Image Morphing of Facial Images Transformation based on Navier Elastic Body Splines

In this paper, we propose a new image morphing algorithm which uses a Navier elastic body splines to generate warp functions for interpolating scattered data points. The spline is based on a partial di erential equation proposed by Navier that describes the equilibrium displacement of an elastic body subjected to forces. The spline maps can be expressed as the linear combination of an a ne transformation and a Navier interpolation spline. The proposed algorithm generates a smooth warp that re ects feature point correspondences. It is e cient in time complexity and smoothly interpolated morphed images with only a remarkably small number of speci ed feature points. The algorithm allows each feature point in the source image to be mapped to the corresponding feature point in the destination image. Once the images are warped to align the positions of features and their shapes, the in-between facial animation from two given facial images can be de ned by cross dissolving the positions of correspondence features and their shapes and colors. We describe an e cient cross dissolve algorithm for generating the in-between images.