Schematical view of scanned object with the random variables introduced.
Different scenarios for the acquisition of CB projections. (a) Two orthogonal projections, (b) two projections with less than 90°, (c) two small orthogonal arcs, (d) one small arc, (e) full 90°, and (f) full 180° arc with a dense set of projections.
The phantom for the experimental verification. Left: The phantom utilized for the measurements. Right: The schematical overview for the positions of the 1 mm chrome balls. The positions of the balls are calculated with . The balls are shifted along radial -direction to represent the plasticity of the phantom.
The detected feature positions in a projection at the imaging angle of 210.2° for the 20 phantom setups. The plot is in the -coordinates of the projection coordinate system with the imaging isocenter at its origin, as it is defined in Appendix A (Fig. 6). Each feature is present by a unique symbol, eventually presenting six detection clusters of the 20 phantom setups. Additionally, the 6 feature positions corresponding to the first phantom setup are framed by diamonds and for the second setup by circles. The detected feature positions of one phantom setup for all imaging angles are the input of the MAP estimation.
The results for the RMSE according to the rule of thumb formula (RoT, solid lines) and to 10 000 numerical simulations for 3D cone beam geometry (3D CB Sim, crosses). Left: The estimation error RMSE depending on the number of projections for different detection errors in reference to the maximal achievable RMSE for . The other parameters are , , and . Right: The estimation error RMSE depending on the number of detectable features for different plasticity parameters of the body . The other parameters are , , and .
Visualization of the coordinate systems used for the derivation of the MAP estimator.
Statistic evaluation of the accuracy of different imaging schemes of Fig. 2, cases a–f, for 20 setups. Shown are the empirical RMSEs as difference between estimated target position and the target position determined by CB-CT reconstruction along each coordinated for setup . They are defined with and analog for and . Additionally, the theoretical value out of the rule of thumb is presented for comparison (with NA due to high asymmetry of imaging directions).
Nomenclature of extended and newly introduced estimates and parameters of the prior knowledge. For clarification of the measured values, see Fig. 6.
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