Image morphing based on partial differential equations

Abstract

Recently, the research for image morphing which constructs an image sequence from a given source image to the target image has been done extensively. A general method for image blending is linear interpolation of color value or pixel intensity. This thesis surveys new approaches for image blending and shape warping. First for the blending, as constructing an energy functional considering symmetric difference of areas between source and target, we show the reasonably-looking results that demonstrate moving of boundary of images. Especially, we suggest a different sign function approximation to relieve the limitation of taking the time step. We illustrate the results by applying this method to synthetic images and cup images and discuss the disadvantage when non-overlapping case happens. Next, we study a method for shape warping with signed distances related to image boundary. Using Euler-Lagrange method and the gradient descent method to the energy functional with the distance information, we get non-linear PDEs to give deformation fields to match the non-overlapping shapes. In particular, we compute two deformation fields corresponding to the source and target images which generate an intermediate shape.