Accurate registration of random radiographic projections based on three spherical references for the purpose of few-view 3D reconstruction.

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.