Speeding up Simplification of Polygonal Curves using Nested Approximations

TL;DR

This paper introduces a multiresolution method for polygonal curve simplification that reduces computational complexity and improves approximation quality, validated through theoretical analysis and experiments on 2D coastal maps.

Contribution

The paper presents a multiresolution algorithm that accelerates polygonal curve simplification while maintaining or improving approximation accuracy, based on theoretical complexity analysis.

Findings

Multiresolution approach reduces complexity to O(N).

Experimental results confirm theoretical complexity improvements.

Method produces closer approximations than classical methods.

Abstract

We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.