Superellipse fitting to partial data

Superellipses can be used to represent in a compact form a large variety of shapes, and are useful for modelling in the fields of computer graphics and computer vision. However, fitting them to data is difficult and computationally expensive. Moreover, when only partial data is available the parameter estimates become unreliable. This paper attempts to improve the process of fitting to partial data by combining gradient and curvature information with the standard algebraic distance. Tests show that the addition of gradient information seems to enhance the robustness of fit and decrease the number of iterations needed. Curvature information appears to have only marginal effects.