Experimental Comparison of Superquadric fitting Objective Functions

This paper present the analysis of superquadrics and find out the required parameters from the image of superquadrics. These images are in different views and with the help of objective function we can find out the deform superquadrics parameters. Most superquadric-based three-dimensional (3D) image representation methods recover superquadric models by minimizing an appropriately de�ned objective function. The objective function serves as an error metric to evaluate how accurately the recovered model �ts the data. Both the accuracy of the recovered superquadric model and the efficiency of the data �tting 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 �rst objective function is based on the implicit de�nition 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 �tting 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.