Direct determination of geometric alignment parameters for cone-beam scanners

Abstract

This paper describes a comprehensive method for determining the geometric alignment parameters for cone-beam scanners (often called calibrating the scanners or performing geometric calibration). The method is applicable to x-ray scanners using area detectors, or to SPECT systems using pinholes or cone-beam converging collimators. Images of an alignment test object (calibration phantom) fixed in the field of view of the scanner are processed to determine the nine geometric parameters for each view. The parameter values are found directly using formulae applied to the projected positions of the test object marker points onto the detector. Each view is treated independently, and no restrictions are made on the position of the cone vertex, or on the position or orientation of the detector. The proposed test object consists of 14 small point-like objects arranged with four points on each of three orthogonal lines, and two points on a diagonal line. This test object is shown to provide unique solutions for all possible scanner geometries, even when partial measurement information is lost by points superimposing in the calibration scan. For the many situations where the cone vertex stays reasonably close to a central plane (for circular, planar, or near-planar trajectories), a simpler version of the test object is appropriate. The simpler object consists of six points, two per orthogonal line, but with some restrictions on the positioning of the test object. This paper focuses on the principles and mathematical justifications for the method. Numerical simulations of the calibration process and reconstructions using estimated parameters are also presented to validate the method and to provide evidence of the robustness of the technique.

Calibration of Robotic Manipulator Systems for Cone-Beam Tomography Imaging

“…Another set of approaches uses calibration phantoms or other measurement devices. For example, [8] and [9] use fixed test objects for calibration, whilst atomic force microscopy has been used in [10].…”

“…Instead, we assume that we have a manipulator that is either manufactured to the required precision or whose movement accuracy has been measured. Our work builds on the work in [8] and [9]. As in [8] and [11], we use calibration scans.…”

“…As in [9] and [11], we define the geometry of our system with all its degrees of freedom and use an optimisation method to optimise the geometric parameters based on an estimate of the centres of the projected spheres. The difference to [9] is that our geometry is less constrained than the traditional cone-beam tomography geometry with a single rotation axis.…”

Axially Extended-Volume C-Arm CT Using a Reverse Helical Trajectory in the Interventional Room

“…The source and the detector positions produced by a C-arm system always need to be estimated by a calibration process. Several methods have been suggested to calibrate a circular trajectory for C-arm systems (see, e.g., [17]- [24]), but none of them is ready to use for the reverse helix. To geometrically calibrate a reverse helix, we decided to extend the method in [22], [23], which has been reliably used in clinical settings.…”

“…Second, an accurate geometrical calibration had to be developed to enable reconstruction, and also to identify how close the realized motion is to the prescribed reverse helix. Many calibration methods for a single circular trajectory are available in the literature (see, e.g., [17]- [24]), however, none of these methods was readily applicable to reverse helical scanning. Third, attention had to be paid to motion repeatability, because it is difficult to perform a single scan that simultaneously provides information for trajectory calibration and tomographic data of the patient.…”