Discrete Frechet distance for closed curves

TL;DR

This paper introduces an efficient algorithm for computing the discrete Frechet distance between closed curves, improving the time complexity from O(mn log mn) to O(mn log* mn), which is useful for shape analysis.

Contribution

The paper proposes a novel algorithm that reduces the computational complexity of measuring discrete Frechet distance for closed curves.

Findings

Algorithm achieves O(mn log* mn) time complexity.

Provides a practical approach for shape comparison.

Improves upon previous methods with faster computation.

Abstract

The paper presents a discrete variation of the Frechet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Frechet distance between two closed sequences of m and n points using binary search takes O(mn log mn) time. We present an algorithm that takes O(mn log* mn) time, where log* is the iterated logarithm.