Smoothing Splines on Riemannian Manifolds, with Applications to 3D Shape Space
黎曼流形上的平滑样条及其在三维形状空间中的应用
Abstract There has been increasing interest in statistical analysis of data lying in manifolds. This paper generalizes a smoothing spline fitting method to Riemannian manifold data based on the technique of unrolling, unwrapping and wrapping originally proposed by Jupp and Kent for spherical data. In particular, we develop such a fitting procedure for shapes of configurations in general m-dimensional Euclidean space, extending our previous work for two-dimensional shapes. We…