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curve deformation, which makes them robust to region inhomogeneities. On the
other hand, they are sensitive to image noise and contour initialization due to the
use of local gradients. Yang and her colleagues proposed an improved algorithm to
segment coronary arteries based on a Bayesian probabilistic framework [
16
]. In
their work, the image force is redefined using posterior probabilities, calculated
from the global histogram distributions, to more accurately terminate the surfaces
at desired boundaries. In their method, the posterior probabilities are obtained from
global statistics, which cannot handle the varying brightness and contrast changes
over the image. Thus, their method is not capable of segmenting small and distal
segments of the coronary arteries due to their relatively low intensity contrast. In
medical images, the borders between different objects are not always clearly
defined by the gradients, and thus, the contour may leak into adjacent regions,
when using the edge function as the stopping criterion. Nain et al. [
17
] incorporate
a soft shape prior into the conventional active contour model. They propose the
application of a shape filter to locally describe the shape of the segmented region.
As illustrated in Fig.
5.3
, the shape filter is defined as a ball structure centred on
each point along the contour with radius r. This measures the percentage of voxels
belonging to both the ball and the object (i.e. the regions inside the contour). The
output of the shape filter is high when the current point belongs to a region
corresponding to leakage. Conversely, lower values of the filter's output indicate
that the current point is within the vessel. The filter response then serves as the
external energy of the active contour, penalising leakages during the curve evo-
lution. However, the shape filter cannot discriminate vessel bifurcations from
leakage
areas,
and
may
result
in
undesired
gaps
in
the
vicinity
of
vessel
bifurcations.
Region-based image segmentation methods, which utilise intensity information
obtained from image regions, are more robust to image noise. In these methods,
region statistics along the contour are calculated to drive the segmentation process.
Under the assumption that the object and the background are approximately uni-
formly distributed, Chan and Vese [
6
] proposed an active contour model using
regional statistics to segment the object of interest in two-phase images. Their
work was later extended to multiple-phase images [
18
], where the N regions
(phases) are represented by log
2
N level set functions. However, empty regions will
be produced when less than N regions are present in the image. To handle more
complex intensity distributions, non-parametric method is applied to estimate
regional statistics [
19
]. The aforementioned methods, however, solely based on
global intensity statistics, are inefficient in cases where regional statistics are
spatially varying across the image. Localised approaches [
20
-
22
], where regional
statistics are calculated in a neighbourhood of the active contour, have recently
emerged to overcome this problem. Such models are more robust to local varia-
tions of the region of interest and therefore improve the overall segmentation
results. However, segmentation based on local decisions alone may not be suffi-
cient to drive the contour to stop at the desired boundaries, since the contour may
be
trapped
in
undesired
local
stationary
points.
Moreover,
the
selection
of
appropriate scales also poses additional difficulties.
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