DEB: Definite Error Bounded Tangent Estimator for Digital Curves

We propose a simple and fast method for tangent estimation of digital curves. This geometric-based method uses a small local region for tangent estimation and has a definite upper bound error for continuous as well as digital conics, i.e., circles, ellipses, parabolas, and hyperbolas. Explicit expressions of the upper bounds for continuous and digitized curves are derived, which can also be applied to nonconic curves. Our approach is benchmarked against 72 contemporary tangent estimation methods and demonstrates good performance for conic, nonconic, and noisy curves. In addition, we demonstrate a good multigrid and isotropic performance and low computational complexity of O(1) and better performance than most methods in terms of maximum and average errors in tangent computation for a large variety of digital curves.