Application of moment and Fourier descriptors to the accurate estimation of elliptical shape parameters

The problem of accurate parameter estimation of elliptical shapes is addressed. Three methods based on elliptical Fourier descriptors, area moments, and perimeter moments of 2-D elliptical shapes are presented. The mathematics of these methods is discussed and, for area moments, a set of new formulas based on Gauss´s theorem is given. To implement a comparative performance study, a method developed by R. Safaee-Rad et al. (1990), the weighted minimum-square-error (MSE) function, is included, and an objective and independent measure of goodness of fit is used. The performance of these methods is compared for two different cases, that of a perfect simulated ellipse and an imperfect imaged ellipse