Conformal Wasserstein distances: comparing surfaces in polynomial time

Details Conformal Wasserstein distances: comparing surfaces in polynomial time Conformal Wasserstein distances: comparing surfaces in polynomial time

2011-03-22

arxiv.org/abs/1103.4408v1

Advances in Mathematics, vol. 227 (2010) pp. 1047-1077

Mathematics

Differential Geometry

23 pages, 3 figures

Scientific paper

10.1016/j.aim.2011.01.020

We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global M\"{o}bius transformations. We present in detail the case where the surfaces to compare are disk-like; we also sketch how the approach can be generalized to other types of surfaces.

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