The method introduced here makes no requirements on the accuracy of the test object. In contrast to many previous autocalibration methods their approach also includes out-of-plane rotations of the detector. Although assuming a perfect rotation, the method seems to be sufficiently accurate for a commercial CBCT scanner. For devices which require higher dimensional geometry models, the method could be used as a initial calibration procedure.
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.
Abstract. This paper presents a three-dimensional GPU-accelerated algebraic reconstruction method in a few-projection cone-beam setting with arbitrary acquisition geometry. To achieve artifact-reduced reconstructions in the challenging case of unconstrained geometry and extremely limited input data, we use linear methods and an artifact-avoiding projection algorithm to provide high reconstruction quality. We apply the conjugate gradient method in the linear case of Tikhonov regularization and the two-point-step-size gradient method in the nonlinear case of total variation regularization to solve the system of equations. By taking advantage of modern graphics hardware we achieve acceleration of up to two orders of magnitude over classical CPU implementations.
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