Precision vs Accuracy Dilemma in Point-Based Rigid-Body Registration

Abstract

The purpose of the registration procedure is to determine a transformation between two coordinate frames: working frame (from which 3D data are transformed) and reference frame (to which the data are transformed). In point based rigid body registration, the six parameters of the transformation (three angles for rotation and three vector components for translation) are calculated from measurements of the same physical points acquired in both frames. These two sets of corresponding points are called fiducials and the quality of registration is frequently gauged by the root mean square (RMSF) of distances between the fiducials measured in the reference frame and corresponding fiducials transformed from the working frame. However, in practical applications another metric is more important: RMS of distances between targets measured in the reference frame and the corresponding targets transformed from working frame, RMST. Targets are points to which registration transformation is applied but they are not used to calculate the parameters of the transformation. Thus, smaller RMST would correspond to a more accurate registration. Noisy measurements of fiducials in both frames yield noisy registration parameters and they cause the uncertainty of the target point transformed to the reference frame to be larger than the uncertainty of the target measured in the working frame.