Abstract
Most superquadric-based three-dimensional (3D) image representation methods recover superquadric models by minimizing an appropriately defined objective function. The objective function serves as an error metric to evaluate how accurately the recovered model fits the data. Both the accuracy of the recovered superquadric model and the efficiency of the data fitting process heavily depend on the objective function used. In this paper, an experimental comparison of two primarily used objective functions in superquadric model recovery is presented. The first objective function is based on the implicit definition of superquadrics, and the other on radial Euclidean distance. A variety of synthetic and real 3D range data of both regular and globally deformed superquadrics are used in experiments. The two objective functions are compared with respect to the accuracy of the recovered parameters, corresponding fitting errors, robustness against noise, sensitivity to viewpoints, and the convergence speed. The conclusion derived in this paper provides a convincing guidance for selecting the optimal objective function in superquadric representation tasks.
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