An error bounded tangent estimator for digital curves

In this paper, we address the fundamental problem of tangent estimation for digital curves encountered in digital image processing. We propose a simple, geometry based tangent estimation method for digital curves. The geometrical proof of the method and the maximum error analysis for digital curves are presented as the theoretical backbone of the method. 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 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.