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SIAM J Imaging Sci. 2013 Apr 3;6(2):730-764.

A PERFECT MATCH CONDITION FOR POINT-SET MATCHING PROBLEMS USING THE OPTIMAL MASS TRANSPORT APPROACH.

Author information

  • 1Mathematics, National Taiwan University ( pengwen@math.ntu.edu.tw ).

Abstract

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 non-rigid 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.

KEYWORDS:

Lung registration; Optimal Monge-Kantorovich mass transport; Point-set matching problems; Wasserstein metrics

PMID:
23687536
PMCID:
PMC3656725
DOI:
10.1137/12086443X
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