Frechet similarity of closed polygonal curves

TL;DR

This paper presents an efficient algorithm to determine the Frechet distance between closed polygonal curves, improving computational complexity from O(mn log(mn)) to O(mn), which is useful for applications requiring precise shape similarity measures.

Contribution

It introduces a new O(mn) time algorithm for computing the Frechet distance between closed polygonal curves, enhancing efficiency over previous methods.

Findings

The algorithm accurately determines if the Frechet distance is below a threshold.

It reduces computational complexity from O(mn log(mn)) to O(mn).

Applicable to shape analysis and pattern recognition tasks.

Abstract

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