An error bounded tangent estimator for digitized elliptic curves

Abstract

In this paper, we address the problem of tangent estimation for digital curves. We propose a simple, geometry based tangent estimation method for digital curves. The geometrical analysis of the method and the maximum error analysis for digital elliptic curves are presented. Numerical results have been tested for digital ellipses of various eccentricities (circle to very sharp ellipses) and the maximum error of the proposed method is bounded and is less than 5.5 degrees for reasonably large ellipses. The error for digital circles is also analyzed and compared with a recent tangent estimation method. In addition, the tangent estimation technique is applied to a flower shaped digital curve with six inflexion points and the results demonstrate good performance. The proposed tangent estimator is applied to a practical application which analyzes the error in a geometric ellipse detection method. The ellipse detection method is greatly benefited by the proposed tangent estimator, as the maximum error in geometrical ellipse detection is no more critically dependent upon the tangent estimation (due to the reduced error in tangent estimation). The proposed tangent estimator also increases the reliability and precision of the ellipse detection method. © 2011 Springer-Verlag.