Table 14. IMLP runtime comparison using different PD-tree bounding methods for computing the most-likely matches.

Search Method	Naive Search	PD-Tree: Spherical Bound	PD-Tree: Simple Ellipsoidal Bound
Runtime (sec.)	18.523	0.141	0.128

Average runtimes are reported for the proposed IMLP algorithm over the 300 registration trials of Experiment 4B, Test Case 1, which involves registering 100 random samples to a point-cloud representation of a hip model (Fig. 1A). Runtimes were recorded for the naive exhaustive search and for the proposed PD-tree search strategy comparing two of the proposed PD-tree bounding methods: the spherical (14) and simple ellipsoidal (15) bounds. The compact ellipsoidal bound (17) was not evaluated.