The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
mm in each dimension, on which 30 control points were 
available, as shown in Figure 1. 
The pixel size and principal distance were unknown, so a pixel 
size of was 0.01 mm was adopted. Calibration using 
PhotoModeler software (PhotoModeler, 2005) and eight images 
(see Figure 1 for an example) yielded a principal distance of 8.1 
mm, and distortions which can be characterised by a radial 
distortion K t value of 0.006, (so that imagery had a radial shift 
of 10 pixels at a radial distance of 400 pixels) and a tangential 
distortion P] value of 0.00009. 
2.3 Teeth as imaging objects 
A major photographic challenge derives from the optical 
characteristics of dental enamel. It is featureless and is 
unsuitable for photogrammetric mapping without some 
augmentation. Tooth enamel is also partially translucent and 
yet highly reflective, the latter causing areas of glare, especially 
from the in-built illumination of an intra-oral camera. In 
addition, imaging difficulties are created by the inevitable 
coating of saliva. 
3. CASE STUDY 
Although a limited number of imaging and basic measurement 
tests have been carried out on teeth in the mouth, realistic 
measurement trials have been carried out on an extracted tooth 
to avoid patient discomfort. It is recognised that its optical 
characteristics are not necessarily identical to those of a live 
tooth. 
In one of the more successful, and also one of the more 
informative cases, a stereo-pair of parallel images was collected 
of an extracted frontal incisor tooth. To make the enamel 
surface opaque and textured, it was painted with a weak water 
colour solution: see Figure 2. The resultant texture had no pre 
designed shapes or patterns. 
Figure 2. Right hand image from stereo-pair, taken at a 
distance of 17 mm from the tooth. 
The tooth was moved a measured distance of 6.00 mm under 
the camera by using a translatable slide fitted with a micrometer. 
The tooth, which was about 8.5 mm across at its widest point, 
was imaged from a distance of about 17 mm, giving a scale of 
about 0.025 mm per pixel. The base distance gave an overlap 
of 60% and a base-to-height ratio of 1:2. 
Monochrome versions of the imagery were searched for 
features using an interest operator; each feature on the left 
image was paired with features on the right image on the basis 
of predicted x and y coordinate differences; points were then 
matched to sub-pixel precision by an in-house area-based 
matching algorithm. Matches were accepted if they exceed 
threshold values of correlation co-efficient and match precision. 
4. RESULTS 
A large number - about 450,000 - of candidate points were 
found using interest operator on each image. With acceptance 
values of a minimum 0.9 for the correlation co-efficient and a 
maximum 0.1 pixels for the match precision, about 600 matches 
on the tooth were accepted. However, the points were localised, 
as areas of low texture (including high reflection) affected a 
significant proportion of the field-of-view of the tooth. 
Moreover, the existence of good matches in the vicinity of the 
texture is very apparent, and emphasises the difficulty of 
texturisation; see Figure 3. 
Figure 3. Distribution of 600 successful matches on a limited 
region of the tooth, shown superimposed on the monochrome 
left image. The paucity of points in the vicinity of glare and 
light texture is very apparent. 
For this work, a single camera has been moved, by an amount 
which has been determined by a relative orientation using the 
PhotoModeler software which requires manual point selection 
(PhotoModeler, 2005), but this manual intervention is not an 
acceptable long-term option. 
The precision of 0.1 pixels represents about 0.003 mm across 
the tooth, or a satisfactory depth precision of about 0.006 mm 
assuming a base-to-height ratio of 1:2. The true accuracy of the 
surface delineation has not yet been evaluated, and indeed it is 
hard to do so. Comparison with replicas by mechanical means 
involves a comparison with a technique of similar accuracy. 
781