Very fast best-fit circular and elliptical boundaries by chord data

Many machine vision tasks require objects to be delineated during image segmentation that have shapes that are well approximated by circles or ellipses. Due to their computational efficiency least-squares, algebraic methods are a popular choice for fitting an elliptic primitive to noisy image data when real-time processing is required. These methods, however, suffer from biased estimates and sensitivity to outlier data. In this paper a real-time, least-squares method is proposed that provides an indirect geometric fit based on the quadratic polynomial form of parallel chord lengths. The algorithm is shown to be more computationally efficient and more easily made robust to outlier data than algebraic methods. Experimental results also suggest that it provides estimates that suffer less from bias error.