concerning its three-dimensional orientation can be done
by one feature. From that point of view DSM matching is
used to determine four identical quasi homologue points
for every tooth to do deformation analysis. This leads to
a very flexible solution for the derivation of 3D position
and rotation changes since even one single tooth can be
used as reference.
To derive the deformation parameters of every single
tooth with respect to the choice of reference space the
features of the reference points in one time period are
transformed on the features in a different time period.
The deformation parameters of the teeth belonging to the
object space are derived by transformation of their
features with respect to the transformation of the
reference teeth. The final result is a set of 6
transformation parameters (3 shifts and 3 rotations) for
every single tooth including the teeth belonging to the
reference space. If they are really a reference their
transformation parameters must be smaller than the
inner accuracy of the measurement system.
7. TESTS AND RESULTS
To investigate the inner accuracy performance of the
measurement system a dental testmodel was measured
three times without moving or rotating any of the teeth.
Image data was processed using different template size
to investigate its influence on the results. The empirical
accuracy measures are calculated from the deformation
parameters treated like true errors corresponding to the
RMS divided by the square root of two. The values given
in table 11 are an average value of three transformations.
DSM I DSM Il
Hshifts | Hrotations
front-teeth |molar-teeth] front-teeth|molar-teeth| [mm] [radians]
21x21 21x21 21x21 21x21 0.091 0.044
21x21 15x15 21x21 15x15 0.096 0.048
15x15 15x15 15x15 15x15 0.167 0.061
15x15 11x11 15x15 11x11 0.186 0.071
21x21 21x21 21x21 15x15 0.103 0.027
21x21 21x21 15x15 15x15 0.260 0.139
21x21 15x15 15x15 11x11 0.298 0.122
Table 11: Empirical measures for inner accuracy
A total of more than 6000 surface points has to be
measured automatically for every version. On a
PENTIUMTM 75 platform approximately 2 hours of
computation time is needed corresponding to 1 second
per surface point (valid for version 21x21,15x15). As
described in chapter 5.2 different template size might be
used for front teeth (number 1-3) and molar teeth
(number 4-8). Since front teeth do not show much natural
structure, due to their smooth surface, they might be
measured using a larger template size than for molar
teeth. Table 11 shows, that best results can be achieved
when all teeth are measured with a template of 21x21
pixel size. But the loss off accuracy when measuring the
molar teeth with a smaller template of 15x15 pixels size
is very small. On the other hand the usage of large
templates increases computation time strongly. Table 11
shows that measuring the front teeth with a template size
smaller than 21x21 pixels the accuracy is decreasing
strongly by a factor of 2. Especially the comparison of
version 21x21,21x21 and version 15x15,15x15 shows
that strong degradation appears.
252
The same dental model was imaged under bad
illumination conditions to show its importance. All teeth
were measured with a template size of 15x15 pixels.
Front teeth number 1 and 2 could not be measured. The
empirical accuracy measures calculated from the
remaining 10 teeth show an accuracy of the shift
parameters of 0.625 mm and for the rotations of 0.193
radians. These results are a factor 4 worse than those
that can be achieved under good illumination conditions.
8. CONCLUSIONS
The investigations show that low cost standard
components can be connected to a powerful
measurement system.
It is possible to measure three-dimensional position and
orientation changes of teeth with an accuracy better than
100 microns for the shift parameters and better than 0.05
radians for the rotations without any artificial target
points fixed on the teeth's surface, provided that
appropriate illumination conditions are given.
Measuring position and orientation changes of teeth
during an orthodontic treatment is an interesting
application of digital photogrammetric techniques. The
results given by the measurement system are shift and
rotation parameters, simple numbers that have to be
interpreted by the orthodontist. Visualisation techiques
like photorealistic rendering and animation techniques
are an excellent tool to interpret the movements of the
teeth. The possibility to view the teeth three-
dimensionally gives the orthodontist the opportunity to
simulate and plan the orthodontic treatment even if the
patient is absent. This shows the great potential of
photogrammetric techniques in medical applications.
9. REFERENCES
Achilli V., 1992. Stereophotogrammetry: a possible
employment in the dental field. IAPRS, Vol. XXIX, part
B5.
Baltsavias E.P., 1992, Multiphoto Geometrically
Constrained Matching. Ph.D. Mitteilungen Nr. 49,
Institute of Geodesy and Photogrammetry, ETH Zurich.
Beyer H.A., 1992, Geometric and Radiometric Analysis
of a CCD-camera based Photogrammetric Close Range
System. Mitteilungen Nr. 51, Institute of Geodesy and
Photogrammetry, ETH Zurich.
Gruen A., 1986. Photogrammetrische Punktbestimmung
mit der Bündelmethode. Mitteilungen Nr. 40, Institute of
Geodesy and Photogrammetry, ETH Zurich.
Gruen A. and Stallmann D., 1991, High accuracy edge
matching with and extension of MPGC-matching
algorithm. SPIE, Vol. 1526, Industrial Vision Metrology,
Winnipeg, p. 42-55.
Mollersten L.; 1989, Comparison between guided and
freehand preparation. The journal of prosthetic dentistry,
August 1989,Vol. 62, number 2.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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