Ex vivo radiographic tooth length measurements with the reference sphere method (RSM)

A reference-based radiographic "reference sphere method" (RSM) for accurate length measurements in (dental) projection radiographs for the assessment of tooth length in dry human mandible sections is evaluated. RSM determines the depth coordinates of reference spheres placed in the object plane from the elliptical distortion of their shadows. Two segments (one canine and one molar) of dry human mandibles were exposed 95 times at different angulations (0-40°) on a dental charge-coupled device receptor. Three steel spheres (diameters d (1) = 2.00 mm, d (2) = 3.00 mm) were attached roughly coplanar with the tooth's main axis. Radiographs were assessed once by visual inspection plus manual landmark identification with a mouse-driven cursor. The results were compared to the true tooth length assessed after extraction and to a conventional method (C), i.e., the rule of proportion based on magnification of the sphere shadows. Mean relative length error was 2.28% (d (1)) and 0.46% (d (2)) for RSM and -13.58% (d (1)) and -9.90% (d (2)) for C. For both methods, length errors were significantly (p <  0.0001) correlated with the inclination relative to the receptor. RSM allows for complete a posteriori determination of the imaging geometry under the assumption of a known source-to-receptor distance. One specific application is foreshortening correction of objects coplanar with the reference spheres. Remaining errors are mainly due to incorrect landmark definition. In our setup, these were exaggerated by the visual/manual image-evaluation process. Automated image analysis has been shown for similar tasks to minimize these errors considerably.