Similarity of closed polygonal curves in Frechet metric

TL;DR

This paper presents an efficient O(mn) algorithm for determining the Frechet distance between closed polygonal curves, which is more suitable than Hausdorff metric in certain applications.

Contribution

It introduces a faster O(mn) algorithm for computing the Frechet distance between closed polygonal curves, improving over previous O(mn log(mn)) methods.

Findings

The algorithm efficiently computes Frechet distance in quadratic time.

It demonstrates improved performance over existing algorithms.

The method is applicable to various shape similarity problems.

Abstract

The article analyzes similarity of closed polygonal curves in Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm that determines whether the Frechet distance between two closed polygonal curves with m and n vertices is less than a given number is described. The described algorithm takes O(mn) time whereas the previously known algorithms take O(mn log(mn)) time.