Derivation of expected registration error for point-based rigid-body registration

This paper presents two new expressions for estimating registration accuracy in point-based rigid-body registration and points out a danger in using the traditional measure of registration accuracy. In this work we present two major results: we first derive an approximate expression for (TRE2), and we then use this to calculate the expected squared alignment error for individual fiducials. This leads to a surprising conclusion--the registration accuracy is generally worst near the fiducials which are most closely aligned. This should demonstrate the danger of relying on the traditional accuracy measure, namely fiducial registration error, to judge the quality of a registration.