Conformal Wasserstein distances: comparing surfaces in polynomial time
Differential Geometry
2011-10-25 v1 Metric Geometry
Abstract
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.
Cite
@article{arxiv.1103.4408,
title = {Conformal Wasserstein distances: comparing surfaces in polynomial time},
author = {Yaron Lipman and Ingrid Daubechies},
journal= {arXiv preprint arXiv:1103.4408},
year = {2011}
}
Comments
23 pages, 3 figures