Conformal Invariants : Period Matrices ∗

Abstract. This work introduces a system of algorithms to compute period matrices for general surfaces with arbitrary topologies. The algorithms are intrinsic to the geometry, independent of surface representation. The computation is efficient, stable and practical for real applications. The algorithms are experimented to real surfaces including human faces and sculptures, and applied for surface identification problem. It is the first work that is both theoretically solid, and practically robust and accurate to handle real surfaces.