Shape-aware MLS deformation for line handles

In this work, we propose a shape-aware extension to the Moving Least Squares (MLS) image deformation algorithm proposed by Schaefer et al. The original algorithm is not applicable to concave shapes since the weights are based on the Euclidean distance. A number of recent MLS-based deformation algorithms have proposed shape-aware extensions, but only for point handles. In contrast, we suggest a closed-form mathematical solution that applies naturally to point handles as well as line handles. In particular, our solution is based on the interior distance metric to the MLS weights for line handles so that they are shape aware and produce plausible deformations.