Multiresolution Approximation of Polygonal Curves in Linear Complexity

TL;DR

This paper introduces a multiresolution algorithm for polygonal curve approximation that achieves linear time and space complexity, offering a practical alternative to optimal methods with comparable accuracy.

Contribution

The paper presents a novel multiresolution algorithm for polygonal curve approximation that maintains near-optimality with linear complexity, validated through theoretical analysis and experiments.

Findings

Algorithm has linear time and space complexity.

Outperforms classical methods in speed or accuracy on coastal maps.

Experimental results confirm theoretical complexity and effectiveness.

Abstract

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic programming. We show theoretically and experimentally that this algorithm has a linear complexity in time and space. We experimentally compare the outcomes of our algorithm to the optimal "full search" dynamic programming solution and finally to classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either show a lower time complexity or provide polygonal approximations closer to the input discrete curves.