  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.
