Extending Superquadrics with Exponent Functions: Modeling and Reconstruction

Superquadrics are a family of parametric shapes which can model a diverse set of objects. They have received significant attention because of their compact representation and robust methods for recovery of 3D models. However, their assumption of intrinsical symmetry fails in modeling numerous real-world examples such as the human body, animals, and other naturally occurring objects. In this paper, we present a novel approach, which is called extended superquadric, to extend superquadric's representation power with exponent functions. An extended superquadric model can be deformed in any direction because it extends the exponents of superquadrics from constants to functions of the latitude and longitude angles in the spherical coordinate system. Thus, extended superquadrics can model more complex shapes than superquadrics. It also maintains many desired properties of superquadrics such as compactness, controllability, and intuitive meaning, which are all advantageous for shape modeling, recognition, and reconstruction. In this paper, besides the use of extended superquadrics for modeling, we also discuss the recovery of extended superquadrics from 3D information (reconstruction). Experiments on both realistic modeling and extended superquadric fitting are presented. Our results are very encouraging and indicate that the use of extended superquadric has potential benefits for the generation of synthetic images for computer graphics and that extended superquadric also is a promising paradigm for shape representation and recovery in computer vision.