3D shape matching and Teichm\"uller spaces of pointed Riemann surfaces
Abstract
Shape matching represents a challenging problem in both information engineering and computer science, exhibiting not only a wide spectrum of multimedia applications, but also a deep relation with conformal geometry. After reviewing the theoretical foundations and the practical issues involved in this fashinating subject, we focus on two state-of-the-art approaches relying respectively on local features (landmark points) and on global properties (conformal parameterizations). Finally, we introduce the Teichm\"uller space of n-pointed Riemann surfaces of genus g into the realm of multimedia, showing that its beautiful geometry provides a natural unified framework for three-dimensional shape matching.
Keywords
Cite
@article{arxiv.1101.5116,
title = {3D shape matching and Teichm\"uller spaces of pointed Riemann surfaces},
author = {Claudio Fontanari and Letizia Pernigotti},
journal= {arXiv preprint arXiv:1101.5116},
year = {2011}
}
Comments
Extended abstract submitted to MEGA 2011: Effective Methods in Algebraic Geometry