Image warping based on elastic body spline transformation: application for facial animations

The warping of scattered data points is a problem that is appearing in science and engineering. The basic problem involves the construction of a reasonable interpolation function that goes through some of the data points. In this paper, we propose a new spatial image warping algorithm which uses an elastic body spline to generate a warp function that interpolates scattered data points. The spline is based on a partial differential equation of Naiver that describes the equilibrium displacement of the elastic body when subjected to certain forces. The spline maps can be expressed as the linear combination of an affine transformation and a Naiver interpolation spline. The proposed algorithm generates a smooth warp that reflects the feature correspondence points. The in-between facial animation from given true facial images could be defined by interpolating the positions of correspondence features and their shapes and colors.