Zhu Jiening, Elkin Rena, Oh Jung Hun, Deasy Joseph O, Tannenbaum Allen
Department of Applied Mathematics & Statistics, Stony Brook University, NY.
Department of Medical Physics, Memorial Sloan Kettering Cancer Center, NY.
IEEE Access. 2020;8:209224-209231. doi: 10.1109/access.2020.3038567. Epub 2020 Nov 17.
Unbalanced optimal mass transport (OMT) seeks to remove the conservation of mass constraint by adding a source term to the standard continuity equation in the Benamou-Brenier formulation of OMT. In this study, we show how the unbalanced case fits into the vector-valued OMT framework simply by adding an auxiliary source layer and taking the flow between the source layer and the original layer(s) as the source term. This allows for unbalanced models both in the scalar and vector-valued density settings. The results are demonstrated on a number of synthetic and real vector-valued data sets.
非平衡最优质量传输（OMT）试图通过在OMT的贝纳穆 - 布雷尼尔公式中的标准连续性方程中添加一个源项来消除质量守恒约束。在本研究中，我们展示了非平衡情况如何简单地通过添加一个辅助源层并将源层与原始层之间的流作为源项，从而纳入向量值OMT框架。这允许在标量和向量值密度设置中都使用非平衡模型。在一些合成和真实的向量值数据集上展示了结果。
