Biomedical Engineering Reference
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provides advantages such as eliminating the need to reparameterize the curve and
automatic handling of topology changes via level set implementation [20].
In this section we present two cell segmentation approaches both using level
setbased geometric active contours: (1) region-based segmentation and our exten-
sions [1, 22]; and (2) edge-based segmentation and our extensions [23, 46]. The
first approach is used for images where cells or nuclei appear as semi-homogeneous
blobs with vague borders. The second approach is used for images where the in-
terior of the cells appears highly heterogeneous or where interior and exterior
intensity distributions are similar. The type of the cells, environmental conditions,
and imaging characteristics such as zoom factor affect the appearance of cells, and
thus choice of the approach.
3.2.1 Region-Based Active Contour Cell Segmentation
Segmentation of multiple cells imaged with a phase contrast microscope is a chal-
lenging problem due to difficulties in segmenting dense clusters of cells. As cells
being imaged have vague borders, close neighboring cells may appear to merge.
Accurate segmentation of individual cells is a crucial step in cell behavior analysis
since both over-segmentation (fragmentation) and under-segmentation (cell clump-
ing) produce tracking errors (i.e., spurious or missing trajectories and incorrect split
and merge events).
In this section, we describe three different region-based level set segmentation
methods and their performance for separating closely adjacent and touching cells in
a dense population of migrating cells. The three techniques described in this section
are all based on the ''active contour without edges'' energy functional [24] with
appropriate extensions. These include a two-phase Chan and Vese algorithm [24]
(
CV-2LS
), an
N
−
level set algorithm with energy-based coupling by Zhang et al.
[25] (
ZZM-NLS
), and an improved version of of our four-color level set algorithm
with energy-based and explicit topological coupling [1] (
NBP-4LS-ETC
). The latter
two techniques use coupling constraints to prevent merging of adjacent cells when
they approach or touch each other.
Chan and Vese Active Contours Formulation
In [24], Chan and Vese presented an algorithm to automatically segment an image
I
into
two
distinct regions (or phases). The segmentation is done by minimizing
the Mumford-Shah functional in (3.14) with respect to the scalar variables
c
1
,
c
2
,andf;withf
(
y
)
(
y
)
being the 2D level set function and
u
(
y
)
being the intensity
image.
m
1
2
H
E
pc
(
c
1
,
c
2
,
f
)=
(
u
(
y
)
−
c
1
)
(
f
(
y
))
d
y
m
2
2
+
(
u
(
y
)
−
c
2
)
(
1
−
H
(
f
(
y
))
d
y
n
+
|∇
H
(
f
(
y
))
|
d
y
(3.14)
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