A Perfect Match Condition for Point-Set Matching Problems Using the Optimal Mass Transport Approach

作者：Chen Pengwen^*; Lin Ching Long; Chern I Liang

来源：SIAM Journal on Imaging Sciences, 2013, 6(2): 730-764.

DOI：10.1137/12086443X

• point-set matching problems
• optimal Monge-Kantorovich mass transport
• Wasserstein metrics
• lung registration

We study the performance of optimal mass transport-based methods applied to point-set matching problems. The present study, which is based on the L2 mass transport cost, states that perfect matches always occur when the product of the point-set cardinality and the norm of the curl of the nonrigid deformation field does not exceed some constant. This analytic result is justified by a numerical study of matching two sets of pulmonary vascular tree branch points whose displacement is caused by the lung volume changes in the same human subject. The nearly perfect match performance verifies the effectiveness of this mass transport-based approach.

• 出版日期2013