Fast noniterative calibration of an external motion tracking device

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Prospective motion correction of magnetic resonance (MR) scans commonly uses an external device, such as a camera, to track the pose of the organ of interest. However, in order for external tracking data to be translated into the MR scanner reference frame, the pose of the camera relative to the MR scanner must be known accurately. Here, we describe a fast, accurate, non-iterative technique to determine the position of an external tracking device de novo relative to the MR reference frame. The method relies on imaging a sparse object that allows simultaneous tracking of arbitrary rigid body transformations in the reference frame of the magnetic resonance imaging (MRI) machine and that of the external tracking device. Large motions in the MRI reference frame can be measured using a sparse phantom with an accuracy of 0.2 mm, or approximately 1/10 of the voxel size. By using a dual quaternion algorithm to solve the calibration problem, a good camera calibration can be achieved with fewer than six measurements. Further refinements can be achieved by applying the method iteratively and using motion correction feedback. Independent tracking of a series of movements in two reference frames allows for an analytical solution to the hand-eye-calibration problem for various motion tracking setups in MRI.