Table 1.

Average transformation error (ATE), inconsistency $\mathcal{C}$, and Pearson correlation $\rho$ of estimated and true registration error magnitude for the two-dimensional MRI experiments using simulated transformations before and after using consistency-based registration rectification (CBRR). We also compare CBRR to locally averaged weighting (LWA), an earlier version of this work [correcting local errors using registration consistency (CLERC)] presented in Ref. 31, and assessing quality using image registration circuits (AQUIRC),¹⁹ which computes a dimensionless estimate of registration error, which can be correlated with the true error.

	Demons			Markov random field (MRF)
	ATE	$\rho$	$\mathcal{C}$	ATE	$\rho$	$\mathcal{C}$
Registration	3.50	—	2.53	1.92	—	1.85
+ LWA	2.34	0.60	1.78	1.83	0.69	1.87
+ CLERC (Ref. 31)	2.66	0.74	0.86	1.28	0.85	0.65
+ CBRR	1.64	0.84	0.35	0.88	0.91	0.22
+ AQUIRC (Ref. 19)	—	0.47	—	—	0.64	—

Note: Bold numbers indicate best results in each category.