Rigid-body, point-based registration is commonly used for image-guided systems. Fiducial markers that can be localized in image and physical space are attached to patient anatomy. The fiducial marker locations in the two spaces are used to obtain the physical-to-image registration. It is a common practice to obtain physical positions via optical systems, whose localization error is anisotropic. Furthermore, the positions are often reckoned relative to a coordinate reference frame (CRF) that is rigidly attached to the patient. The use of a CRF enables patient movement relative to the tracking system, but it tends to exacerbate the anisotropy. It is common practice to ignore the localization anisotropy and employ a closed-form solution, which is available for isotropic weighting but not for anisotropic weighting. Iterative methods are available for anisotropic weighting but are quite complex. We present a new iterative algorithm for anisotropic weighting that is simple, intuitive, and has only one adjustable parameter. We show using simulations that our algorithm is more accurate than the isotropic solution for anisotropic localization error. In particular, we show that the new algorithm reduces target registration error when anisotropic localization error is present. When all the localization errors are isotropic, the new algorithm performs as well as the closed-form solution.
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Balachandran et al. (2009) studied this question.