Multi-Level Shape Representation

Abstract

We present a method for the multi-level shape estimation and abstraction of an object’s surface from range data. The surface shape is estimated based on the parameters of a superquadric that is subjected to global deformations (tapering and bending) and a variable number of levels of local deformations. Local deformations are implemented based on locally adaptive finite elements, whose shape functions guaranteeC¹continuity. The surface pose is estimated based on the model’s translational and rotational degrees of freedom. The method is a generalization of the shape representation and estimation method presented in the previous chapters due to the introduction of multiple levels of local deformations. Through the application of Lagrangian mechanics, the model’s translational, rotational, global and local deformation parameters are modified based on forces that originate from the range datapoints. These forces are computed from approximation errors between the model and the data.