Auto calibration of a cone‐beam‐CT
Authors: Gross Daniel , Heil Ulrich , Schulze Ralf , Schoemer Elmar , Schwanecke Ulrich 
Published: September 2012

Purpose:

This paper introduces a novel autocalibration method for cone‐beam‐CTs (CBCT) or flat‐panel CTs, assuming a perfect rotation. The method is based on ellipse‐fitting. Autocalibration refers to accurate recovery of the geometric alignment of a CBCT device from projection images alone, without any manual measurements.

Methods:

The authors use test objects containing small arbitrarily positioned radio‐opaque markers. No information regarding the relative positions of the markers is used. In practice, the authors use three to eight metal ball bearings (diameter of 1 mm), e.g., positioned roughly in a vertical line such that their projection image curves on the detector preferably form large ellipses over the circular orbit. From this ellipse‐to‐curve mapping and also from its inversion the authors derive an explicit formula. Nonlinear optimization based on this mapping enables them to determine the six relevant parameters of the system up to the device rotation angle, which is sufficient to define the geometry of a CBCT‐machine assuming a perfect rotational movement. These parameters also include out‐of‐plane rotations. The authors evaluate their method by simulation based on data used in two similar approaches[L. Smekal, M. Kachelriess, S. E, and K. Wa, “Geometric misalignment and calibration in cone‐beam tomography,” Med. Phys. 31(12), 3242–3266 (2004) 10.1118/1.1803792; K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, “A geometric calibration method for cone beam CT systems,” Med. Phys. 33(6), 1695–1706 (2006) 10.1118/1.2198187]. This allows a direct comparison of accuracy. Furthermore, the authors present real‐world 3D reconstructions of a dry human spine segment and an electronic device. The reconstructions were computed from projections taken with a commercial dental CBCT device having two different focus‐to‐detector distances that were both calibrated with their method. The authors compare their reconstruction with a reconstruction computed by the manufacturer of the CBCT device to demonstrate the achievable spatial resolution of their calibration procedure.

Results:

Compared to the results published in the most closely related work [K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, “A geometric calibration method for cone beam CT systems,” Med. Phys. 33(6), 1695–1706 (2006) 10.1118/1.2198187], the simulation proved the greater accuracy of their method, as well as a lower standard deviation of roughly 1 order of magnitude. When compared to another similar approach [L. Smekal, M. Kachelriess, S. E, and K. Wa, “Geometric misalignment and calibration in cone‐beam tomography,” Med. Phys. 31(12), 3242–3266 (2004) 10.1118/1.1803792], their results were roughly of the same order of accuracy. Their analysis revealed that the method is capable of sufficiently calibrating out‐of‐plane angles in cases of larger cone angles when neglecting these angles negatively affects the reconstruction. Fine details in the 3D reconstruction of the spine segment and an electronic device indicate a high geometric calibration accuracy and the capability to produce state‐of‐the‐art reconstructions.

Conclusions:

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.