Lscm Based Non-Rigid Registration For Craniofacial Surfaces

The Least Squares Conformal Maps (LSCM) is an approximation of the conformal mapping in the least-squares sense, and it can map the corresponding feature points on two 3D surfaces into the same 2D location. This paper proposes a non-rigid registration method for craniofacial surfaces based on LSCM parameterization. Firstly, craniofacial surfaces are normalized in pose and scale by using a unified coordinate system. Secondly, by pinning six landmarks, which include the outer corners of the eyes, two corners of the mouth, two side points of the nose wing, each craniofacial surface is mapped into a nearly equal 2D domain by using LSCM. Finally, an iso-parameter mesh of each craniofacial surface can be obtained by 2D to 3D mapping, which establishes a unique correspondence among different craniofacial surfaces. To evaluate the proposed method, the target surface is deformed into the reference surface using TPS algorithm with dense correspondences being control points, and then the sum of the distance between two correspondence point sets are computed, and vice versa. According to the average distance, the proposed method is compared with ICP and a TPS based method. The comparison shows that the proposed approach is more accurate and effective.