Conformal Wasserstein distances: Comparing surfaces in polynomial time

By Yaron Lipman, Ingrid Daubechies. 2011

90 citations recorded by the source corpus.

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 Mobius 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.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9ce4895b45e26a3f1d8b208e8836cb8b5940eecb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Roee Litman
2. Daniel Cremers
3. Emanuele Rodolà
4. Matthias Vestner
5. A. Bronstein

In Statistical and Nonlinear Physics

1. Roee Litman
2. Daniel Cremers
3. Emanuele Rodolà
4. Matthias Vestner
5. A. Bronstein

Citations in the corpus

• Product Manifold Filter: Non-rigid Shape Correspondence via Kernel Density Estimation in the Product Space (2017, methodology): “[25, 20, 21] used conformal embeddings into disks and spheres to parametrize correspondences between homeomorphic surfaces as Möbius transformations.”
• Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, methodology): “[24, 19, 20] used conformal embeddings into disks and spheres to parametrize correspondences between homeomorphic surfaces as Möbius transformations.”