Coherent Point Drift Revisited for Non-Rigid Shape Matching and Registration

Aoxiang Fan, Jiayi Ma, Xin Tian, Xiaoguang Mei, Wei Liu; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022, pp. 1424-1434

In this paper, we explore a new type of extrinsic method to directly align two geometric shapes with point-to-point correspondences in ambient space by recovering a deformation, which allows more continuous and smooth maps to be obtained. Specifically, the classic coherent point drift is revisited and generalizations have been proposed. First, by observing that the deformation model is essentially defined with respect to Euclidean space, we generalize the kernel method to non-Euclidean domains. This generally leads to better results for processing shapes, which are known as two-dimensional manifolds. Second, a generalized probabilistic model is proposed to address the sensibility of coherent point drift method to local optima. Instead of directly optimizing over the objective of coherent point drift, the new model allows to focus on a group of most confident ones, thus improves the robustness of the registration system. Experiments are conducted on multiple public datasets with comparison to state-of-the-art competitors, demonstrating the superiority of our method which is both flexible and efficient to improve the matching accuracy due to our extrinsic alignment objective in ambient space.