(a) Experimental setup for geometric calibration of the prototype C-arm. (b) Coronal, (c) sagittal, (d) axial, and (e) volumetric renderings illustrating CBCT image quality over the volumetric field of view. The anthropomorphic head phantom contains soft-tissue simulating spheres (denoted S) and a natural human skeleton, with anatomical regions of interest denoted SB (skull base), SS (sphenoid sinus), MS (maxillary sinus), C (cochlea), M (mastoid air cells), and AC (auditory canal).
(a) System geometry of the CBCT C-arm. The world coordinate system is the reference frame for object positions (e.g., source and detector) and CBCT volume reconstructions. The piercing point is the projection of the origin of the world coordinate system (i.e., the C-arm isocenter) on the detector plane . The positions of the source and detector with respect to the world coordinate system are shown. (b) Illustration of detector tilt ( and ) and rotation angles applied on the virtual detector coordinate system to produce the real detector coordinate system (not shown), which results after rotation by . (c) Example projection image of the calibration phantom, illustrating the relationship between diametrically opposed BB locations and the piercing point. The geometric system parameters are computed analytically based on two five-parameter fits to the ellipses defined by centroids of the 16 BBs as shown.
Geometric parameters from ten repeat CBCT scans over , with one of the scans (selected arbitrarily) highlighted by the thicker black line. The system parameters computed as a function of the gantry angle include: (a) the piercing point and source-to-detector distance (SDD), (b) source position , (c) detector position , and (d) detector tilt ( and ) and rotation angles. Parameters prefixed by “” are plotted as a difference from their average value over the semicircular orbit.
Geometric reproducibility of the C-arm calibration over a six-month time period. (a)–(j) Axial images of a steel wire ( diameter) placed within the two-circle calibration phantom shown as a function of the time interval, , between scanning of the wire and calibration phantom. The calibration phantom was repositioned between each scan. (k) Plots of FWHM and normalized maximum signal in axial wire images as a function of (logarithmic time scale).
Sensitivity analysis of each geometric system parameter on the spatial resolution and image quality of CBCT reconstructions. Each case shows an axial image of the anthropomorphic head phantom in the region of the skull base, with axial images of a steel wire shown as insets to demonstrate the effect on the point-spread function. (a) Image reconstructed using the complete geometric calibration. (b)–(l) Image reconstructions for which a given geometric parameter was replaced by its average value over the semicircular orbit.
Comparison of three geometric calibration methods. (a) The full geometric calibration method, which accounts for nonidealities in the positions of the source and detector and the tilt and rotation angles of the detector. (b) A “single-BB” calibration method simulated by correcting only the detector offsets of the piercing point. (c) Calibration assuming a semicircular orbit. The inset images are axial slices of a wire, and the full images are axial views of the temporal bone region within an anthropomorphic head phantom.
Tolerance to (a–e) systematic and (f–j) random errors in the source position, . Plots of as a function of gantry angle are shown for (a) systematic offsets of and (f) zero-mean gaussian perturbations with variance . Images in (b)–(e) and (g)–(j) are axial reconstructions of a steel wire (inset) and a head phantom in the region of the skull base, with the position of the cochlea (C) marked by the arrow.
Tolerance to (a–e) systematic and (f–j) random errors in the detector offset, . Plots of as a function of gantry angle are shown for (a) systematic offsets of (i.e., 0, 1, 2, and 4 pixels) and (f) zero-mean gaussian perturbations with variance . Corresponding axial wire profiles and head phantom images are shown in (b)–(e) and (g)–(j), with the posterior aspects of the skull base (SB) and maxillary sinus (MS) circled.
Tolerance to (a–e) systematic and (f–j) random errors in the detector rotation, . Plots of as a function of gantry angle are shown for (a) systematic offsets of and (f) zero-mean gaussian perturbations with variance . Corresponding axial wire profiles and head phantom images are shown in (b)–(e) and (g)–(j).
Glossary of geometric parameters computed by the calibration algorithm, along with results summarizing the magnitude of geometric nonideality on the CBCT C-arm and the reproducibility of geometric parameters. Geometric nonideality is reported as the maximum deviation from the average semicircular orbit over the gantry motion. Geometric reproducibility is computed as the average of the angle-dependent standard deviations evaluated for ten calibrations of the C-arm.
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