For example, on the first film, the upper incisor was chosen
as a feature, and reduced to a boundary representation by
the system (Figure 3). The corner of the tooth was chosen
as the point at which tooth displacement would be reported.
On the second digital image, the system extracted a larger
patch from the region of the image where the feature had
been located on the first image. This patch was searched
until the incisor boundary was found. Note on Figure 3 the
change in feature appearance and orientation that occurred
during the one year interval between films. In addition, the
extracted feature boundaries vary due to smearing of the
edges on the films themselves. The two boundaries were
matched using the algorithm described in Section 4, and the
displacement of the point on the feature was computed.
This process was repeated for the remaining features on the
second film, and for the third film. Note that the timepoint
three boundary in Figure 3 is quite different, due to the
placement of an orthodontic appliance on the tooth. For
comparison purposes, the same feature points were digitized
on each of the x-ray films themselves with a 0.1 mm
resolution Summagraphics digitizer. The registration points
were also digitized, and the feature point displacements
reported in the anatomic coordinate system defined by the
registration points.
5.2 Analysis
The anatomic feature comparisons were performed with four,
five, and six parameter transformations, and the six
parameter solution was again the best. As a result of the
boundary length tests performed in Section 6.3, a larger
number of feature boundary pixels (25) were used in these
tests. The average error in computed point displacement was
0.3 pixels (0.21mm at the image scale), slightly smaller
than the overall average from Section 4. The reduction in
error is likely due to the larger number of boundary pixels
included in the feature transformations. The results
indicate that the matching algorithm performs well, even in
the presence of changes in feature shape and orientation due
to anatomic growth. There was no significant difference in
the results of the transformation of the timepoint 2 film
onto the timepoint 1 film, compared to transformation of the
timepoint 3 film.However, in this case the improvement over
the 5 parameter transformation was significant at the .01
level, indicating the non-orthogonality of feature growth
over the two year period.
These results do not have the effects of pointing error
removed, as did the tests in Section 4. When a feature was
initially selected on the first x-ray of the series, a
feature point was designated as the point at which
displacement would be computed. For example, the
displacement of the upper incisor would be reported at the
tooth edge. Assume that this point selection was exact, and
only limited by the resolution of the digital image. When
the x-rays were manually digitized to compute the comparison
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