Biomedical Engineering Reference
In-Depth Information
the proposed J-divergence-based active contour model to brain tissue segmenta-
tion for MR images. A lot of contributions [20, 21, 22, 23] have been made in this
area.
The remainder of the chapter is organized as follows. In Section 2 we briefly
introduce the variational segmentation model using J-divergence and derive the
corresponding evolution equation. Experimental results are demonstrated in Sec-
tion 3, and we conclude our work in Section 4.
2.
METHODS
In this section, we first introduce the energy functional based on J-divergence,
as well as its level set representation. The evolution equation coupled with the
level set is then derived and numerical implementation is briefly presented.
2.1. Variational Segmentation Model
The proposed energy functional is composed of region- and edge-based en-
ergies, which are complementary during the evolution of the hypersurface, as
suggested in [24, 10]. In our work, the regional energy is well suited for voxels far
from the object boundary, but degenerated in the vicinity of the boundary because
that local region may contain pixels sampled from more than one region. Hence,
edge-based energy is needed to reduce segmentation errors.
We first introduce the definition of region homogeneity. We follow the def-
inition from [16]: “A region
R
is considered to be homogeneous if its intensity
values are consistent with having been generated by one of a family of prespecified
probability distributions
p
(
I
θ
), where
θ
are the parameters of the distribution.” A
global region defined in this chapter is a homogeneous region. An image is made
up of global regions and their boundaries. A local region is the neighborhood
of a voxel, including itself. We confine our approach to the intensity image. It
can be extended easily to a vector image by using a multidimensional probability
distribution.
Next, let
I
|
q
be an input image, where Ω is an open and
bounded image domain (
p
=2or
p
=3)in Euclidean space,
q
is the dimension
of the observed data.
:Ω
∈
R
p
→
R
For example,
q
=1is an intensity image,
q
=3is a
color image.
Image
I
is composed of non-overlapping regions
{
R
i
}
and their
i
=1
m
boundaries
{
Γ
i
=
∂R
i
}
. They satisfy
R
i
∩
R
j
=
∅
when
i
=
j,
R
i
=Ω
/
Γ,
m
m
and Γ=
∂R
i
.
Based on the aforementioned definitions, we make the following assumptions:
Γ
i
=
i
=1
i
=1
1. The voxel intensity value in every global region
R
i
and local region that is
not nearby the object boundary are homogeneous. In other words, voxel
