Analytic Expressions for Fiducial and Surface Target Registration Error

Localization and registration accuracy in image guided neurosurgery: a clinical study

“…The differences between the FRE and the TRE were addressed in previous studies, and new methods were developed to obtain a better TRE estimation [2][3][4][5][6][7][8][9][10][11]. These methods usually incorporate fiducial localization error (FLE).…”

On Fiducial Target Registration Error in the Presence of Anisotropic Noise

“…The model of fiducial registration published in [7] treated each noise-free fiducial location as an end point of a zero-length linear spring. Noise in the registered marker location was considered as a small extension of the spring.…”

“…For the purposes of this article, we will assume that we are working with fiducials measured in the optical tracker coordinate system so that the noise covariance matrix for the marker locations is diagonal. Our derivation of the anisotropic stiffness matrix follows that of [7]. Let the j th fi-…”

“…The stiffness quantities were first described by Lin and colleagues [12]; refer to [12] for details on computing the principal stiffnesses. It was previously shown that the rotational and translational stiffnesses are independent for fiducial registration [7]; thus, we are justified in using addition in quadrature of the two components of TRE in Equation 1. Only the rotational component of Equation 1 depends on the target location r.…”

“…Ma and Ellis [7] presented analytic expressions based on a spatial stiffness model for TRE for both fiducial and surface-based registration. Their expression for fiducial TRE was identical to that published by [5]; thus, their approach was only applicable to isotropic Gaussian iid noise.…”