Convergent Tangent Estimator for Discrete Objects Based on Isothetic Covers

Abstract

In this article, we propose a tangent estimation method for discrete object based on isothetic covers. We introduce a concept of maximal isothetic straight segments as a maximal segment of isothetic covers that are linearly separable. A new tangent estimator is proposed as a function of maximal isothetic straight segments. Upper bound for the tangent estimator are derived and show that it tends toward the directions of the tangents of the underlying real curve as we reduce the grid size. We show how consecutive isothetic tangents are related to the convexity of the isothetic covers. The new tangent estimator is optimal i.e., linear to the number of given points and shows good performance in the presence of noise.