Abstract
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 mean single-step error, Freeborough
proposed the formula, True TRE = k × 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
point registration Freeborough’s formula greatly underestimates TRE. The simulations further reveal that, to an excellent
approximation, True TRE = k ×square-root-of-TREc, where k depends not only on the number of points but also on their
configuration. We investigate the usefulness of this formula as a means to estimate true TRE. We find that it is less
reliable than a standard formula published in 1998.
