Biomedical Engineering Reference
In-Depth Information
where
c
i
is the local curvature vector at vertex
i
. The definition of
f
in
i
as in Eq. (4a)
prevents the DDC from collapsing to a point in the absence of image forces. Such
a collapse would occur if
f
in
i
were simply taken to be proportional to
c
i
.
The damping force
f
i
is used to prevent oscillation of the DDC and to ensure
convergence to the desired equilibrium state.
f
i
is taken to be proportional to the
velocity (
v
i
) at vertex
i
:
f
i
=
w
i
v
i
,
(5)
where
w
i
is a negative weighting factor.
2.2. Prostate Segmentation Algorithm
2.2.1. Modifications to the DDC
Our experience shows that it is difficult to apply the DDC directly to 2DTRUS
images of the prostate because the images suffer from speckle, shadowing, and
refraction. Moreover, the contrast between the prostate and surrounding tissues
is low and dependent on the system's transducer and ultrasound frequency. In
order to overcome these effects, the user must draw the initial outline accurately
if the DDC is to converge to the correct boundary features, and not to nearby non-
prostate edges. However, accurate initialization requires substantial user effort
since many points may need to be entered. Therefore, we have focused our efforts
on developing an initialization routine that uses prostate-specific shape information
to obtain a good estimate of the prostate boundary with very little user input. To
aid the deformation algorithm in converging on the prostate boundary rather than
edges corresponding to surrounding tissues, we have incorporated edge direction
information into the image force field. Finally, we have developed editing tools to
allow the user to guide the DDC in problematic regions. Each of the modifications
is described below and in detail in the literature [31].
2.2.2. Initialization
Our initialization routine requires the user to select only four seed points,
labeled from (1) to (4) in Figure 2a. Points (1) and (3) form the approximate axis
of symmetry, and points (2) and (4) lie at the extremities in a direction perpendicular
to the axis of symmetry. An
x
y
coordinate system is defined with the
y
-axis
directed from point (1) to point (3). The
x
-axis is perpendicular to the
y
-axis, and
is oriented toward point (2). The origin of the coordinate system is at the average
of points (1) and (3).
The four seed points subdivide the prostate boundary into four unique seg-
ments: segment 1-2 starting from point 1 and ending on point 2, as well as seg-
ments 2-3, 3-4, and 4-1. The initial shape is estimated by cubic interpolation of
the endpoints to automatically generate points within each segment. The initial
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