Abstract: We present a non-rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrained locally as conformal as possible such that the angles of triangle meshes are preserved, yet local scales are allowed to change. Based on our conformal registration technique, we devise an automatic registration and interactive registration technique, which can reduce user interventions during template fitting. We demonstrate the versatility of our technique on a wide range of surfaces.