Coupled Optimal Transport with Landmark Constraints

2026-08-20

AI Summary

该论文提出了一种结合少量标注地标的新耦合最优传输框架，以解决仅通过最小化传输成本无法找到几何上有意义的分布变换的问题。

Abstract

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 the cost-driven transport plan are coupled through a mutual-consistency constraint. As a result, the deformation is jointly determined by the annotated landmarks and cost-driven distribution matching. The proposed framework provides a principled connection between landmark-based registration and transport-based distribution matching, enabling the recovery of transport maps from sparse geometric supervision. We establish the well-definedness of the proposed model in a general variational setting and develop a finite-element-based numerical algorithm for computation whose convergence properties are systematically analyzed. The practical effectiveness of the proposed approach is verified in shape matching.

Problem

• optimal transport
• landmark constraints
• geometric transformation
• deformation field
• transport cost

Innovation

• coupled optimal transport
• landmark constraints
• deformation field
• mutual-consistency constraint
• sparse geometric supervision