Biomedical Engineering Reference
In-Depth Information
2.
PROSTATE BOUNDARY SEGMENTATION FROM 2D TRUS IMAGES
2.1. Discrete Dynamic Contour (DDC)
2.1.1. Overview of the DDC
Our 2D segmentation algorithm [31] is described in Section 2.2, and is based
on the Discrete Dynamic Contour (DDC) developed by Lobregt and Viergever
[32]. We utilized the DDC because of its proven performance on noisy medical
images and because of its simplicity of implementation. The DDC is represented
by a sequence of vertices connected by straight-line segments that automatically
deform to fit features in an image. When using the DDC to segment the boundary
of an object from an image, the user must first initialize the DDC by drawing
an
approximate
outline of the object. This initial outline defines the DDC, and
is automatically and iteratively deformed to fit nearby features (e.g., edges) that
presumably lie on the object's boundary. In principle, less user effort is required
to outline an object using the DDC than to outline the object manually because
the initial definition need only be approximate and can be drawn quickly with
only a few vertices. Furthermore, because the deformation of the contour drives
it toward edges automatically, there is a potential for less intra- and interoperator
variability compared to manual outlining. Intuitive editing mechanisms can also
be incorporated to allow the user to modify the DDC in problematic areas, where
it is not able to find the object's boundary. Mathematical details of the operation of
our DDC approach used to segment the prostate boundary from ultrasound images
are given below.
2.1.2. Structure of the DDC
The structure of the DDC at a particular iteration
t
(analogous to time) during
the deformation process is depicted in Figure 1a. The DDC consists of vertices
(
V
i
) with coordinates (
x
i
,y
i
) that are connected by straight-line segments. A unit
edge vector
d
i
is defined such that it points from vertex
i
to vertex
i
+1.A
local tangential unit vector at vertex
i
, denoted
t
i
, is defined from the two edge
vectors associated with the vertex by the vector addition of
d
i
and
d
i−
1
, and then
normalizing the sum. A local outer radial unit vector at vertex
i
, denoted
r
i
,is
defined from
t
i
by rotating
t
i
by
π/
2 radians.
The position of each vertex at
t
=0(i.e., at the beginning of the iterative
deformation process) is specified by the user-drawn contour.
2.1.3. Dynamics
Once initialized, the DDC is iteratively and automatically deformed. The
deformation process is based on Newtonian mechanics. At a particular iteration
t
,
a net force,
f
i
, is computed for each vertex
i
; the force serves to drive each vertex
