Abstract
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.
Highlights
O PTIMAL mass transport (OMT) is a very important subject in mathematics, originating with the French civil engineer and mathematician Gaspard Monge in 1781 [11, 18, 20, 21]
We show that unbalanced OMT can fit into the model of vector OMT by taking a special set of weight parameters, which gives us a fresh way to treat the problem
In the L2 setting, both extensions arise from the computational fluid dynamics (CFD) approach to OMT introduced by Benamou and Brenier [2], which was a major development in OMT theory
Summary
JIENING ZHU1, RENA ELKIN2, JUNG HUN OH2, JOSEPH O.
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