Fast Coherent Point Drift
This work addresses efficiency issues in point set registration for computer vision and pattern recognition applications, offering an incremental improvement over the classical CPD method.
The paper tackles the high computational cost of Coherent Point Drift (CPD) for nonrigid point set registration by introducing a fast implementation that avoids matrix inversion, reducing time complexity from O(M^3) to approximately O(M^2) per iteration while maintaining comparable accuracy in 3D point cloud data.
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.