doi:10.1016/j.imavis.2006.01.009 
Copyright © 2006 Elsevier B.V. All rights reserved.
Automatic registration of overlapping 3D point clouds using closest points
Yonghuai Liu
, a, 
aDepartment of Computer Science, University of Wales, Penglais, Aberystwyth, Ceredigion SY23 3DB, Wales, UK
Received 14 March 2005;
revised 9 January 2006;
accepted 31 January 2006.
Available online 2 June 2006.
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Abstract
While the SoftAssign algorithm imposes a two-way constraint embedded into the deterministic annealing scheme and the EMICP algorithm imposes a one-way constraint, they represent the state of the art technique for the automatic registration of overlapping free form shapes. They both have a time complexity of O(n2). While the former has a space complexity also of O(n2), the latter has a space complexity of O(n). The heavy demand for computation and storage memory renders either the SoftAssign or EMICP algorithm to hardly operate on whole shapes with thousands of points. In this case, they often have to reduce the number of points to an order of 100s on the free form shapes to be registered. This paper proposes using closest points in conjunction with either the one-way or two-way constraint for the automatic registration of overlapping 3D point clouds and thus, combining the accuracy of both the SoftAssign and EMICP algorithms with the efficiency of the traditional ICP algorithm. A comparative study based on both synthetic data and real images has shown that the proposed algorithm does not significantly sacrifice accuracy and stability of either the SoftAssign or EMICP algorithm, but gains remarkable efficiency of the traditional ICP algorithm for the automatic registration of overlapping 3D point clouds. Since, the proposed algorithm is of general use and has an advantage of easy implementation, it is likely to become in the future a benchmark for the automatic registration of overlapping 3D point clouds.
Keywords: 3D point clouds; Automatic registration; SoftAssign; EMICP; Combinatorial optimization; Entropy maximization; Deterministic annealing; Optimised k-D tree
Fig. 1. Diagram for principles of a structured light system operation [36].
Fig. 2. The relative calibration errors of the parameters of interest as a function of the rotation angle. Top row, rotation axis; middle row, rotation angle; bottom row, translation vector. Left column, mme; right column, me.
Fig. 3. The me of calibration errors (%) of the parameters of interest using synthetic points data with different percentages of disappearing and appearing points in the 3D point clouds to be registered. Left column, rotation axis; middle column, rotation angle. Right column: translation vector. Top row: SoftAssign. Second row: EMICP. Third row: SoftICP. Fourth row: WeightICP. Bottom row: GICP.
Fig. 4. The relative calibration error of the parameters of interest and calibration time in seconds in a trial as a function of n. Top left, rotation axis; top right,: rotation angle; bottom left, translation vector; bottom right, calibration time in a trial.
Fig. 5. The real range images used. Left two, valve; right two, tubby.
Fig. 6. The results for the registration of 200 randomly selected points with uniform distribution from the first images. Left column,: before registration; right column, after registration. Top two rows,: valve1-2; bottom two rows, tubby1-2. Odd rows, SoftICP; even rows, WeightICP.
Fig. 7. The real range images used. Left two, cow; middle two, dinosaur; right two, lobster.
Fig. 8. The results for the matching of 200 randomly selected points with uniform distribution from the first images. Left column: before registration; right column, after registration. Top two rows, cow1-2; middle two rows, dinosaur1-2. Bottom two rows, lobster1-2. Odd rows, SoftICP; even rows, WeightICP.
Table 1.
The final ragged matching array M estimated by the proposed SoftICP algorithm using synthetic points data (n=6) with θ=25° to be described in Section 4
Table 2.
The final probabilities of point correspondences estimated by the proposed WeightICP algorithm using synthetic points data (n=6) with θ=25° to be described in Section 4
Table 3.
The average μ and standard deviation σ of mmes and mes of calibration errors (%) of rotation axis 
, rotation angle 
, and translation vector 
using synthetic points data (n=100) with different motions and different levels of noise
Table 4.
The average μ and standard deviation σ of mmes and mes of calibration errors (%) of rotation axis 
, rotation angle 
, and translation vector 
using synthetic points data (n=100) with different percentages of disappearance and appearance of points in the point clouds to be registered
Table 5.
The average μ and standard deviation σ of calibration errors (%) of rotation axis 
, rotation angle 
, and translation vector 
and the calibration time in seconds using different numbers of points in the overlapping 3D point clouds to be registered
Table 6.
The number n of valid points and the average lμ and standard deviation lδ of the interpoint distances in millimetres in different range images
Table 7.
The average eμ and standard deviation eσ of registration errors (mm), expected rotation angle θ and calibrated rotation angle 
in degrees, the registration time in seconds, the number N of finally established RCs for different range images with small motions
The numbers in parentheses are the numbers of sampled non-background points.
Table 8.
The number n of valid points and the average lμ and standard deviation lδ of the interpoint distances in millimetres in different range images
Table 9.
The average eμ and standard deviation eσ of registration errors (mm), expected rotation angle θ and calibrated rotation angle 
in degrees, the registration time in seconds, the number N of finally established RCs for different range images with large motions
The numbers in parentheses are the numbers of sampled non-background points.
Table 10.
The average eμ and standard deviation eσ of registration errors in millimetres based on RCs, the number N of finally established RCs for the SoftICP and WeightICP algorithms over sampled 200 points from the first images
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