Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
(e)
(f)
Figure 14.
Evolution of region information-based snake for left ventricle segmentation from
MR images. The homogeneity parameter is used in conjunction with the other standard
energy functions, like geometric and edge functional, to evolve to the final contour, as
shown by the white line in (g) from the initial contour in (a). See attached CD for color
version.. Reprinted with permission from [29]. Copyright c
1997, Institute of Physics.
by maximizing the probability that the contour traverses through a high-gradient
region and encloses a region having similar regional features. The regional fea-
ture can be defined in terms of the homogeneity of intensity or any other desired
attribute. The intensity feature was used in the work reported by Chakraborty and
colleagues [35], Thus, mathematically the work contour searches for minimizing
the entropy or maximizing the likelihood function, defined by
ma
p
{
P
(
p
|
I
g
,I
s
)
}
= ma
p
[ln
P
(
p
)+ln
P
(
I
g
|
p
)+ln
P
(
I
s
|
p
)]
,
(15)
where the first term on the right-hand side (RHS) defines the geometric shape
parameter, and the second term is defined by the gradient along the contour. This
term can be defined by computing the gradient, using the derivative of the Gaussian
convolved with the intensity. The integral is taken over the entire curve. Thus,
maximizing this function represents that for a given pattern of geometric shape the
maximum possible need of the contour to cover the high-gradient region. In most
medical images, due to the previously mentioned causes, the gradients in many
