Hierarchical Shape Representation Using Locally Adaptive Finite Elements

This paper presents a physics-based algorithm for hierarchical shape representation using deformable models with locally adaptive finite elements. Our new adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties of conformity, non-degeneracy and smoothness are maintained. Through our algorithm, we locally subdivide the triangular finite elements based on the distance between the given datapoints and the model. In this way, we can very efficiently and accurately represent the shape of an object with a resulting small number of model nodes. Furthermore, using our locally adaptive subdivision algorithm in conjunction with our model's global deformations we construct a hierarchical representation of the given 3D data.

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