Efficient shape representation using deformable models with locally adaptive finite elements

This paper presents a physics-based algorithm to efficiently represent shape using deformable models with locally adaptive finite elements. We implement our technique using our previously developed dynamic deformable models which support local and global deformations. We express global deformations with a few parameters which represent the gross shape of an object, while local deformations capture shape details of objects through their many local parameters. Using triangular finite elements to represent local deformations our algorithm ensures that during subdivision the desirable finite element mesh properties of conformity, non-degeneracy, and smoothness are maintained. Through our algorithm, we locally subdivide the triangles used for the local deformations based on the distance between the given datapoints and the model. Furthermore, to improve our results we use a new algorithm to calculate the forces that datapoints exert on the model which is based on the minimal distance to a finite element instead of to a model node. In this way not only can we represent more accurately an object surface, but also more efficiently because new model nodes are added only when necessary in a local fashion. We present model fitting experiments to 3-D range data.