Rigid point registration circuits

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, …, N_c –1 to N_c , and N_c to 1 where N_c 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 TRE_c, 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 × TRE_c, and suggested that k = 1/square-root-of-N_c. 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-TRE_c, 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.