Biomedical Engineering Reference
In-Depth Information
is initiated from small random selection of contour-boundary and non-contour-
boundary examples and should be terminated when a reasonable classification
(on a given slice) is achieved.
The MLP classified each pixel independently of the others, and therefore has
no notion of a closed contour. Consequently, the contour boundaries it produces
are often fragmented and noisy (false negatives and false positives, respectively).
Then, with this initial set of points classified as contour boundaries, a deformable
model is used to link the boundary segments together, while attempting to ignore
noise.
In [25] the
elastic net
algorithm is used. This technique is based on the
following equations:
N
G
ij
p
i
,
l
−
u
t
j
,
l
+
K
β
u
t
j
+
1
,
l
−
2
u
t
j
,
l
+
u
t
j
−
1
,
l
,
u
t
+
1
(7.25)
j
,
l
=
α
i
=
1
u
t
+
1
j
,
l
−
1
u
t
+
1
j
,
l
+
1
−
2
u
t
+
1
j
,
l
+
u
t
+
1
j
,
l
=
K
γ
(7.26)
,
where
u
t
+
1
j
,
l
is an interslice smoothing force,
K
is a simulated annealing term,
α, β, γ
are predefined parameters, and
G
ij
is a normalized Gaussian that weights
the action of the force that acts over the net point
u
j
,
l
due to edge point
p
i
,
l
(
l
is
the slice index).
The deformable model initialization is performed by using a large circle
encompassing the lung boundary in each slice. This process can be improved
by using the training set.
As an example, let us consider the work [74] in handwritten digit recogni-
tion. In this reference, each digit is modeled by a cubic B-spline whose shape is
determined by the positions of the control points in the object-based frame. The
models have eight control points, except for the one model which has three,
and the model for the number seven which has five control points. A model
is transformed from the object-based frame to the image-based frame by an
affine transformation which allows translation, rotation, dilation, elongation,
and shearing. The model initialization is done by determining the correspond-
ing parameters. Next, model deformations will be produced by perturbing the
control points away from their initial locations.
There are ten classes of handwritten digits. A feedforward neural network is
trained to predict the position of the control points in a normalized 16
×
16 gray-
level image. The network uses a standard three-layer architecture. The outputs
are the location of the control points in the normalized image. By inverting the
