Image morphing with conformal welding

We address the issue of deforming an image of a source object to that of a target. Previous works including barycentric coordinates and functional maps can hardly enforce shape consistency, especially for the objects with complex nested shape components. We leverage the conformal welding theory that maps 2D shapes (planar contours) to the automorphisms of the unit circle, named shape signatures. Conformal welding enables us to apply the Laplacian constraint to deformations in the signature space (or unit circle domain), which renders efficiency and flexibility. Additionally, we are able to fully reconstruct complex shape contours from deformed signatures, and hence generate the morphed images for target shapes. The experiments on complex shape contours and facial images, where multiple components exist, validate the effectiveness of the proposed approach.