Closed-form Blending of Local Symmetries

Abstract

We present a closed-form solution for the symmetrization problem, solving for the optimal deformation that reconciles a set of local bilateral symmetries. Given as input a set of point-pairs which should be symmetric, we first compute for each local neighborhood a transformation which would produce an approximate bilateral symmetry. We then solve for a single global symmetry which includes all of these local symmetries, while minimizing the deformation within each local neighborhood. Our main motivation is the symmetrization of digitized fossils, which are often deformed by a combination of compression and bending. In addition, we use the technique to symmetrize articulated models.