This work presents a shape aware extension to the Moving Least Squares (MLS) deformation algorithm proposed by Schaefer et al. The classical MLS deformation suffers from quality of deformation for concave objects since the weights are based on the L2 norm of coordinates in 2D. We introduce interior distance metric to the MLS weights so that they are shape aware and produce plausible deformations. In particular, we derive closed form expressions for line handles for deformation.
O. Sharma, R. Tharayil, and K. N. Iyer. Shape aware image deformation system using line handles, 258/CHE/2014, 2014. (Patent)