  There is a growing interest in shape analysis in recent years and in this
paper we present a novel contour-based shape representation named Beltrami
signature for 2D bounded simple connected domain. The proposed representation
is based on conformal welding. With suitable normalization, the uniqueness of
welding is guaranteed up to a rotation. Then it can be extended to a harmonic
function and finally quasi-conformal theory get rid of the only uncertainty by
computing Beltrami coefficient of harmonic extension. The benifits of the
proposed signature is it keeps invariant under simple transformations like
sacling, transformation and rotation and is roubost under slight deformation
and distortion. Experiments demonstrates the above properties and also shows
the excellent classification performance.
