As a generalization of the optimal mass transport (OMT) approach of Benamou and Brenier's, the regularized optimal mass transport (rOMT) formulates a transport problem from an initial mass configuration to another with the optimality defined by the total kinetic energy, but subject to an advection-diffusion constraint equation. Both rOMT and the Benamou and Brenier's formulation require the total initial and final masses to be equal; mass is preserved during the entire transport process. However, for many applications, e.g., in dynamic image tracking, this constraint is rarely if ever satisfied. Therefore, we propose to employ an unbalanced version of rOMT to remove this constraint together with a detailed numerical solution procedure with applications to analyzing fluid flows in the brain.

翻译：作为Benamou和Brenier最优质量输运（OMT）方法的推广，正则化最优质量输运（rOMT）将输运问题表述为：从初始质量分布到目标质量分布的输运过程，以总动能定义最优性，但需满足平流-扩散约束方程。rOMT与Benamou和Brenier的公式均要求初始总质量与最终总质量相等，且整个输运过程中质量守恒。然而，在许多应用场景中（例如动态图像追踪），这一约束条件几乎从未满足过。因此，我们提出采用非均衡版本的rOMT来取消该约束，并给出详细的数值求解流程，同时将其应用于分析脑部流体流动。