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 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 our research into the recovery of extended superquadrics from 3D information (reconstruction). Experimental results of fitting extended superquadrics to 3D real data are presented. Our results are very encouraging and indicate that the use of extended superquadric is a promising paradigm for shape representation and recovery in computers vision and has potential benefits for the generation of synthetic images for computer graphics.
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