Biomedical Engineering Reference
In-Depth Information
1
D
w
j
¼
þ e
;
2
ð
dx
j
dx
c
Þ
(11.4)
1
d
w
j
¼
;
2
ð
dx
j
dx
0
Þ
þ e
where
dx
c
is the correct pin-hole displacement,
dx
0
is the recognized pin-hole
displacement,
w
j
are the positive and the negative training factors for
the
j
th neuron, and
dx
j
is the pin-hole displacement corresponding to the
j
th neuron
(Fig.
11.11
). For coordinate
Y
, similar formulas are used.
The results of the investigation of the neural interpolator are shown in Table
11.2
for coordinate
X
and Table
11.3
for coordinate
Y
. In Tables 11.1, 11.2, and 11.3, the
average results for six independent experiments are presented. The experiments
show that the computer vision system can recognize a relative pin-hole position
with a 0.1 mm tolerance. The neural classifier for this tolerance gives the correct
recognition in 100% of cases for
X
and 86.7% of cases for
Y
(Table
11.1
). The neural
interpolator gives 100% for axis
X
(Table
11.2
) and 99.86% for axis
Y
(Table
11.3
).
The neural interpolator also permits us to obtain data for smaller tolerances. For
example, for axis
X
with 0.05 mm tolerance, it gives an 88.6% recognition rate, and
for axis
Y
with 0.05 mm tolerance, it gives a 79.1% recognition rate. The experi-
ments show that the neural interpolator gives better results in estimating pin-hole
relative positions.
It is interesting to observe that the 0.05 mm tolerance for the
Y
axis is less than
one pixel in the image. In this case, the recognition rate of 79.1% shows that
recognition possibilities are not limited by the resolution of one pixel. This result
could be explained by the fact that each object in the image contains many pixels,
which give much more detailed information than one pixel.
D
w
j
and
d
E
Correct pin-hole
displacement
D
w
j
dx
d
w
j
Recognized pin-hole
displacement
Fig. 11.11 Correct and
recognized displacements
