Pose determination of a cylindrical (dental) implant in three-dimensions from a single two-dimensional radiograph

OBJECTIVES

The aim was to develop an analytical algorithm capable of determining localization and orientation of a cylindrical (dental) implant in three-dimensional (3D) space from a single radiographic projection.

METHODS

An algorithm based on analytical geometry is introduced, exploiting the geometrical information inherent in the 2D radiographic shadow of an opaque cylindrical implant (RCC) and recovering the 3D co-ordinates of the RCC's main axis within a 3D Cartesian co-ordinate system. Prerequisites for the method are a known source-to-receptor distance at a known locus within the flat image receptor.

RESULTS

Accuracy, assessed from a small feasibility experiment in atypical dental radiographic geometry, revealed mean absolute errors for the critical depth co-ordinate ranging between 0.5 mm and 5.39 mm. This translates to a relative depth error ranging from 0.19% to 2.12%.

CONCLUSIONS

Experimental results indicate that the method introduced is capable of providing geometrical information important for a variety of applications. Accuracy has to be enhanced by means of automated image analysis and processing methods.

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.