In this paper, we study a spline collocation method for a numerical solution to the optimal transport problem We mainly solve the \MAE with the second boundary condition numerically by proposing a center matching algorithm. We prove a pointwise convergence of our iterative algorithm under the assumption the boundedness of spline iterates. We use the \MAE with Dirichlet boundary condition and some known solutions to the \MAE with second boundary condition to demonstrate the effectiveness of our algorithm. Then we use our method to solve some real-life problems. One application problem is to use the optimal transportation for the conversion of fisheye view images into standard rectangular images.

翻译：本文研究了一种样条配置法以数值求解最优传输问题。我们主要通过提出一种中心匹配算法，数值求解带有第二边界条件的Monge-Ampère方程（\MAE）。在样条迭代有界性的假设下，我们证明了该迭代算法的逐点收敛性。我们利用带有Dirichlet边界条件的\MAE以及已知具有第二边界条件的\MAE解，验证了算法的有效性。随后，我们将该方法应用于解决实际生活中的问题。其中一个应用问题是通过最优传输方法将鱼眼视图图像转换为标准矩形图像。