Efficient and consistent method for superellipse detection

Superellipses are a flexible representation for a variety of objects and the detection of such a primitive is an interesting issue in machine vision research. Least-mean-square fitting using an algebraic distance has been suggested to determine the parameters of a superellipse, but the computational cost is high and a high curvature bias problem is involved. An efficient, consistent and threshold-free scheme is derived for the estimation of superellipse parameters. The closed solutions for the centre, orientation and squareness parameters are obtained by using the zeroth harmonic of its Fourier description, the consistent symmetric axis method and the theorem of diagonal segment, respectively. Only the lengths of the major and the minor axes are repeatedly estimated by Powell´s conjugate direction technique to reduce the sensitivity of noise. The proposed method is suitable for use on relatively complete, closed superellipse curves. Both convex and concave superellipses have been considered, and a compensation technique is suggested for concave superellipses. Experiments with complete and disjoint superellipses, defective superellipses and superellipses extracted from a photograph of a real object indicate the efficiency, accuracy and reliability of the proposed method, both theoretically and practically