Coupled Optimal Transport with Landmark Constraints

Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion. However, minimizing transport cost or distortion alone may fail to identify a geometrically meaningful transformation between the two distributions. To address this limitation, this paper proposes a novel coupled OT framework that leverages a small number of annotated landmarks to guide the recovery of an underlying deformation governing the distribution transformation. The coupled OT framework integrates the optimization of the transport plan and the deformation field into a unified model, where the landmark-guided deformation field and th...

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