A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance

Abstract

In this paper, we propose an algorithm that, from a maximum error and a digital curve (4- or 8-connected), computes a simplification of the curve (a polygonal curve) such that the Fréchet distance between the original and the simplified curve is less than the error. The Fréchet distance is known to nicely measure the similarity between two curves. The algorithm we propose uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in O(n log(n)), experiments show a linear behaviour in practice.