In this paper, we explore the untapped intersection of the graph connection Laplacian and discrete optimal transport to propose a novel framework for studying optimal parallel transport between vector fields on graphs. Our study establishes feasibility conditions for the resulting convex optimization problem on connection graphs. Furthermore, we establish strong duality for the so-called connection Beckmann problem, and extend our analysis to encompass strong duality and duality correspondence for a quadratically regularized variant. Then, we implement the model across a selection of several examples leveraging both synthetic and real-world datasets drawn from computer graphics and meteorology.

翻译：本文探索了图连接拉普拉斯算子与离散最优传输之间尚未被发掘的交集，提出了一种研究图上向量场间最优平行传输的新框架。我们的研究建立了连接图上所得凸优化问题的可行性条件。此外，我们为所谓的连接Beckmann问题建立了强对偶性，并将分析扩展至二次正则化变体，涵盖了其强对偶性与对偶对应关系。随后，我们利用来自计算机图形学和气象学的合成及真实数据集，在多个示例中实现了该模型。