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8 2 Corresponding points distance (b) Fig. 10) using different MSE ranges. 5 (b) Fig. 5] . 05 0 0 500 1000 1500 2000 2500 3000 3500 4000 Point position (b) Fig. 8: (a) shows 395 points considered non-interpenetrating points in the ICP registration and interpenetrating points in the registration by our approach for the same point positions; and (b) shows 141 points considered non-interpenetrating points in the registration by our approach and interpenetrating points in the ICP registration for the same point positions.

Furthermore, a large window may yield incorrect local measurements for correct alignments. 17. 02% Fig. 8(d), respectively; (b)-(d) are the results of the SIM calculated on (a) with pm1 set to 3, 5 and 7, respectively; (f)-(h) are the results of the SIM calculated for (e) with pm1 set to 3, 5 and 7, respectively. 18 shows the results of SIM with different values for pm1 for an example with an incorrect alignment. This example shows that the region of the interpenetration becomes thicker when the size of the window increases.

The units of MSE are in terms of range values. 6 demonstrates the results of the MSE and SIM measures for different alignments. In this experiment we computed 496 alignments obtained by exhaustive ICP-based registrations using point-topoint and point-to-plane correspondence methods [Besl and McKay (1992), Chen and Medioni (1992)]. Different combinations of adjacent views of four objects were used, totaling 124 alignments for each object. 2, page 125 for details of the objects and registration results obtained in this experiment).

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