Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration
TL;DR: This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the inline-formula notation, and derives novel upper and lower bounds for the registration error function.
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Abstract: The Iterative Closest Point (ICP) algorithm is one of the most widely used methods for point-set registration. However, being based on local iterative optimization, ICP is known to be susceptible to local minima. Its performance critically relies on the quality of the initialization and only local optimality is guaranteed. This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the $L_2$ error metric defined in ICP. The Go-ICP method is based on a branch-and-bound scheme that searches the entire 3D motion space $SE(3)$ . By exploiting the special structure of $SE(3)$ geometry, we derive novel upper and lower bounds for the registration error function. Local ICP is integrated into the BnB scheme, which speeds up the new method while guaranteeing global optimality. We also discuss extensions, addressing the issue of outlier robustness. The evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization. Go-ICP can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available.
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Figures
TABLE 1: Running time (in seconds) of Go-ICP with DTs for the registration of the partially overlapping point-sets in Fig. 16. 100 random relative poses were tested for each point-set pair and 1 000 data points were used. ρ is the trimming percentage. 
Fig. 16: Registration with partial overlap. Go-ICP with the trimming strategy successfully registered the 10 point-set pairs with 100 random relative poses for each of them. The point-sets in red and blue are denoted as point-setA and point-setB, respectively. The trimming settings and running times are presented in Table 1. 
Fig. 17: Registration with high optimal error. Left: Gaussian noise was added to the data point-set to increase the RMS error. Right: the global minimum was found at about 25s with a DT; the remainder of the time was devoted solely to increasing the lower bound. 
Fig. 15: Registration with different levels of Gaussian noise. 
Fig. 14: Running time histograms of Go-ICP with DTs for the bunny (left) and dragon (right) point-sets. 
Fig. 13: Running time of the Go-ICP method with DTs on the bunny and dragon point-sets with respect to different factors. The evaluation was conducted on 10 data point-sets with 100 random poses (i.e., 1 000 pairwise registrations).
Citations
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