Fast Coherent Point Drift

TL;DR

This paper introduces a fast, matrix-inversion-free implementation of the Coherent Point Drift algorithm for nonrigid point set registration, significantly reducing computational complexity while maintaining accuracy.

Contribution

The authors develop a novel CPD variant that avoids matrix inversion by using eigenvalue decomposition and low-rank approximation, enhancing efficiency.

Findings

Reduces registration computation time by avoiding matrix inversion.

Maintains comparable accuracy to standard CPD.

Effective in 3D point cloud registration tasks.

Abstract

Nonrigid point set registration is widely applied in the tasks of computer vision and pattern recognition. Coherent point drift (CPD) is a classical method for nonrigid point set registration. However, to solve spatial transformation functions, CPD has to compute inversion of a M*M matrix per iteration with time complexity O(M3). By introducing a simple corresponding constraint, we develop a fast implementation of CPD. The most advantage of our method is to avoid matrix-inverse operation. Before the iteration begins, our method requires to take eigenvalue decomposition of a M*M matrix once. After iteration begins, our method only needs to update a diagonal matrix with linear computational complexity, and perform matrix multiplication operation with time complexity approximately O(M2) in each iteration. Besides, our method can be further accelerated by the low-rank matrix approximation. Experimental results in 3D point cloud data show that our method can significantly reduce computation burden of the registration process, and keep comparable performance with CPD on accuracy.