Rigid point registration circuits

In 1996 Freeborough proposed a method for estimating target registration error (TRE) in the absence of ground truth. In his approach, a circuit of registrations is performed using the same registration method on multiple views of the same object: 1 to 2, 2 to 3, ..., NC –1 to NC , and NC to 1 where NC is at least three and the last registration completes the circuit. Any difference between the original and final positions, which we call the “Circuit TRE” or TREC, indicates that at least one step in the registration method suffers from TRE. To estimate the single-step error, TRE1, Freeborough proposed the formula, TRE1 = k x TREC, and suggested that k = 1/square-root-of-NC. Multiple articles have employed Freeborough’s approach to estimate the accuracy of intensity-based registration methods with various values of k, but no theoretical analysis of the expected accuracy of such estimates has been attempted for any registration method. As a first step in this direction, the current work provides such an analysis for the method of rigid point registration, also known as fiducial registration. The analysis, which is validated via computer simulation, reveals that for fiducial registration TREC is zero to first order in FLE and that to second order TRE1 ≈ k x square-root-of-TREC, where k depends on the fiducialtarget configuration. Our new formula, which is shown to be superior to Freeborough’s formula and yet inferior to an earlier one for fiducial registration, is likely to be useful for intensity-based methods.