Automatic storage of location, size, and orientation of the found structures with this software can be used for future anatomical studies. Thus, statistical tables with canal locations will be derived, which can improve anatomical knowledge of the teeth to alleviate root canal detection in the future. For this purpose the software is freely available at: http://www.dental-imaging.zahnmedizin.uni-mainz.de/.

A method is introduced, inferring the three-dimensional (3-D) location from the 2-D radiographic shadow of an opaque spherical reference body of known radius by considering its elliptical distortion, the 2-D shadow location and a known source-to-receptor distance. Three noncollinear spheres fixed to a rigid object constitute all possible degrees of freedom, i.e., the entire 3-D imaging geometry. The method may be used (a) to determine the 3-D imaging geometry from a single 2-D view and (b) to correct for foreshortening of object distances coplanar with the plane defined by the sphere triplet. Apart from the mathematical background the article describes a small feasibility experiment, performed with four different sphere diameters and a commercial dental ccd-receptor system (pixel length: 0.0195 mm). The mouse-cursor based image evaluation revealed an average underestimation of the critical depth- (x-) coordinate decreasing with increasing radius (-30.3% for r=0.5 mm to 2.8% for r=2.5 mm). Intraobserver reliability (the standard deviation between three single cursor-based assessments) ranged between 0% and 8% of the actual true depth. The main source of the input error is associated with the assessment of the amount of elliptical distortion, where subpixel accuracy is demanded. Consequently, software-based automated image evaluation is required using available methods for pattern recognition and point-spread correction. Provided sufficient accuracy, the method provides an important tool for foreshortening correction, depth assessment, motion analysis, and 3-D reconstruction from two or more 2-D views.

Precise registration of radiographic projection images acquired in almost arbitrary geometries for the purpose of three-dimensional (3D) reconstruction is beset with difficulties. We modify and enhance a registration method [R. Schulze, D. D. Bruellmann, F. Roeder, and B. d'Hoedt, Med. Phys. 31, 2849-2854 (2004)] based on coupling a minimum amount of three reference spheres in arbitrary positions to a rigid object under study for precise a posteriori pose estimation. Two consecutive optimization procedures (a, initial guess; b, iterative coordinate refinement) are applied to completely exploit the reference's shadow information for precise registration of the projections. The modification has been extensive, i.e., only the idea of using the sphere shadows to locate each sphere in three dimensions from each projection was retained whereas the approach to extract the shadow information has been changed completely and extended. The registration information is used for subsequent algebraic reconstruction of the 3D information inherent in the projections. We present a detailed mathematical theory of the registration process as well as simulated data investigating its performance in the presence of error. Simulation of the initial guess revealed a mean relative error in the critical depth coordinate ranging between 2.1% and 4.4%, and an evident error reduction by the subsequent iterative coordinate refinement. To prove the applicability of the method for real-world data, algebraic 3D reconstructions from few (< or = 9) projection radiographs of a human skull, a human mandible and a teeth-containing mandible segment are presented. The method facilitates extraction of 3D information from only few projections obtained from off-the-shelf radiographic projection units without the need for costly hardware. Technical requirements as well as radiation dose are low.

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