All the surfaces in real life are Riemann surfaces, therefore with conformal structures.
Two surfaces share the same conformal structure, if there exists a conformal (angle-preserving)
mapping between them. Conformal modules are the complete invariants of conformal structures,
which can be treated as shape descriptors for shape analysis applications.
¶ This work focuses on the computational methods of conformal modules for genus zero surfaces
with boundaries, including topological quadrilaterals, annuli, multiply connected annuli. The algo-
rithms are based on both holomorphic 1-forms and discrete curvature flows, which are rigorous and
practical. The conformal module shape descriptors are applied for shape classification and compari-
son. Experiments on surfaces acquired from real world demonstrate the efficiency and efficacy of the
conformal module method.