Registration of 3D shapes under anisotropic scaling: Anisotropic-scaled iterative closest point algorithm.

PURPOSE: Several medical imaging modalities exhibit inherent scaling among the acquired data: The scale in an ultrasound image varies with the speed of sound and the scale of the range data used to reconstruct organ surfaces is subject to the scanner distance. In the context of surface-based registration, these scaling factors are often assumed to be isotropic, or as a known prior. Accounting for such anisotropies in scale can potentially dramatically improve registration and calibrations procedures that are essential for robust image-guided interventions.
METHODS: We introduce an extension to the ordinary iterative closest point (ICP) algorithm, solving for the similarity transformation between point-sets comprising anisotropic scaling followed by rotation and translation. The proposed anisotropic-scaled ICP (ASICP) incorporate a novel use of Mahalanobis distance to establish correspondence and a new solution for the underlying registration problem. The derivation and convergence properties of ASICP are presented, and practical implementation details are discussed. Because the ASICP algorithm is independent of shape representation and feature extraction, it is generalizable for registrations involving scaling.
RESULTS: Experimental results involving the ultrasound calibration, registration of partially overlapping range data, whole surfaces, as well as multi-modality surface data (intraoperative ultrasound to preoperative MR) show dramatic improvement in fiducial registration error.
CONCLUSION: We present a generalization of the ICP algorithm, solving for a similarity transform between two point-sets by means of anisotropic scales, followed by rotation and translation. Our anisotropic-scaled ICP algorithm shares many traits with the ordinary ICP, including guaranteed convergence, independence of shape representation, and general applicability.