Optimal transport-guided multivariable model for point set matching problems

With the rapid development of computer vision, the demand for point set matching in complex environments is increasing, especially in cases with large-scale deformation and high noise. However, existing algorithms often exhibit low accuracy or high computational costs. To enhance algorithmic efficiency while maintaining precision, we propose a new point sets matching method named multivariable entropic-regularized optimal transport model (MeROT), which handles the point sets more flexibly. Compared with the traditional optimal transport model, the proposed model introduces an orthogonal transformation matrix and a stretching transformation matrix, which can better handle the rotation and stretch transformation of the point set. In addition, an entropic-regularization term is incorporated to enhance the model’s robustness against noise and to decrease the computational expense. Subsequently, an alternate iteration algorithm is proposed. Thanks to the special properties of the two matrices and the entropy regularization term, each subproblem within the algorithm can be resolved either through a closed-form solution or by employing an efficient computational method. Therefore, MeROT offers both high matching accuracy and computational efficiency, making it well-suited for point cloud matching problems in the current complex environment. Finally, several experiments on 3D point sets are designed to show the efficiency of the proposed model.