Numerical algorithms for spatial registration of line fiducials from cross-sectional images

We present several numerical algorithms for six-degree-of-freedom rigid-body registration of line fiducial objects to their marks in cross-sectional planar images, such as those obtained in CT and MRI, given the correspondence between the marks and line fiducials. The area of immediate application is frame-based stereotactic procedures, such as radiosurgery and functional neurosurgery. The algorithms are also suitable to problems where the fiducial pattern moves inside the imager, as is the case in robot-assisted image-guided surgical applications. We demonstrate the numerical methods on clinical CT images and computer-generated data and compare their performance in terms of robustness to missing data, robustness to noise, and speed. The methods show two unique strengths: (1) They provide reliable registration of incomplete fiducial patterns when up to two-thirds of the total fiducials are missing from the image; and (2) they are applicable to an arbitrary combination of line fiducials without algorithmic modification. The average speed of the fastest algorithm is 0.3236 s for six fiducial lines in real CT data in a Matlab implementation.