Digital Signal Processing Reference
In-Depth Information
Figure 13.4
Part of the training set. The first row consists of 20x20-pixel image patches that
contain cells; the lower row consists of non cell image patches.
Sample set
After fixing the patch size - in the following we will use 20
20 pixel
gray-level image patches - a training set of cell and non cell patches
has to be manually generated by the expert. The image set is enlarged
by adding rotated, flipped copies of the patches. The image patches are
then to be classified by a neural network. Figure 13.4 shows some cell
and non cell patches.
Interpreting each 20
×
20 image patch as a 400-dimensional vector,
wegetasetof
L
training vectors
×
T
:=
{
(
x
1
,t
1
)
,...,
(
x
L
,t
L
)
}
(13.12)
with
x
i
∈ R
n
-here
n
=20
2
- representing the image patch and
t
i
∈{
either 0 or 1, depending on whether
x
i
is a non cell or a
cell. This can easily be generalized to classify different types of cells.
The goal is to find a mapping that correctly classifies this data set that
is a mapping a
ζ
:
0
,
1
}
n
[0
,
1] with
ζ
(
x
i
)=
t
i
for
i
=1
,...,L
.Wecall
such a mapping
cell classifier
.Ofcourse
ζ
is not uniquely defined by
the above property, so some regularization has to be introduced. Any
interpolation technique, such as a Fourier or a Taylor approximation, can
be used to find
ζ
; we will use single-layer and multilayer perceptrons, as
explained in the following sections.
R
→
Preprocessing
Before we apply neural network learning, we preprocess the data as
follows. Denote
x
as the underlying
n
-dimensional random vector from
which the samples
x
have been drawn.
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