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Conformal Wasserstein distances: comparing surfaces in polynomial time. (English) Zbl 1217.53026
Summary: 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 Möbius 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.

MSC:
53B50 Applications of local differential geometry to the sciences
58D17 Manifolds of metrics (especially Riemannian)
53B20 Local Riemannian geometry
Software:
EMD
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