超二次関数を用いた三次元物体形状の定量的・定性的モデルの獲得

抄録

In this paper, we propose a method of acquiring models of 3D objects in a class. In this method, quantitative and qualitative models of an object are acquired from range images within the same class. The quantitative model is obtained as a typical shape and a shape distribution of the class, whereas the qualitative model is linguistic description of shapes. A primitive shape is expressed by superquadrics which can represent geometric property of the 3D shape by some parameters. A compound shape is considered as combination of the primitive shapes, and is represented by geometrical positions of connected parts. This representation makes it possible to place the 3D shape in the parameter space. Since similar shapes are located close in the parameter space, a quantitative model of the class is acquired as parameter distribution in the parameter space. Thus, the typical shape is obtained by averaging parameters of the representation, and the shape distribution is acquired as variances of the parameters. Then, linguistic description of geometrical property of an object is obtained by interpreting the parameters of the shape representation. This interpretation enables acquisition of a qualitative model flom the quantitative model. As a result, the experiment demonstrates that the proposed method provides valid models for both simple and compound shapes.