points
x
i
in
d
-dimensional space. The general multivariate kernel
density estimator with kernel
K
(
x
)
is defined as
n
i
=
1
K
H
(
x
−
x
i
)
.
1
n
f
=
(1.4)
h
2
I
,(
1.4
) can be
For the radially symmetric kernel with the identity matrix
H
=
rewritten by
i
=
1
K
x
−
x
i
n
1
nh
d
f
=
.
(1.5)
h
By taking the gradient of (
1.5
) and employing some algebra, a mean shift vector
can be obtained by
f
C
∇
(
x
)
m
(
x
)=
,
(1.6)
f
(
x
)
where
C
is a positive constant and
i
x
−
x
i
h
2
1
x
i
g
(
)
)=
∑
=
(
)
−
.
m
x
x
(1.7)
x
−
x
i
i
1
g
(
2
∑
=
h
Note that the function
g
(
x
)
is the derivative of the kernel profile
k
(
x
)
, i.e.,
k
(
g
(
x
.
In general, the kernel
K
)=
−
x
)
is usually broken into the product of two differ-
ent radially symmetric kernels, namely the spatial domain and the color range.
For a still image, the mean shift segmentation algorithm [
35
] can be described as
following steps:
(1) Given an image, perform the mean shift filtering procedure until convergence.
(2) Grouping together all points that are closer than spatial and range kernel band-
widths.
(
x
)
