Numerical Investigation of an Axis-based Approach to Rigid Registration

The term rigid registration identifies the process that optimally aligns different data sets whose information has to be merged, as in the case of robot calibration, image-guided surgery or patient-specific gait analysis. One of the most common approaches to rigid registration relies on the identifica-tion of a set of fiducial points in each data set to be registered to compute the rototranslational matrix that optimally aligns them. Both measurement and hu-man errors directly affect the final accuracy of the process. Increasing the number of fiducials may improve registration accuracy but it will also increase the time and complexity of the whole procedure, since correspondence must be estab-lished between fiducials in different data sets. The aim of this paper is to present a new approach that resorts to axes instead of points as fiducial features. The fundamental advantage is that any axis can be easily identified in each data set by least-square linear fitting of multiple, un-sorted measured data. This provides a way to filtering the measurement error within each data set, improving the registration accuracy with a reduced effort. In this work, a closed-form solution for the optimal axis-based rigid registration is presented. The accuracy of the method is compared with standard point-based rigid registration through a numerical test. Axis-based registration results one or-der of magnitude more accurate than point-based registration.