Spline-based Motion Recovery for 3D Surfaces Using Nonrigid Shape Properties

We present a spline-based nonrigid motion and point correspondence recovery method for 3D surfaces. This method is based on differential geometry. Shape information is used to recover the point correspondences. In contrast to the majority of shape-based methods which assume that shape (unit normal, curvature) changes are minimumafter motion, our method focuses on the nonrigid relationship between before-motion and after-motion shapes. This nonrigid shape relationship is described by modeling the underlying non-rigid motion; we model it as a spline transformation which has global control over the entire motion field along with the local deformation integrated within. This provides our method certain advantages over some pure differential geometric methods which also utilize the nonrigid shape relationship but only work on local areas without a global control. For example, motion regularity is hard to implement in these pure differential geometric methods but is not a problem when the motion field is controlled by a spline transformation. Furthermore, the small deformation constraint introduced by the previous works is relaxed in our method. Experiments on both synthetic and real motions have been conducted. The quantitive and qualitative evaluations of our method are presented in this paper.