Area- and angle-preserving parameterization for vertebra surface mesh

This paper proposes a parameterization method of vertebra models by mapping them onto the parameterized surface of a torus. Our method is based on a modified Self-organizing Deformable Model (mSDM) [1], which is a deformable model guided by competitive learning and an energy minimization approach. Unlike conventional mapping methods, the mSDM finds the one-to-one mapping between arbitrary surface model and the target surface with the same genus as the model. At the same time, the mSDM can preserve geometrical properties of the original model before and after mapping. Moreover, users are able to control mapping positions of the feature vertices in the model. Using the mSDM, the proposed method maps the vertebra model onto a torus surface through an intermediate surface with the approximated shape of the vertebra. The use of the intermediate surface results in the stable mapping of the vertebra to a torus compared with the direct mapping from the model to the torus.