Abstract
Point set registration aims to find a spatial transformation that best aligns two point sets. Algorithms which can handle partial overlap and are invariant to the corresponding transformations are particularly desirable. To this end, we first reduce the objective of the robust point matching (RPM) algorithm to a function of a low dimensional variable. The resulting function is nevertheless only concave over a finite region including the feasible region, which prohibits the use of the popular branch-and-bound (BnB) algorithm. To address this issue, we propose to use the polyhedral annexation (PA) algorithm for optimization, which enjoys the merit of only operating within the concavity region of the objective function. The proposed algorithm does not need regularization on transformation and thus is invariant to the corresponding transformation. It is also approximately globally optimal and thus is guaranteed to be robust. Moreover, its most computationally expensive subroutine is a linear assignment problem which can be efficiently solved. Experimental results demonstrate better robustness of the proposed method over the state-of-the-art algorithms. Our method’s matching error is on average 44% (resp. 65%) lower than that of Go-ICP in 2D (resp. 3D) synthesized tests. It is also efficient when the number of transformation parameters is small.
Highlights
Point set registration aims to find a spatial transformation that best aligns two point sets to a common coordinate system
One way of achieving point set registration is by minimizing the objective of the robust point matching (RPM) algorithm [5]
Aiming at aligning partially overlapping point sets, in this paper, we propose an alternative approach to optimizing the objective of RPM
Summary
Point set registration aims to find a spatial transformation that best aligns two point sets to a common coordinate system. The method requires that one point set can be embedded in another point set, which may not be satisfied in many applications By relaxing this requirement, [19] reduces the objective of RPM to a concave function of point correspondence, which, albeit not quadratic, still has a low rank structure. The method is not invariant to the corresponding transformation and can not be used in applications where, e.g., rotation invariance is required To address this issue, the BnB based approach of [20] utilizes the constraints of 2D/3D rigid transformations to develop a new objective function of point correspondence which is always concave. Aiming at aligning partially overlapping point sets, in this paper, we propose an alternative approach to optimizing the objective of RPM. A new type of rotation-invariant feature was proposed in [22], leading to a more efficient BnB based registration algorithm. DeepGMR [39] designs a neural network to extract pose-invariant correspondences between point sets and GMM parameters
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