A new regularized approach for contour morphing
In this paper, we propose a new approach for interpolating curves (contour morphing) in time, which is a process of gradually changing a source curve (known) through intermediate curves (unknown) into a target curve (known). The novelty of our approach is in the deployment of a new regularization term and the corresponding Euler equation. Our method is applicable to implicit curve representation and it establishes a relationship between curve interpolation and a two dimensional function. This is achieved by minimizing the supremum of the gradient, which leads to the infinite Laplacian equation (ILE). ILE is optimal in the sense that interpolated curves are equally distributed along their normal direction. We point out that the existing distance field manipulation (DFM) methods are only an approximation to the proposed optimal solution and that the relationship between ILE and DFM is not local as it has been asserted before. The proposed interpolation can also be used to construct multiscale curve representation.