A method to calculate angular disparities between object and receptor in "paralleling technique"

A new digital tool for radiographic bone level measurements in longitudinal studies

Background

The reproducibility of measurements on radiographs is influenced by the techniques by which the images as well as the measurements are obtained. Thus, bias resulting from errors in the image and/or image examinations at two points in time may result in wrongful registrations of true biological or pathological changes. The aim of the present study was to propose and evaluate an indirect radiological examination technique, by which bias, when measuring radiographic bone level, could be substantially reduced as compared to the technique using direct mm measurements.

Methods

A plugin to ImageJ was designed to reduce bias when measuring bone loss on radiographic images. In human dry mandibles, radiographic images of 20 teeth were obtained parallel with the tooth axis (alpha = 0) and at an angle of 30° deviation. The direct technique of measuring radiographic bone level (RBL) and the indirect, length-adjusted RBL were registered by four researchers in a double blinded fashion.

Results

When mean RBL measured at 0° angle was 7.0 mm, the corresponding mean RBL measured at 30° angle was 7.8 mm, signifying an 11.4 % increase (p = 0.032), whereas the mean length-adjusted RBL increased by 0.6 % (p = 0.9).

Conclusions

This study showed that the use of the original, direct technique (ImageJ) resulted in markedly biased radiographic bone level at 30° angle, while the proposed indirect length-adjusted technique (ImageJ plugin) did not.

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.

Software for automated application of a reference-based method for a posteriori determination of the effective radiographic imaging geometry

OBJECTIVES

Presentation and validation of software developed for automated and accurate application of a reference-based algorithm (reference sphere method: RSM) inferring the effective imaging geometry from quantitative radiographic image analysis.

METHODS

The software uses modern pattern recognition and computer vision algorithms adapted for the particular application of automated detection of the reference sphere shadows (ellipses) with subpixel accuracy. It applies the RSM algorithm to the shadows detected, thereby providing three-dimensional Cartesian coordinates of the spheres. If the three sphere centres do not lie on one line, they uniquely determine the imaging geometry. Accuracy of the computed coordinates is investigated in a set of 28 charge-coupled device (CCD)-based radiographs of two human mandible segments produced on an optical bench. Each specimen contained three reference spheres (two different radii r1=1.5 mm, r2=2.5 mm). True sphere coordinates were assessed with a manually operated calliper. Software accuracy was investigated for a weighted and unweighted algebraic ellipse-fitting algorithm.

RESULTS

The critical depth- (z-) coordinates revealed mean absolute errors ranging between 1.1+/-0.7 mm (unweighted version; r=2.5 mm) and 1.4+/-1.4 mm (weighted version, r=2.5 mm), corresponding to mean relative errors between 5% and 6%. Outliers resulted from complete circular dense structure superimposition and one obviously deformed reference sphere.

CONCLUSIONS

The software provides information fundamentally important for the image formation and geometric image registration, which is a crucial step for three-dimensional reconstruction from > or =2 two-dimensional views.