On the Bijectivity of Thin-plate Splines
The thin-plate spline (TPS) has been widely used in a number of areas such as image warping, shape analysis and scattered data interpolation. Introduced by Bookstein[1], it is a natural interpolating function in two dimensions, parameterized by a finite numb er of landmarks. However, even though the thin-plate spline has a very elegant intuitive interpretation as well as mathematical formulation i