3D shape matching and Teichmüller spaces of pointed Riemann surfaces

Details 3D shape matching and Teichmüller spaces of pointed Riemann surfaces 3D shape matching and Teichmüller spaces of pointed Riemann surfaces

2011-01-26

arxiv.org/abs/1101.5116v1

Mathematics

Algebraic Geometry

Extended abstract submitted to MEGA 2011: Effective Methods in Algebraic Geometry

Scientific paper

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.

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