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5.2 MATCHING ALGORITHM FOR DSM GENERATION 
It seems as if the whole system is not reliable since only two images are used. Therefore, algorithms have to be developed that can 
provide good results with only two images. Matching errors, especially convergence to wrong minima have to be avoided since 
there is no posibility to detect them. 
Using least squares template matching algorithms good approximations are needed. They can be derived from an artificial digital 
teeth model. The relative position of teeth and mirror is similar in all cases of image acquisition. Assuming that all teeth are in the 
same plane, every ray of one image can be intersected with this plane to derive approximate coordinates in object space. These. 
coordinates lead to approximate coordinates for the patch in the other image. 
Geometric constrained least squares template matching is applied to generate the DSM (Baltsavias 1992). Six geometric and two 
radiometic parameters are estimated. Radiometric parameters are not treated as model parameters, they are calculated during the 
iterations. Non determinable parameters are detected automatically and excluded from estimation. This is very important as a lot of 
structures showing gradients only in x or y direction (contoures of the teeth) appear in the images. To solve this problems 
geometric constraints are used. 
5.3 IMPLEMENTATION OF THE ALGORITHM 
All software was written in Standard Borland C on an IBM?M compatible 486-DX2-66 machine. Borland C under DOS is only used 
for the development of algorithms. The final version of DigiDent will be implemented under Microsoft Windows™, 
First of all the influence of template size on the results was investigated. A optimum patch size of 15 x 15 pixel was selected. On 
a 486 DX2-66 platform an average matching time of 0.6 seconds was reached. 12 iterations were needed in average. o, a 
posteriori was less than 5 grayvalues. 
Problems came up matching reflecting areas of the teeth surface. Depth errors of some millimeters appeared. Compared to the 
depth-range of a single tooth two or three millimeters are quite a lot and not tolerable. These matching errors have to be eliminated 
automatically. 
  
Fig.15: Rendered DSM showing matching errors due to reflections Fig.16: Tooth with projected DSM 
Figure 16 shows an image of a single molar tooth with a projected wire frame model. 713 surface points were measured in a 
regular array of 31 x 23 points. Approximately 150 surface points were deleted. They were elinimated with respect to o, a 
posteriori, correlation of shift parameters and accuracy of the shift parameters. Thresholds were selected manually. Most 
eliminated points are situated around the reflecting area of the tooth. Figure 15 shows all measured surface points of the same tooth 
as shown in figure 16. The left part of figure 15 shows a smooth surface with only few mismatches. In the middle part the 
structured surface of the tooth can be recognized, but the right part shows many matching errors. Comparing the location of the 
matching errors shown in figure 15 with the image of the tooth in figure 16 one can see easily, that the matching errors appear in 
the reflecting rigth part of the tooth. 
6. DEFORMATION ANALYSIS 
No artificial points have to be marked or shall be marked on the teeth surface. Therefore special algorithms and techniques have to 
be devéloped to derive geometric parameters of 3D shifts and rotations for every single tooth. Every tooth has to be described by 
features that are related to its three-dimensional position and orientation. Feature extraction has to be robust, so that features are 
not strongly influenced by missing or wrongly matched surface points. Applying a three-dimensional matching algorithm on the 
features of the same tooth but in two different time periods its change of position and rotation can be derived. These results have 
to be analysed using statistic tests and related algorithms. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995