Even Faster Algorithm for the Chamfer Distance

Fuente: arXiv
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Main Authors: Feng, Ying, Indyk, Piotr
Format: Preprint
Published: 2025
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_version_ 1866916930565177344
author Feng, Ying
Indyk, Piotr
author_facet Feng, Ying
Indyk, Piotr
contents For two d-dimensional point sets A, B of size up to n, the Chamfer distance from A to B is defined as CH(A,B) = \sum_{a \in A} \min_{b \in B} \|a-b\|. The Chamfer distance is a widely used measure for quantifying dissimilarity between sets of points, used in many machine learning and computer vision applications. A recent work of Bakshi et al, NeuriPS'23, gave the first near-linear time (1+eps)-approximate algorithm, with a running time of O(ndlog(n)/eps^2). In this paper we improve the running time further, to O(nd(loglog(n)+log(1/eps))/eps^2). When eps is a constant, this reduces the gap between the upper bound and the trivial Omega(dn) lower bound significantly, from O(log n) to O(loglog n).
format Preprint
id arxiv_https___arxiv_org_abs_2505_08957
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Even Faster Algorithm for the Chamfer Distance
Feng, Ying
Indyk, Piotr
Computational Geometry
Data Structures and Algorithms
For two d-dimensional point sets A, B of size up to n, the Chamfer distance from A to B is defined as CH(A,B) = \sum_{a \in A} \min_{b \in B} \|a-b\|. The Chamfer distance is a widely used measure for quantifying dissimilarity between sets of points, used in many machine learning and computer vision applications. A recent work of Bakshi et al, NeuriPS'23, gave the first near-linear time (1+eps)-approximate algorithm, with a running time of O(ndlog(n)/eps^2). In this paper we improve the running time further, to O(nd(loglog(n)+log(1/eps))/eps^2). When eps is a constant, this reduces the gap between the upper bound and the trivial Omega(dn) lower bound significantly, from O(log n) to O(loglog n).
title Even Faster Algorithm for the Chamfer Distance
topic Computational Geometry
Data Structures and Algorithms
url https://arxiv.org/abs/2505.08957